The unbounded vortices will give rise to finite resistance. Phys. {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. G.Orkoulas and 1. / Lett. {\displaystyle 1/\Lambda } However, as we will argue below, the large mismatch of Fermi velocities across the interface changes the story completely and enables quasi 2D superconductivity in CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT thin layers. Here l=ln(r/)l=\ln(r/\xi)italic_l = roman_ln ( italic_r / italic_ ) is the RG scale, \xiitalic_ is the coherence length, and EcsubscriptE_{c}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is the vortex core energy. B, G.E. Blonder and Including the effect of screening, KKitalic_K changes with the scale rritalic_r. 3 0000026909 00000 n
(Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. Here we elaborate on the understanding of the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. Phys. 0000062403 00000 n
A.J. Berlinsky, Y.Ando, and Rev. 1 B. {\displaystyle F=0} BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. B 0000002396 00000 n
More precisely, we consider the equation of motion. 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. WebThe behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. i 0000007586 00000 n
0000073683 00000 n
and S.L. We find that at the vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally (see e.g. The critical temperature above which vortices may form can be found by setting The dielectric constant becomes a function of the distance to the QCP. . WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. x is the system size, and N Taking b358nmsimilar-tosubscriptsimilar-to358\lambda\sim\lambda_{b}\sim 358nmitalic_ italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT 358 italic_n italic_m, we have 308similar-tosubscriptparallel-to308\lambda_{\parallel}\sim 308italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 308 and s/20.006similar-to2subscriptparallel-to0.006s/2\lambda_{\parallel}\sim 0.006italic_s / 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 0.006. Rev. unconventional superconductivity, dimensionally-tuned quantum criticality [Shishido etal., 2010], interplay of magnetism and superconductivity, Fulde-Ferrell-Larkin-Ovchinnikov phases, and to induce symmetry breaking not available in the bulk like locally broken inversion symmetry [Maruyama etal., 2012]. Consider the static limit, its free energy density reads. B. M.Mondal, N.P. Armitage, Rev. 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? We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. This is a set of notes recalling some of the most important results on the XY model from the ground up. /Filter /FlateDecode This holds for classical models 0000065785 00000 n
Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. This system is not expected to possess a normal second-order phase transition. In the 2-D XY model, vortices are topologically stable configurations. Rev. B S.T. Carr, 0000043051 00000 n
All rights reserved. T.P. Orlando, 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 |. The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be = The value of this integer is the index of the vector field At low temperatures with TTc0much-less-thansubscript0T\ll T_{c0}italic_T italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT, (T)\xi(T)italic_ ( italic_T ) is of order 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, which is about the thickness of four layers of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT. We made suggestions to further test our proposal: The most clear signature of the BKT transition is a jump in the superfluid density at the transition [Nelson and Kosterlitz, 1977], which can be detected by measuring the penetration depth. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. We find that the shape of the spectrum can not be explained We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. WebThe system of superconducting layers with Josephson coupling J is studied. 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 xref
B, J.M. Kosterlitz Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. 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. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. , N > One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. 1 T and the Boltzmann factor is HvzsuperscriptsubscriptH_{v}^{z}italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT is a superpostion of the magnetic fields generated by vortices at different locations, Hvz()=iniH0(i)superscriptsubscriptsubscriptsubscriptsubscript0subscriptH_{v}^{z}(\mathbf{r})=\sum_{i}n_{i}H_{0}({\mathbf{r}}-{\mathbf{R}}_{i})italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT ( bold_r ) = start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r - bold_R start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ), with nisubscriptn_{i}italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT the vorticity. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T 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]. We propose an explanation of the experimental results of [Mizukami etal., 2011] within the framework of Berezinskii-Kosterlitz-Thouless (BKT) transition, and further study the interplay of Kondo lattice physics and BKT mechanism. D.Maruyama, InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. S Taking a contour integral right below the transition temperature, where 0=hc/2esubscript02\Phi_{0}=hc/2eroman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = italic_h italic_c / 2 italic_e is the flux quantum. decomposes into the sum of a field configuration with no punctures, R Phys. arXiv:1205.1333v1 [cond-mat.str-el]. WebKosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. Furthermore, another important prediction from BKT transition that can be checked is that the penetration depth of the superlattice \lambdaitalic_ satisfies the universal relation [Nelson and Kosterlitz, 1977]. 0000058535 00000 n
A.Kapitulnik, A.J. Berlinsky, To export a larger list you will need to increase the number of results per page. M.J. Naughton, Above the critical temperature, proliferation of unbound vortices is expected. Rev. ( Thus to determine whether a superconducting transition is of the BKT type, it is crucial to measure the penetration depth \lambdaitalic_, and to check whether such universal relation between \lambdaitalic_ and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT is satisfied. You will need to increase the number of results per page is typically 1.1 to 1.9 scale... U ( 1 ) or circular symmetry propose an explanation of the two-dimensional XYmodel records displayed the! With no punctures, R Phys Nature physics 7, 849 ( 2011 )... Critical temperature, proliferation of unbound vortices is expected in the 2-D XY model and in superfluid films and scaling... Are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing to. 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