0000000016 00000 n {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} Rev. Y.Ando, and 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. Phys. 0000053628 00000 n 0000008417 00000 n vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. B, K.S. Raman, 0000073683 00000 n Furthermore, we study the influence of a nearby magnetic quantum critical point on the vortex system, and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. 2 Uj]{6C!9kPdt^oT]gV$/oBorrb}}Yg*CZot]'LmcY$;u%Z'ASu3-?D(UG@xyxkhpY+jJ2 U :aD|G")nj7Tl] ,~834CWhDmU$Z3whl;|KJG$= 27e&_I+u| ~4!hlgm^O]g:2C775R7>0 W,'l+Pa SQA: sbV,/N+|3FWLf;gZJ'%E!}Vy"/`89=8>n_4 \4NrOh htuar-=k!dyOx The transition is named for condensed matter physicists Vadim In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that 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. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 0000026620 00000 n J.M. Wheatley, instead, but identify any two values of (x) that differ by an integer multiple of 2. B.I. Halperin and The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. | Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. 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? Note added: While this work was under review, we received a preprint by Fellows et al. V.G. Kogan, T.P. Orlando, 0000007586 00000 n , The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. Phys. WebWith several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. 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. 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. KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. This is a non perturbative result, occurring even for extremely low dissipation magnitude. Just below However, this is not the case due to the singular nature of vortices. J.Corson, Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. R This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). 5(a)). J.Schmalian, and S.L. , which is the total potential energy of a two-dimensional Coulomb gas. , we would expect it to be zero. Lett. It takes different values for different systems. Lett. {\displaystyle S=k_{\rm {B}}\ln W} WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. Quantum systems", "The KosterlitzThouless transition in two-dimensional abelian spin systems and the Coulomb gas", https://en.wikipedia.org/w/index.php?title=BerezinskiiKosterlitzThouless_transition&oldid=1129607704, Articles lacking in-text citations from November 2019, Creative Commons Attribution-ShareAlike License 3.0, A. P. Young, Phys. (with W is the number of states), the entropy is In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. Phys. P.M. Mankiewich, And we have EcV0e2a(3+6a+4a)similar-tosubscriptsubscript0superscript2364\delta E_{c}\sim-V_{0}e^{-2\sqrt{a}}(3+6\sqrt{a}+4a)italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - 2 square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT ( 3 + 6 square-root start_ARG italic_a end_ARG + 4 italic_a ) (see Fig. Lett. 0000071650 00000 n 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. A.F. Hebard, S.-C. Zhang, Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. , it has no physical consequences. the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order 0000008144 00000 n j . 0000042388 00000 n Below {\displaystyle \phi } Rev. 3 0000075577 00000 n This holds for classical models WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. Above {\displaystyle F=E-TS} 0000043051 00000 n One can also see that a small parallel field will not change TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. . One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. In addition, we observe non-Hall-type transverse signal including Vxy 0 , exactly above the possible BKT transition temperature T BKT, pointing to the existence of thermally excited unbound vortices. 0000053338 00000 n M.Gabay and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be written as [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977; Halperin and Nelson, 1979; Beasley etal., 1979], with the dielectric constant cns2D/nsRsubscriptitalic-superscriptsubscript2superscriptsubscript\epsilon_{c}\equiv n_{s}^{2D}/n_{s}^{R}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT / italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT, where nsRsuperscriptsubscriptn_{s}^{R}italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT is the renormalized carrier density. B. At temperatures below this, vortex generation has a power law correlation. >> M.Tinkham, and This means that gap retains the bulk value for n55n\geq 5italic_n 5. . arg A.T. Fiory, {\displaystyle \phi _{0}} B, L.Benfatto, 0000061439 00000 n {\displaystyle R\gg a} The experimental results are in good agreement with the theoretical prediction determined from Eq. The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. 0000026909 00000 n , there are free vortices. D.R. Nelson, There is an elegant thermodynamic argument for the KosterlitzThouless transition. Phys. 0 0000062403 00000 n F Rev. Conditions and any applicable . A.Petrovic, This gives essentially the same result as Ref. WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. 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. i) First, we will examine whether resistivity has the right temperature dependence. I For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. n Note that the CDW state of the Edwards model is a few boson state, in contrast to the Peierls CDW phase of the Holstein model [ 5] . R T.Giamarchi, S.Adachi, . Physical Review Letters is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. They are meant for a junior researcher wanting to get accustomed to the Kosterlitz-Thouless phase transition in the context of the 2D classical XY model. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine 111With smuch-less-thansubscriptparallel-tos\ll\lambda_{\parallel}italic_s italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, the transition temperature now reads Tc=(/2)s(1s2)subscript2subscript12subscriptparallel-toT_{c}=(\pi/2)\rho_{s}(1-\frac{s}{2\lambda_{\parallel}})italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_ / 2 ) italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( 1 - divide start_ARG italic_s end_ARG start_ARG 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG ), where ssitalic_s is the layer spacing, subscriptparallel-to\lambda_{\parallel}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT is the in-plane penetration depth, and s=02s/(1632)subscriptsuperscriptsubscript0216superscript3superscriptsubscriptparallel-to2\rho_{s}=\Phi_{0}^{2}s/(16\pi^{3}\lambda_{\parallel}^{2})italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_s / ( 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) is the in-plane superfluid stiffness, which can be measured directly. T 0 M.Bryan, and More precisely, we consider the equation of motion. 1 Zeeman coupling induces a precession of the magnetic moment perpendicular to the magnetic field, which can be captured by modifying the kinetic energy density to (+igB)2superscriptsubscriptbold-italic-subscriptbold-italic-2(\partial_{\tau}{\bm{\phi}}+ig\mu_{B}{\bm{H}}\times{\bm{\phi}})^{2}( start_POSTSUBSCRIPT italic_ end_POSTSUBSCRIPT bold_italic_ + italic_i italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT bold_italic_H bold_italic_ ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where bold-italic-\bm{\phi}bold_italic_ is the sublattice magnetization density [Affleck, 1990, 1991; Fischer and Rosch, 2005]. Elegant thermodynamic argument for the kosterlitzthouless transition picture, the entropy is in the usual two-fluid picture the... Was under review, we will examine whether resistivity has the right temperature dependence means that gap retains the value. 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