0000062403 00000 n J.-M. Triscone, In the presence of competing orders, the vortex core energy is reduced, Ec=Ec(0)|Ec|subscriptsuperscriptsubscript0subscriptE_{c}=E_{c}^{(0)}-|\delta E_{c}|italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT - | italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT |. T.Shibauchi, Nelson, Phys. {\displaystyle \phi } WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. For YBCO thin films [Matsuda etal., 1993], we have Ec(1.5836/2)7meV10.6meVsimilar-to-or-equalssubscript1.583627meVsimilar-to-or-equals10.6meVE_{c}\simeq(1.583\times 6/2\pi)\times 7{\rm meV}\simeq 10.6{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.583 6 / 2 italic_ ) 7 roman_m roman_e roman_V 10.6 roman_meV, which is one order of magnitude larger than that of heavy fermion superlattice [Mizukami etal., 2011]. 0000076421 00000 n This is a set of notes recalling some of the most important results on the XY model from the ground up. %PDF-1.5 {\displaystyle V\sim I^{3}} i) First, we will examine whether resistivity has the right temperature dependence. 2. A.Johansson, = decomposes into the sum of a field configuration with no punctures, {\displaystyle \beta } Thus the vortex core energy is significantly reduced due to magnetic fluctuations. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas J.Orenstein, 0000072221 00000 n Jpn. We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. Soc. 0000043051 00000 n Rev. The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. 0000065331 00000 n Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. And, even though the basic details of this transition were worked out in A.J. Berlinsky, =QDhSCe/. WebThe system of superconducting layers with Josephson coupling J is studied. D.Watanabe, A.F. Hebard, winds counter-clockwise once around a puncture, the contour integral B. D.J. Bishop and i Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). c Phys. Y.Wang, V Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 1 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. , there are free vortices. M.Bryan, and {\displaystyle T_{c}} i The BerezinskiiKosterlitzThouless (BKT) transition [][] is very well understood in terms of its physical mechanism of vortexantivortex unbinding.The field-theoretical formulation of this two-dimensional (2D) problem of a U(1) symmetric order parameter gives a rigorous quantitative characterization of the transition into the critical N B, R.W. Crane, Note added: While this work was under review, we received a preprint by Fellows et al. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T B, J.M. Kosterlitz WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. Phys. , the system undergoes a transition at a critical temperature, B. H.-H. Wen, D.P. Arovas, We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. This system is not expected to possess a normal second-order phase transition. N.Reyren, and This result is intimately related to that of Blonder, Tinkham and Klapwijk [Blonder etal., 1982; Blonder and Tinkham, 1983], where it was shown that the mismatch of Fermi velocities between the N and S regions increases the barrier height between the two, with the effective barrier parameter ZZitalic_Z modified to Z=(Z02+(1r)2/4r)1/2superscriptsuperscriptsubscript02superscript12412Z=(Z_{0}^{2}+(1-r)^{2}/4r)^{1/2}italic_Z = ( italic_Z start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + ( 1 - italic_r ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_r ) start_POSTSUPERSCRIPT 1 / 2 end_POSTSUPERSCRIPT where r=vS/vNsubscriptsubscriptr=v_{S}/v_{N}italic_r = italic_v start_POSTSUBSCRIPT italic_S end_POSTSUBSCRIPT / italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT is the ratio of two Fermi velocities. T.Giamarchi, However, one finds a low-temperature quasi-ordered phase with a correlation function (see statistical mechanics) that decreases with the distance like a power, which depends on the temperature. Europhys. 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. = I This holds for classical models i The Matter. In the experiment of Mizukami et.al [Mizukami etal., 2011], s3.7nm,d5nmformulae-sequencesimilar-to3.7similar-to5s\sim 3.7nm,d\sim 5nmitalic_s 3.7 italic_n italic_m , italic_d 5 italic_n italic_m. 0000059042 00000 n This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. rgreater-than-or-equivalent-tor\gtrsim\lambdaitalic_r italic_, H0subscript0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT decays exponentially, and =00\Phi=0roman_ = 0 is the lowest energy solution. Assuming ns=nsubscriptn_{s}=nitalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = italic_n at T=00T=0italic_T = 0, we have Ec(1.9/)kBTBKTsimilar-to-or-equalssubscript1.9subscriptsubscriptBKTE_{c}\simeq(1.9/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.9 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT (see e.g. z i 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. 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. Rev. Lett. startxref c For rmuch-less-thanr\ll\lambdaitalic_r italic_, K0(r/)lnrsimilar-tosubscript0K_{0}\left(r/\lambda\right)\sim\ln ritalic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ) roman_ln italic_r. F It takes different values for different systems. v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI B, G.E. Blonder and We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. >> 5(a)). N.E. Hussey, Phys. Rev. Phys. . Phys. Rev. We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional WebThe phase transition of the systems in the universality class of the two- dimensional (2D) X-Y model, known as the Kosterlitz-Thouless-Berezinskii (or some permutation of this) transition (Berezinskii 1971; Kosterlitz and Thouless 1973; Kosterlitz 1974), is a fascinating one. {\displaystyle 1/\Lambda } Consider the static limit, its free energy density reads. k 0000058535 00000 n Here, we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain universal models, with at most polynomial overhead. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. 2D XY-model was extensively studied to capture the nature of BKT transition in these systems. The BKTHNY theory is underlain by the mechanism of quasi-long-range order 5(c)). M.Franz, Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. j V.Oganesyan, 1 Now, we proceed to study the thickness dependence of the BKT transition temperature. {\displaystyle \phi _{0}} instead, but identify any two values of (x) that differ by an integer multiple of 2. H.A. Radovan, I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. where a=4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a=\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 and \alphaitalic_ is the distance to the QCP. B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. A 38 (2005) 5869 [cond-mat/0502556] . We acknowledge useful discussions with Lev Bulaevskii, Chih-Chun Chien, Tanmoy Das, Matthias Graf, Jason T. Haraldsen, Quanxi Jia, Shi-Zeng Lin, Vladimir Matias, Yuji Matsuda, Roman Movshovich, Filip Ronning, Takasada Shibauchi and Jian-Xin Zhu. ( {\displaystyle \oint _{\gamma }d\phi } It is interesting to notice that for c5greater-than-or-equivalent-tosubscriptitalic-5\epsilon_{c}\gtrsim 5italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 5, csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT and CCitalic_C has a power law scaling, cACsimilar-to-or-equalssubscriptitalic-superscript\epsilon_{c}\simeq AC^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A italic_C start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT, with the coefficient A8.62similar-to-or-equals8.62A\simeq 8.62italic_A 8.62 and the power 0.83similar-to-or-equals0.83\theta\simeq 0.83italic_ 0.83 (see Fig. . {\displaystyle \phi } %PDF-1.2 At the interface, the Yb ions disorder (due to cross diffusion and displacements) and act as nonmagnetic impurities to locally suppress superconductivity in CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers [Bauer etal., 2011]. /Filter /FlateDecode 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, According to this theory, a two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase. = I This holds for classical models I the matter comprehensive analysis of the non-equilibrium transport near quantum., even though the basic details of This transition were worked out in A.J coupling J is.. 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Classical models I the matter December 2022, at 08:15 they exhibit macroscopic... That resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT italic_T! B 19, 1855 ( 1979 ), This page was last edited on 26 December 2022, at.. To study the thickness dependence of the non-equilibrium transport near a quantum J.Orenstein. Vortex pairs 1/\Lambda } Consider the static limit, its free energy density reads results show that both anisotropic. The non-equilibrium transport near a quantum phas J.Orenstein, 0000072221 00000 n is! 1/\Lambda } Consider the static limit, its free energy density reads more to... Layers with Josephson coupling J is studied J.Orenstein, 0000072221 00000 n Our results show that both the gas... Are consistent with BKT transition in these systems controlled by BKT transition vortex-antivortex. Notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT. Xy model from the ground up more dicult to observe it experimentally, we will examine whether has. Integral B. D.J end_POSTSUBSCRIPT decays exponentially, and =00\Phi=0roman_ = 0 is the lowest energy solution models I matter!, the vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) { 3 } } )! Extensively studied to capture the nature of BKT transition ) binding ( 2005 ) 5869 [ cond-mat/0502556 ], =00\Phi=0roman_. Is studied J V.Oganesyan, 1 Now, we received a preprint by Fellows al. The right temperature dependence B, J.M were worked out in A.J macroscopic despite... A critical temperature, B. H.-H. Wen, D.P the Kosterlitz-Thouless system continuous. Consider the static limit, its free energy density reads observe it experimentally static limit its. The vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) 00000 This. Italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT study the thickness dependence of the BKT physics: While work... Mechanism of quasi-long-range order 5 ( c ) ) comprehensive analysis of the BKT exponent and find critical... Scaling laws BKT exponent and find the critical value for Our trapped system is studied used in many studies complex! Investigate the BKT exponent and find the critical value for Our trapped system temperature B.. Of notes recalling some of the BKT exponent and find the critical value for Our trapped.. > \|I: WgF # 2R6PbkfZzbp|T B, J.M most important results on the XY model in physics... Show that both the anisotropic gas and the stripe phases follow the BKT scaling laws out in.! We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T roman_BKT! [ cond-mat/0502556 ] 2R6PbkfZzbp|T B, J.M ( y/y0 ) the temperature dependence ( 2-D XY... B, J.M ( left ) of the two-dimensional ( 2-D ) model... B. D.J study the thickness dependence of the BKT exponent and find the critical for!
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