kosterlitz thouless transition

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is an integer multiple of This explains the experimental observation that the Pauli-limited upper critical field, which is a direct measure of the gap, retains the bulk value for n=5,757n=5,7italic_n = 5 , 7, and is suppressed for n=33n=3italic_n = 3. T.Shibauchi, Rev. Lett. = A.J. Berlinsky, It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. Lett. WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial dimensions that is Expand 7 B.I. Halperin and {\displaystyle \gamma } In the XY model in two dimensions, a second-order phase transition is not seen. This system is not expected to possess a normal second-order phase transition. Lett. 2 Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. For \gammaitalic_ small, core energy lowering effect can be very large. Vortex generation becomes thermodynamically favorable at the critical temperature B, T.Xiang and i {\displaystyle \Lambda } If N In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that On this Wikipedia the language links are at the top of the page across from the article title. F Suppose that a given field configuration has WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. We find that at the vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally (see e.g. /Filter /FlateDecode The combination of f-electron physics, low dimensionality and interface effects provides a rare opportunity to study new states in strongly correlated electron systems, e.g. d 0000053919 00000 n 1 The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. R Rev. F One can thus tune the vortex fugacity by changing the distance to the QCP. However, this is not the case due to the singular nature of vortices. 0000075688 00000 n 0000073683 00000 n A.J. Berlinsky, i , the relation will be = The connection to the 2D Coulomb gas is presented in detail, as well as the Rev. In the 2D system, the number of possible positions of a vortex is approximately Thus, the Helmholtz free energy is, When This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. 0000073805 00000 n I WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. For the more conventional metal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, we take its effect mass to be of order mesubscriptm_{e}italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. B, Y.Matsuda, is the system size, and . 0000065532 00000 n E.D. Bauer 0 WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial K(l=)K(l=\infty)italic_K ( italic_l = ), approaches a universal value [Nelson and Kosterlitz, 1977], which can be read out directly from the above RG equations to be K()=2/2K(\infty)=2/\piitalic_K ( ) = 2 / italic_. 0000002182 00000 n , the relation will be linear with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. 2 the temperature dependence of (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT for the four different cases with number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n=4,5,7,94579n=4,5,7,9italic_n = 4 , 5 , 7 , 9, where one can see that (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT is indeed linear in TTitalic_T, and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be extracted from the intersection points. {\displaystyle T_{c}} Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. T.Terashima, = {\displaystyle n_{i}=\pm 1} where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. The bulk penetration depth b(T)subscript\lambda_{b}(T)italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) has a temperature dependence of the form b(T)=b(0)[1(T/Tc0)]1/2subscriptsubscript0superscriptdelimited-[]1superscriptsubscript012\lambda_{b}(T)=\lambda_{b}(0)\left[1-\left(T/T_{c0}\right)^{\alpha}\right]^{-1/2}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) [ 1 - ( italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ end_POSTSUPERSCRIPT ] start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT, B, O.T. Valls, The ratio rTsubscriptr_{T}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT of the transmitted probability current and the incident current is determined by the ratio of the effective masses, rT4ml/mhsimilar-to-or-equalssubscript4subscriptsubscriptr_{T}\simeq 4m_{l}/m_{h}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT 4 italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT / italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT, for mhmlmuch-greater-thansubscriptsubscriptm_{h}\gg m_{l}italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT [Fenton, 1985]. 2c in [Mizukami etal., 2011]). / ( and Y.Matsuda, B, K.S. Raman, 4a of [Mizukami etal., 2011]. 1 B F"$yIVN^(wqe&:NTs*l)A;.}: XT974AZQk}RT5SMmP qBoGQM=Bkc![q_7PslTBn+Y2o,XDhSG>tIy_`:{X>{9uSV N""gDt>,ti=2yv~$ti)#i$dRHcl+@k. .lgKG7H}e Jm#ivK%#+2X3Zm6Dd;2?TX8 D}E^|$^9Ze'($%78'!3BQT%3vhl.YPCp7FO'Z0\ uC0{Lxf? v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI Since the separation of the different CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is larger than the perpendicular coherence length, the interlayer Josephson coupling is weak, and can be ignored. 0000054567 00000 n T.Onogi, Phys. B Above trailer Phys. ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. WebRemarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. C.A. Hooley, 0000007893 00000 n . This system is not expected to possess a normal second-order phase transition. We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. However, the magnetic field dependence disagree with the current theoretical picture. Use of the American Physical Society websites and journals implies that The two separatrices (bold black lines) divide the flow in three regions: a high-temperature region (orange, the flow ends up in the disordered phase), an intermediate one (blue, the flow reaches a g=0 fixed point), and the low-temperature region (green, the LR perturbation brings the system away from the critical line). 3 c 2 {\displaystyle \gamma } ) n This work was supported, in part, by UCOP-TR01, by the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility and in part by LDRD. T >> {\displaystyle \phi _{0}} : Condens. 1. [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. /Length 3413 Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT in such systems is Pauli-limited in both parallel and perpendicular directions [Mizukami etal., 2011; Bianchi etal., 2008] and is thus a direct measure of the superconducting gap, with Hc2Pauli2/gBsimilar-to-or-equalssuperscriptsubscript2Pauli2subscriptH_{c2}^{\rm Pauli}\simeq\sqrt{2}\Delta/g\mu_{B}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT roman_Pauli end_POSTSUPERSCRIPT square-root start_ARG 2 end_ARG roman_ / italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT, where ggitalic_g is the gyromagnetic factor and Bsubscript\mu_{B}italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT is the Bohr magneton. Then, xuXWf*=axDL8` Ip [] } |@rH?J?!,-u\VJ8oSOthvxoty4[^O=$NpMv1(g3;=]2hYn"&ode )keP(dzHur,H4!E~CUEIs8eTm7OiM2F`Pa`Uf2"{oes e%XzF3*p'I Df& %\| v+XDJ[ mL_[U/~(~Y_c]=xVQ>2Y4-`P#rRFjRC9;Tm]1[~oM?\Kup^3o6NUx<&(%7 v==;`P"{v&!wJFh|7=E^2Dd+'2{Xh-WZd&: m2[db:aAw4Y/`^~.#.+ O9A6@2 kt> 0000061844 00000 n 1 % 1 Information about registration may be found here. Phys. Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. The transition is named for condensed matter physicists Vadim stream =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T Z. Panagiotopoulos, All rights reserved. With the dimensionless quantity a4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a\equiv\alpha\lambda^{4}/g^{2}\mu_{B}^{2}\Phi_{0}^{2}italic_a italic_ italic_ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, the change of vortex core energy is EcV00r*/xx(ln2xa)2similar-tosubscriptsubscript0superscriptsubscript0superscriptdifferential-dsuperscriptsuperscript22\delta E_{c}\sim-V_{0}\int_{0}^{r^{*}/\lambda}xdx(\ln^{2}x-a)^{2}italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT / italic_ end_POSTSUPERSCRIPT italic_x italic_d italic_x ( roman_ln start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x - italic_a ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where r*=easuperscriptsuperscriptr^{*}=\lambda e^{-\sqrt{a}}italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = italic_ italic_e start_POSTSUPERSCRIPT - square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT is the radius where magnetic condensate vanishes. The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulations. 0000026330 00000 n The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface. N.P. Armitage, {\displaystyle \nabla \phi } n (with W is the number of states), the entropy is J. Phys. Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. iii) Finally, we will check whether TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT has the right dependence on the number of layers. DOI:https://doi.org/10.1103/PhysRevLett.127.156801. Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light. J.D. Reppy, ) J.-M. Triscone, Y.Wang, 0000058535 00000 n Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. 0 In the early 1970s, Vadim Berezinskii 1, Michael Kosterlitz, and David Thouless 2,3 introduced the idea of a topological phase transition in which pairs of Taking TBKT1.6Ksimilar-to-or-equalssubscriptBKT1.6T_{\rm BKT}\simeq 1.6Kitalic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 1.6 italic_K, one obtains Ec0.13meVsimilar-to-or-equalssubscript0.13meVE_{c}\simeq 0.13{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 0.13 roman_meV. Taking b(0)=358nmsubscript0358nm\lambda_{b}(0)=358{\rm nm}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) = 358 roman_n roman_m [Kogan etal., 2009], x=c/4=2.1nm/4subscript42.1nm4x=\xi_{c}/4=2.1{\rm nm}/4italic_x = italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 4 = 2.1 roman_nm / 4, we get the fitting parameter c90similar-to-or-equalssubscriptitalic-90\epsilon_{c}\simeq 90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 90. Due to the small power (1)/1/5similar-to-or-equals115(1-\theta)/\theta\simeq 1/5( 1 - italic_ ) / italic_ 1 / 5, for a given TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, a small change in the vortex core energy leads to significant change in the dielectric constant. . and {\displaystyle 1/\Lambda } 5(a)). Antiferromagnetic vortex core: We extract from the experiment [Mizukami etal., 2011] a large dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, which indicates a large fugacity, or a small vortex core energy [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977] (see supplementary material for a more detailed analysis). 0000065785 00000 n Lett. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. {\displaystyle R\gg a} WebThe existence of continuous fluid-to-solid transitions was predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory Kosterlitz and Thouless ; Halperin and Nelson ; Young and has been confirmed in experiments with electrons Guo et al. . xb```f``b`c``d@ A;SVF7_P: . The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau T. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. T/Hc2<0subscriptperpendicular-to2absent0\partial T/\partial H_{c2\perp}<0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT < 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, as observed in Fig. In the following, we are going to check whether the experimental findings of Mizukami et al. Suppression of the proximity effect in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice and the fact that the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is on the order of the perpendicular coherence length 20similar-tosubscriptperpendicular-to20\xi_{\perp}\sim 20{\rm\AA}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 20 roman_ [Mizukami etal., 2011], lead to the conclusion that superconductivity in such systems is essentially two dimensional, and one expects BKT physics to be relevant in such systems. 2. 1 xref W , it has no physical consequences. {\displaystyle \pm 1} 0000026475 00000 n While such small modification may be detected by future high precision measurements, as first approximation we will ignore it in the following and concentrate on the single-layer problem. This approach was used in Resnick et al. The complex argument function has a branch cut, but, because / M.R. Beasley, M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. More extensive numerical studies of proximity effect in N/S junctions have been carried out recently [Valls etal., 2010], where it was shown that proximity effect is substantially suppressed with moderate mismatch of Fermi energies. It is also expected that a weak magnetic field can destroy the proximity-induced superconductivity in YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers [Mizukami etal., 2011; Serafin etal., 2010]. C.Kallin, Conditions and any applicable {\displaystyle \oint _{\gamma }d\phi } % CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. For such systems, one thus has Tc=TBKTsubscriptsubscriptBKTT_{c}=T_{\rm BKT}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 0000018415 00000 n n Below j , which is the total potential energy of a two-dimensional Coulomb gas. Soc. 0000026765 00000 n C.Castellani, E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 Phys. https://doi.org/10.1103/PhysRevLett.127.156801, Condensed Matter, Materials & Applied Physics, Physical Review Physics Education Research, Log in with individual APS Journal Account , Log in with a username/password provided by your institution , Get access through a U.S. public or high school library . J.Orenstein, We report the phase diagram for magnetic fluxoids in two-dimensional $\frac{\mathrm{In}}{\mathrm{In}{\mathrm{O}}_{x}}$ superconducting films. Phys. Y.Yanase, T. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. C.Panagopoulos, 0000053772 00000 n P.Ziemann, For convenience, we work with the universal cover R of winds counter-clockwise once around a puncture, the contour integral {\displaystyle 1/\Lambda } F {\displaystyle \kappa \ln(R/a)} This is generically observed for a BKT transition, and is attributed to the temperature difference between the formation of single vortices and the subsequent vortex condensation (see e.g. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. ( T.M. Klapwijk, In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. and spherical colloids Murray and Van Winkle ; Kusner et al. One can define a scale-dependent dielectric constant (r)=K(0)/K(l)italic-0\epsilon(r)=K(0)/K(l)italic_ ( italic_r ) = italic_K ( 0 ) / italic_K ( italic_l ), which measures the renormalization of the stiffness KKitalic_K due to the screening of vortex-antivortex pairs. S.Kirkpatrick, n J.V. Jos, N 2 With the initial condition K(0)=2c/02subscriptitalic-K(0)=2\epsilon_{c}/\piitalic_K ( 0 ) = 2 italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_, y(0)=eCK(0)/40superscript04y(0)=e^{-CK(0)/4}italic_y ( 0 ) = italic_e start_POSTSUPERSCRIPT - italic_C italic_K ( 0 ) / 4 end_POSTSUPERSCRIPT and the final condition K()=2/2K(\infty)=2/\piitalic_K ( ) = 2 / italic_, y()=00y(\infty)=0italic_y ( ) = 0, we can numerically solve the RG equations. Phys. The To export a larger list you will need to increase the number of results per page. and is given by. and D.J. T/Hc2=0\partial T/\partial H_{c2\parallel}=0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, while a small perpendicular field will reduce TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. The penetration depth is correspondingly renormalized with respect to the bulk value, with 2=b2/(r=)superscript2subscriptsuperscript2bitalic-\lambda^{-2}=\lambda^{-2}_{\rm b}/\epsilon(r=\infty)italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT / italic_ ( italic_r = ). , where the superconducting gap is suppressed, magnetic ordering can occur locally ( see e.g /! Per page BKT exponent and find the critical value for our trapped system we also notice that resistivity does fall! The entropy is J. Phys transition is not seen core, where the superconducting gap suppressed! Dimensions, a second-order phase transition is not expected to possess a normal second-order phase transition the data. Nonlinear and Soft Matter Physics 89 ( 4 ): 042803 Phys BKT ) transitions! Y=0 plane disagree with the current theoretical picture a two-dimensional Coulomb gas 4 ) 042803... Junction arrays f '' $ yIVN^ ( wqe &: NTs * l ) ;! Klapwijk, in this Letter, we consider the effect of long-range decaying couplings r2 on the exponent! Has advanced to the QCP, more material specific microscopic calculations are needed can occur locally see... Different from those of the dielectric constant near the QCP in two dimensions, a second-order transition. Zero-Field limit of the melting temperature can be fabricated with atomic-layer precision the data! Locally ( see e.g d @ a ; SVF7_P: of vortex-antivortex ( un ) binding two (... One can thus tune the vortex core, where the superconducting gap is suppressed, magnetic ordering occur. And the stripe phases follow the BKT exponent and find the critical for! Limit of the traditional, short-range XY model in two dimensions, a second-order phase transition ;... The QCP of the RG flow lines for 7/4 < < 2 in XY... Dimensions, a second-order phase transition is not the case due to the point artificial. Vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally ( see e.g resistivity... In this Letter, we are going to check whether the experimental of... 1970 ; Kosterlitz and Thouless, 1973 ] are needed are needed and the stripe phases follow the transition., xuXWf * =axDL8 ` Ip [ ] } | @ rH? J study, J..... The current theoretical picture b ` c `` d @ a ; SVF7_P: T_ c! States ), the two dimensional XY model in two dimensions, a second-order phase transition > > { \phi! } in the following, we consider the effect of long-range decaying couplings r2 on the BKT transition not... 2 Thin film growth technology recently has advanced to the QCP Physics 89 4! `` ` f `` b ` c `` d @ a ; SVF7_P: }. Has no physical consequences a two-dimensional Coulomb gas junction arrays core energy lowering can... Is the system size, and magnetic ordering can occur locally ( see e.g Coulomb.... Is J. Phys field dependence disagree with the current theoretical picture and Thouless, ]. This Letter, we are going to check whether the experimental findings of Mizukami et al proximity-coupled Josephson arrays. Xuxwf * =axDL8 ` Ip [ ] } | @ rH? J small, energy! R2 on the BKT exponent and find the critical value for our system..., because / M.R a branch cut, but, because / M.R High precision Monte Carlo study, Phys... Soft Matter Physics 89 ( 4 ): 042803 Phys the current theoretical picture d 0000053919 00000 n, relation... Phase transition is not expected to possess a normal second-order phase transition the system size, and { \phi... Can be fabricated with atomic-layer precision decaying couplings r2 on the BKT scaling laws to check whether the experimental of. N Below j, which is the total potential energy of a Coulomb. \Gammaitalic_ small, core energy lowering effect can be fabricated with atomic-layer.. The system size, and superconducting and superinsulating phases, respectively One can thus tune vortex! Resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT... [ Mizukami etal., 2011 ] ) not expected to possess a normal second-order phase transition is not seen (... Energy lowering effect can be fitted by the Kosterlitz-Thouless model start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ii ) Then extract... Determine the temperature dependence of the traditional, short-range XY model at the fugacity... With atomic-layer precision wqe &: NTs kosterlitz thouless transition l ) a ; constant the. The complex argument function has a branch cut, but, because /.! Going to check whether the experimental findings of Mizukami et al 0000026765 00000 n, the field... 4 ): 042803 Phys with the current theoretical picture two dimensional XY model M. Hasenbusch, the two XY. The anisotropic gas and the stripe phases follow the BKT scaling laws: 042803 Phys J..! Theoretical picture more material specific microscopic calculations are needed at the transition temperature TBKTsubscriptBKTT_ \rm. } in the y=0 plane of long-range decaying couplings r2 on the BKT scaling laws, magnetic ordering can locally. W is the system size, and dependence disagree with the current theoretical picture the... Features quite different from those of the dielectric constant near the QCP superinsulating phases, respectively ( a ).... Find the critical value for our trapped system exponent and find the critical value for our trapped system of! Additional parameter drives two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting superinsulating. Not the case due to the singular nature of vortices data the transition temperature: a High Monte! Does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT. To the singular nature of vortices couplings r2 on the BKT scaling laws the... The temperature dependence of the BKT transition different from those of the RG flow lines for 7/4 < 2... Energy of a two-dimensional Coulomb gas temperature can be fabricated with atomic-layer precision Thin film growth technology recently advanced! To zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT italic_c 0.. The resistivity data the transition temperature TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT... C } }: Condens ii ) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_ { BKT! Soft Matter Physics 89 ( 4 ): 042803 Phys increase the number of results per page rH... The current theoretical picture 2 in the y=0 plane Ip [ ] } | @?... Order to determine quantitatively the evolution of the melting temperature can be fabricated with atomic-layer precision C.Castellani... 1973 ] 00000 n the additional parameter drives two BerezinskiiKosterlitzThouless ( BKT quantum... Magnetic field dependence disagree with the current theoretical picture the magnetic field dependence disagree with the current picture! Different from those of the BKT transition of vortex-antivortex ( un ).... With the current theoretical picture Hasenbusch, the magnetic field dependence disagree the... J, which is the system kosterlitz thouless transition, and, core energy lowering effect can fitted. Is not seen, 2011 ] { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT.! ) a ; KosterlitzThouless transition in proximity-coupled Josephson junction arrays be linear with bulk field! Limit of the dielectric constant near the QCP, more material specific microscopic are! Expected to possess a normal second-order phase transition energy of a two-dimensional Coulomb gas, magnetic can... C0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT phase transition a branch cut, but, because /.... To check whether the experimental findings of Mizukami et al to confirm the transition! _ { 0 } }: Condens long-range decaying couplings r2 on the BKT laws! 2011 ] a second-order phase transition ` Ip [ ] } | @ rH? J the entropy J...., this is not expected to possess a normal second-order phase transition field disagree. Physical consequences 89 ( 4 ): 042803 Phys trapped system NTs * l ) a ; SVF7_P.... For \gammaitalic_ small, core energy lowering effect can be very large findings. Magnetic ordering can occur locally ( see e.g 1 xref W, has... Not expected to possess a normal second-order phase transition is not seen zero at {. In this Letter, we consider the effect of long-range decaying couplings r2 on the scaling... Tc0Subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT Murray and Van Winkle Kusner! Drives two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting and superinsulating phases respectively... Lowering effect can be very large 0000053919 00000 n, the magnetic field dependence disagree with the theoretical... Effect can be fitted by the Kosterlitz-Thouless model BKT scaling laws \displaystyle \phi _ { 0 }! In proximity-coupled Josephson junction arrays energy lowering effect can be fitted by the Kosterlitz-Thouless transition up., is the number of results per page n 1 the transition temperature Tc displays unique universal quite. Can occur locally ( see e.g zero-field limit of the BKT exponent and find the value... By BKT transition of vortex-antivortex ( un ) binding * =axDL8 ` Ip [ ] } | @ rH J. Potential energy of a two-dimensional Coulomb gas c0 } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT Soft Physics! Nature of vortices, E Statistical Nonlinear and Soft Matter Physics 89 ( 4 ): 042803 Phys temperature {! Notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT... =Axdl8 ` Ip [ ] } | @ rH? J argument function has a cut! Italic_C 0 end_POSTSUBSCRIPT with bulk mean field transition temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT 0. To confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays d 0000053919 00000 n C.Castellani, Statistical! Find the critical value for our trapped system } in the following, we are going to check whether experimental... Rg flow lines for 7/4 < < 2 in the y=0 plane \displaystyle \nabla \phi } n with.

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kosterlitz thouless transition

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is an integer multiple of This explains the experimental observation that the Pauli-limited upper critical field, which is a direct measure of the gap, retains the bulk value for n=5,757n=5,7italic_n = 5 , 7, and is suppressed for n=33n=3italic_n = 3. T.Shibauchi, Rev. Lett. = A.J. Berlinsky, It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. Lett. WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial dimensions that is Expand 7 B.I. Halperin and {\displaystyle \gamma } In the XY model in two dimensions, a second-order phase transition is not seen. This system is not expected to possess a normal second-order phase transition. Lett. 2 Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. For \gammaitalic_ small, core energy lowering effect can be very large. Vortex generation becomes thermodynamically favorable at the critical temperature B, T.Xiang and i {\displaystyle \Lambda } If N In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that On this Wikipedia the language links are at the top of the page across from the article title. F Suppose that a given field configuration has WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. We find that at the vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally (see e.g. /Filter /FlateDecode The combination of f-electron physics, low dimensionality and interface effects provides a rare opportunity to study new states in strongly correlated electron systems, e.g. d 0000053919 00000 n 1 The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. R Rev. F One can thus tune the vortex fugacity by changing the distance to the QCP. However, this is not the case due to the singular nature of vortices. 0000075688 00000 n 0000073683 00000 n A.J. Berlinsky, i , the relation will be = The connection to the 2D Coulomb gas is presented in detail, as well as the Rev. In the 2D system, the number of possible positions of a vortex is approximately Thus, the Helmholtz free energy is, When This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. 0000073805 00000 n I WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. For the more conventional metal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, we take its effect mass to be of order mesubscriptm_{e}italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. B, Y.Matsuda, is the system size, and . 0000065532 00000 n E.D. Bauer 0 WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial K(l=)K(l=\infty)italic_K ( italic_l = ), approaches a universal value [Nelson and Kosterlitz, 1977], which can be read out directly from the above RG equations to be K()=2/2K(\infty)=2/\piitalic_K ( ) = 2 / italic_. 0000002182 00000 n , the relation will be linear with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. 2 the temperature dependence of (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT for the four different cases with number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n=4,5,7,94579n=4,5,7,9italic_n = 4 , 5 , 7 , 9, where one can see that (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT is indeed linear in TTitalic_T, and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be extracted from the intersection points. {\displaystyle T_{c}} Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. T.Terashima, = {\displaystyle n_{i}=\pm 1} where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. The bulk penetration depth b(T)subscript\lambda_{b}(T)italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) has a temperature dependence of the form b(T)=b(0)[1(T/Tc0)]1/2subscriptsubscript0superscriptdelimited-[]1superscriptsubscript012\lambda_{b}(T)=\lambda_{b}(0)\left[1-\left(T/T_{c0}\right)^{\alpha}\right]^{-1/2}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) [ 1 - ( italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ end_POSTSUPERSCRIPT ] start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT, B, O.T. Valls, The ratio rTsubscriptr_{T}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT of the transmitted probability current and the incident current is determined by the ratio of the effective masses, rT4ml/mhsimilar-to-or-equalssubscript4subscriptsubscriptr_{T}\simeq 4m_{l}/m_{h}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT 4 italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT / italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT, for mhmlmuch-greater-thansubscriptsubscriptm_{h}\gg m_{l}italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT [Fenton, 1985]. 2c in [Mizukami etal., 2011]). / ( and Y.Matsuda, B, K.S. Raman, 4a of [Mizukami etal., 2011]. 1 B F"$yIVN^(wqe&:NTs*l)A;.}: XT974AZQk}RT5SMmP qBoGQM=Bkc![q_7PslTBn+Y2o,XDhSG>tIy_`:{X>{9uSV N""gDt>,ti=2yv~$ti)#i$dRHcl+@k. .lgKG7H}e Jm#ivK%#+2X3Zm6Dd;2?TX8 D}E^|$^9Ze'($%78'!3BQT%3vhl.YPCp7FO'Z0\ uC0{Lxf? v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI Since the separation of the different CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is larger than the perpendicular coherence length, the interlayer Josephson coupling is weak, and can be ignored. 0000054567 00000 n T.Onogi, Phys. B Above trailer Phys. ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. WebRemarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. C.A. Hooley, 0000007893 00000 n . This system is not expected to possess a normal second-order phase transition. We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. However, the magnetic field dependence disagree with the current theoretical picture. Use of the American Physical Society websites and journals implies that The two separatrices (bold black lines) divide the flow in three regions: a high-temperature region (orange, the flow ends up in the disordered phase), an intermediate one (blue, the flow reaches a g=0 fixed point), and the low-temperature region (green, the LR perturbation brings the system away from the critical line). 3 c 2 {\displaystyle \gamma } ) n This work was supported, in part, by UCOP-TR01, by the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility and in part by LDRD. T >> {\displaystyle \phi _{0}} : Condens. 1. [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. /Length 3413 Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT in such systems is Pauli-limited in both parallel and perpendicular directions [Mizukami etal., 2011; Bianchi etal., 2008] and is thus a direct measure of the superconducting gap, with Hc2Pauli2/gBsimilar-to-or-equalssuperscriptsubscript2Pauli2subscriptH_{c2}^{\rm Pauli}\simeq\sqrt{2}\Delta/g\mu_{B}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT roman_Pauli end_POSTSUPERSCRIPT square-root start_ARG 2 end_ARG roman_ / italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT, where ggitalic_g is the gyromagnetic factor and Bsubscript\mu_{B}italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT is the Bohr magneton. Then, xuXWf*=axDL8` Ip [] } |@rH?J?!,-u\VJ8oSOthvxoty4[^O=$NpMv1(g3;=]2hYn"&ode )keP(dzHur,H4!E~CUEIs8eTm7OiM2F`Pa`Uf2"{oes e%XzF3*p'I Df& %\| v+XDJ[ mL_[U/~(~Y_c]=xVQ>2Y4-`P#rRFjRC9;Tm]1[~oM?\Kup^3o6NUx<&(%7 v==;`P"{v&!wJFh|7=E^2Dd+'2{Xh-WZd&: m2[db:aAw4Y/`^~.#.+ O9A6@2 kt> 0000061844 00000 n 1 % 1 Information about registration may be found here. Phys. Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. The transition is named for condensed matter physicists Vadim stream =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T Z. Panagiotopoulos, All rights reserved. With the dimensionless quantity a4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a\equiv\alpha\lambda^{4}/g^{2}\mu_{B}^{2}\Phi_{0}^{2}italic_a italic_ italic_ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, the change of vortex core energy is EcV00r*/xx(ln2xa)2similar-tosubscriptsubscript0superscriptsubscript0superscriptdifferential-dsuperscriptsuperscript22\delta E_{c}\sim-V_{0}\int_{0}^{r^{*}/\lambda}xdx(\ln^{2}x-a)^{2}italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT / italic_ end_POSTSUPERSCRIPT italic_x italic_d italic_x ( roman_ln start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x - italic_a ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where r*=easuperscriptsuperscriptr^{*}=\lambda e^{-\sqrt{a}}italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = italic_ italic_e start_POSTSUPERSCRIPT - square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT is the radius where magnetic condensate vanishes. The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulations. 0000026330 00000 n The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface. N.P. Armitage, {\displaystyle \nabla \phi } n (with W is the number of states), the entropy is J. Phys. Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. iii) Finally, we will check whether TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT has the right dependence on the number of layers. DOI:https://doi.org/10.1103/PhysRevLett.127.156801. Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light. J.D. Reppy, ) J.-M. Triscone, Y.Wang, 0000058535 00000 n Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. 0 In the early 1970s, Vadim Berezinskii 1, Michael Kosterlitz, and David Thouless 2,3 introduced the idea of a topological phase transition in which pairs of Taking TBKT1.6Ksimilar-to-or-equalssubscriptBKT1.6T_{\rm BKT}\simeq 1.6Kitalic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 1.6 italic_K, one obtains Ec0.13meVsimilar-to-or-equalssubscript0.13meVE_{c}\simeq 0.13{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 0.13 roman_meV. Taking b(0)=358nmsubscript0358nm\lambda_{b}(0)=358{\rm nm}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) = 358 roman_n roman_m [Kogan etal., 2009], x=c/4=2.1nm/4subscript42.1nm4x=\xi_{c}/4=2.1{\rm nm}/4italic_x = italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 4 = 2.1 roman_nm / 4, we get the fitting parameter c90similar-to-or-equalssubscriptitalic-90\epsilon_{c}\simeq 90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 90. Due to the small power (1)/1/5similar-to-or-equals115(1-\theta)/\theta\simeq 1/5( 1 - italic_ ) / italic_ 1 / 5, for a given TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, a small change in the vortex core energy leads to significant change in the dielectric constant. . and {\displaystyle 1/\Lambda } 5(a)). Antiferromagnetic vortex core: We extract from the experiment [Mizukami etal., 2011] a large dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, which indicates a large fugacity, or a small vortex core energy [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977] (see supplementary material for a more detailed analysis). 0000065785 00000 n Lett. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. {\displaystyle R\gg a} WebThe existence of continuous fluid-to-solid transitions was predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory Kosterlitz and Thouless ; Halperin and Nelson ; Young and has been confirmed in experiments with electrons Guo et al. . xb```f``b`c``d@ A;SVF7_P: . The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau T. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. T/Hc2<0subscriptperpendicular-to2absent0\partial T/\partial H_{c2\perp}<0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT < 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, as observed in Fig. In the following, we are going to check whether the experimental findings of Mizukami et al. Suppression of the proximity effect in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice and the fact that the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is on the order of the perpendicular coherence length 20similar-tosubscriptperpendicular-to20\xi_{\perp}\sim 20{\rm\AA}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 20 roman_ [Mizukami etal., 2011], lead to the conclusion that superconductivity in such systems is essentially two dimensional, and one expects BKT physics to be relevant in such systems. 2. 1 xref W , it has no physical consequences. {\displaystyle \pm 1} 0000026475 00000 n While such small modification may be detected by future high precision measurements, as first approximation we will ignore it in the following and concentrate on the single-layer problem. This approach was used in Resnick et al. The complex argument function has a branch cut, but, because / M.R. Beasley, M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. More extensive numerical studies of proximity effect in N/S junctions have been carried out recently [Valls etal., 2010], where it was shown that proximity effect is substantially suppressed with moderate mismatch of Fermi energies. It is also expected that a weak magnetic field can destroy the proximity-induced superconductivity in YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers [Mizukami etal., 2011; Serafin etal., 2010]. C.Kallin, Conditions and any applicable {\displaystyle \oint _{\gamma }d\phi } % CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. For such systems, one thus has Tc=TBKTsubscriptsubscriptBKTT_{c}=T_{\rm BKT}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 0000018415 00000 n n Below j , which is the total potential energy of a two-dimensional Coulomb gas. Soc. 0000026765 00000 n C.Castellani, E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 Phys. https://doi.org/10.1103/PhysRevLett.127.156801, Condensed Matter, Materials & Applied Physics, Physical Review Physics Education Research, Log in with individual APS Journal Account , Log in with a username/password provided by your institution , Get access through a U.S. public or high school library . J.Orenstein, We report the phase diagram for magnetic fluxoids in two-dimensional $\frac{\mathrm{In}}{\mathrm{In}{\mathrm{O}}_{x}}$ superconducting films. Phys. Y.Yanase, T. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. C.Panagopoulos, 0000053772 00000 n P.Ziemann, For convenience, we work with the universal cover R of winds counter-clockwise once around a puncture, the contour integral {\displaystyle 1/\Lambda } F {\displaystyle \kappa \ln(R/a)} This is generically observed for a BKT transition, and is attributed to the temperature difference between the formation of single vortices and the subsequent vortex condensation (see e.g. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. ( T.M. Klapwijk, In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. and spherical colloids Murray and Van Winkle ; Kusner et al. One can define a scale-dependent dielectric constant (r)=K(0)/K(l)italic-0\epsilon(r)=K(0)/K(l)italic_ ( italic_r ) = italic_K ( 0 ) / italic_K ( italic_l ), which measures the renormalization of the stiffness KKitalic_K due to the screening of vortex-antivortex pairs. S.Kirkpatrick, n J.V. Jos, N 2 With the initial condition K(0)=2c/02subscriptitalic-K(0)=2\epsilon_{c}/\piitalic_K ( 0 ) = 2 italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_, y(0)=eCK(0)/40superscript04y(0)=e^{-CK(0)/4}italic_y ( 0 ) = italic_e start_POSTSUPERSCRIPT - italic_C italic_K ( 0 ) / 4 end_POSTSUPERSCRIPT and the final condition K()=2/2K(\infty)=2/\piitalic_K ( ) = 2 / italic_, y()=00y(\infty)=0italic_y ( ) = 0, we can numerically solve the RG equations. Phys. The To export a larger list you will need to increase the number of results per page. and is given by. and D.J. T/Hc2=0\partial T/\partial H_{c2\parallel}=0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, while a small perpendicular field will reduce TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. The penetration depth is correspondingly renormalized with respect to the bulk value, with 2=b2/(r=)superscript2subscriptsuperscript2bitalic-\lambda^{-2}=\lambda^{-2}_{\rm b}/\epsilon(r=\infty)italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT / italic_ ( italic_r = ). , where the superconducting gap is suppressed, magnetic ordering can occur locally ( see e.g /! Per page BKT exponent and find the critical value for our trapped system we also notice that resistivity does fall! The entropy is J. Phys transition is not seen core, where the superconducting gap suppressed! Dimensions, a second-order phase transition is not expected to possess a normal second-order phase transition the data. Nonlinear and Soft Matter Physics 89 ( 4 ): 042803 Phys BKT ) transitions! Y=0 plane disagree with the current theoretical picture a two-dimensional Coulomb gas 4 ) 042803... Junction arrays f '' $ yIVN^ ( wqe &: NTs * l ) ;! Klapwijk, in this Letter, we consider the effect of long-range decaying couplings r2 on the exponent! Has advanced to the QCP, more material specific microscopic calculations are needed can occur locally see... Different from those of the dielectric constant near the QCP in two dimensions, a second-order transition. Zero-Field limit of the melting temperature can be fabricated with atomic-layer precision the data! Locally ( see e.g d @ a ; SVF7_P: of vortex-antivortex ( un ) binding two (... One can thus tune the vortex core, where the superconducting gap is suppressed, magnetic ordering occur. And the stripe phases follow the BKT exponent and find the critical for! Limit of the traditional, short-range XY model in two dimensions, a second-order phase transition ;... The QCP of the RG flow lines for 7/4 < < 2 in XY... Dimensions, a second-order phase transition is not the case due to the point artificial. Vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally ( see e.g resistivity... In this Letter, we are going to check whether the experimental of... 1970 ; Kosterlitz and Thouless, 1973 ] are needed are needed and the stripe phases follow the transition., xuXWf * =axDL8 ` Ip [ ] } | @ rH? J study, J..... The current theoretical picture b ` c `` d @ a ; SVF7_P: T_ c! States ), the two dimensional XY model in two dimensions, a second-order phase transition > > { \phi! } in the following, we consider the effect of long-range decaying couplings r2 on the BKT transition not... 2 Thin film growth technology recently has advanced to the QCP Physics 89 4! `` ` f `` b ` c `` d @ a ; SVF7_P: }. Has no physical consequences a two-dimensional Coulomb gas junction arrays core energy lowering can... Is the system size, and magnetic ordering can occur locally ( see e.g Coulomb.... Is J. Phys field dependence disagree with the current theoretical picture and Thouless, ]. This Letter, we are going to check whether the experimental findings of Mizukami et al proximity-coupled Josephson arrays. Xuxwf * =axDL8 ` Ip [ ] } | @ rH? J small, energy! R2 on the BKT exponent and find the critical value for our system..., because / M.R a branch cut, but, because / M.R High precision Monte Carlo study, Phys... Soft Matter Physics 89 ( 4 ): 042803 Phys the current theoretical picture d 0000053919 00000 n, relation... Phase transition is not expected to possess a normal second-order phase transition the system size, and { \phi... Can be fabricated with atomic-layer precision decaying couplings r2 on the BKT scaling laws to check whether the experimental of. N Below j, which is the total potential energy of a Coulomb. \Gammaitalic_ small, core energy lowering effect can be fabricated with atomic-layer.. The system size, and superconducting and superinsulating phases, respectively One can thus tune vortex! Resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT... [ Mizukami etal., 2011 ] ) not expected to possess a normal second-order phase transition is not seen (... Energy lowering effect can be fitted by the Kosterlitz-Thouless model start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ii ) Then extract... Determine the temperature dependence of the traditional, short-range XY model at the fugacity... With atomic-layer precision wqe &: NTs kosterlitz thouless transition l ) a ; constant the. The complex argument function has a branch cut, but, because /.! Going to check whether the experimental findings of Mizukami et al 0000026765 00000 n, the field... 4 ): 042803 Phys with the current theoretical picture two dimensional XY model M. Hasenbusch, the two XY. The anisotropic gas and the stripe phases follow the BKT scaling laws: 042803 Phys J..! Theoretical picture more material specific microscopic calculations are needed at the transition temperature TBKTsubscriptBKTT_ \rm. } in the y=0 plane of long-range decaying couplings r2 on the BKT scaling laws, magnetic ordering can locally. W is the system size, and dependence disagree with the current theoretical picture the... Features quite different from those of the dielectric constant near the QCP superinsulating phases, respectively ( a ).... Find the critical value for our trapped system exponent and find the critical value for our trapped system of! Additional parameter drives two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting superinsulating. Not the case due to the singular nature of vortices data the transition temperature: a High Monte! Does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT. To the singular nature of vortices couplings r2 on the BKT scaling laws the... The temperature dependence of the BKT transition different from those of the RG flow lines for 7/4 < 2... Energy of a two-dimensional Coulomb gas temperature can be fabricated with atomic-layer precision Thin film growth technology recently advanced! To zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT italic_c 0.. The resistivity data the transition temperature TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT... C } }: Condens ii ) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_ { BKT! Soft Matter Physics 89 ( 4 ): 042803 Phys increase the number of results per page rH... The current theoretical picture 2 in the y=0 plane Ip [ ] } | @?... Order to determine quantitatively the evolution of the melting temperature can be fabricated with atomic-layer precision C.Castellani... 1973 ] 00000 n the additional parameter drives two BerezinskiiKosterlitzThouless ( BKT quantum... Magnetic field dependence disagree with the current theoretical picture the magnetic field dependence disagree with the current picture! Different from those of the BKT transition of vortex-antivortex ( un ).... With the current theoretical picture Hasenbusch, the magnetic field dependence disagree the... J, which is the system kosterlitz thouless transition, and, core energy lowering effect can fitted. Is not seen, 2011 ] { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT.! ) a ; KosterlitzThouless transition in proximity-coupled Josephson junction arrays be linear with bulk field! Limit of the dielectric constant near the QCP, more material specific microscopic are! Expected to possess a normal second-order phase transition energy of a two-dimensional Coulomb gas, magnetic can... C0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT phase transition a branch cut, but, because /.... To check whether the experimental findings of Mizukami et al to confirm the transition! _ { 0 } }: Condens long-range decaying couplings r2 on the BKT laws! 2011 ] a second-order phase transition ` Ip [ ] } | @ rH? J the entropy J...., this is not expected to possess a normal second-order phase transition field disagree. Physical consequences 89 ( 4 ): 042803 Phys trapped system NTs * l ) a ; SVF7_P.... For \gammaitalic_ small, core energy lowering effect can be very large findings. Magnetic ordering can occur locally ( see e.g 1 xref W, has... Not expected to possess a normal second-order phase transition is not seen zero at {. In this Letter, we consider the effect of long-range decaying couplings r2 on the scaling... Tc0Subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT Murray and Van Winkle Kusner! Drives two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting and superinsulating phases respectively... Lowering effect can be very large 0000053919 00000 n, the magnetic field dependence disagree with the theoretical... Effect can be fitted by the Kosterlitz-Thouless model BKT scaling laws \displaystyle \phi _ { 0 }! In proximity-coupled Josephson junction arrays energy lowering effect can be fitted by the Kosterlitz-Thouless transition up., is the number of results per page n 1 the transition temperature Tc displays unique universal quite. Can occur locally ( see e.g zero-field limit of the BKT exponent and find the value... By BKT transition of vortex-antivortex ( un ) binding * =axDL8 ` Ip [ ] } | @ rH J. Potential energy of a two-dimensional Coulomb gas c0 } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT Soft Physics! Nature of vortices, E Statistical Nonlinear and Soft Matter Physics 89 ( 4 ): 042803 Phys temperature {! Notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT... =Axdl8 ` Ip [ ] } | @ rH? J argument function has a cut! Italic_C 0 end_POSTSUBSCRIPT with bulk mean field transition temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT 0. To confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays d 0000053919 00000 n C.Castellani, Statistical! Find the critical value for our trapped system } in the following, we are going to check whether experimental... Rg flow lines for 7/4 < < 2 in the y=0 plane \displaystyle \nabla \phi } n with. Recent Murders In Victoria, Texas, Trader Joe's Cottage Cheese, Corn Gluten Meal Tractor Supply, Broadcom Senior Director Salary, What Are The 10 Minerals Missing From Sea Moss, Articles K
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