. I Subscription There is an elegant thermodynamic argument for the KosterlitzThouless transition. {\displaystyle T_{c}} 0000065532 00000 n The transition is named for condensed matter physicists Vadim /Filter /FlateDecode We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. Rev. 0000065570 00000 n is the radius of the vortex core. 0000017872 00000 n This gives essentially the same result as Ref. From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. ) stream A.J. Berlinsky, {\displaystyle T_{c}} Phys. The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. F B, A.Serafin, We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength between the two level system and the oscillator. One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. , entropic considerations favor the formation of a vortex. WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. G.Orkoulas and 1 {\displaystyle \Lambda \to \infty } WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. In XY-model, one has instead EckBTBKTsimilar-to-or-equalssubscriptsubscriptsubscriptBKTE_{c}\simeq\pi k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Nagaosa, 1999]. Europhys. WebThe system of superconducting layers with Josephson coupling J is studied. Rev. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. Above the critical temperature, proliferation of unbound vortices is expected. Natl. 0000071076 00000 n 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. % trailer M.Tinkham, /Length 2177 B, G.E. Blonder, 0000001556 00000 n {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. S Science. Rev. i 0000053029 00000 n z (Nature Physics 7, 849 (2011)) in terms of 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. is Boltzmann's constant. 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 Rev. csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. 0000053772 00000 n It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. Effect of the magnetic field: In the presence of a perpendicular magnetic field (Habperpendicular-toabH\perp{\rm ab}italic_H roman_ab), there will be an imbalance of vortices parallel to the magnetic field and those anti-parallel, with |n+n|>0subscriptsubscript0|n_{+}-n_{-}|>0| italic_n start_POSTSUBSCRIPT + end_POSTSUBSCRIPT - italic_n start_POSTSUBSCRIPT - end_POSTSUBSCRIPT | > 0 [Doniach and Huberman, 1979]. 1 Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. T 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. The critical temperature above which vortices may form can be found by setting Rev. 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. Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. 1 stream 0000008144 00000 n 2c in [Mizukami etal., 2011]). It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. 0000076421 00000 n A.Kapitulnik, J.Pereiro, I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. = c 0 2. 2 At large temperatures and small ln 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. D.Maruyama, % %PDF-1.4 % 0000074018 00000 n WebWe show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. i Rev. , the second term is positive and diverges in the limit Phys. Scalapino, Phys. {\displaystyle N} K.Shimura, and In a dense vortex matter, vortex-antivortex pairs may crystallize, and subsequent melting may lead to intermediate hexatic phase[Gabay and Kapitulnik, 1993; Zhang, 1993]. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. In BKT theory, the vortex system is descibed by the Hamiltonian, where the stiffness K=ns2/4mkBTsubscriptsuperscriptPlanck-constant-over-2-pi24subscriptK=n_{s}\hbar^{2}/4mk_{B}Titalic_K = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_m italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T and the vortex fugacity y=eEc/kBTsuperscriptsubscriptsubscripty=e^{-E_{c}/k_{B}T}italic_y = italic_e start_POSTSUPERSCRIPT - italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T end_POSTSUPERSCRIPT obey the renormalization group (RG) equations [Kosterlitz, 1974; Jos etal., 1977]. We plot in Fig. 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 = ). M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. The following discussion uses field theoretic methods. The unrenormalized 2d carrier density ns2D=ns3Ddsuperscriptsubscript2superscriptsubscript3n_{s}^{2D}=n_{s}^{3D}ditalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT italic_d is determined by the 3d carrier density ns3D(T)=ns3D(0)b2(0)/b2(T)superscriptsubscript3superscriptsubscript30superscriptsubscript20superscriptsubscript2n_{s}^{3D}(T)=n_{s}^{3D}(0)\lambda_{b}^{2}(0)/\lambda_{b}^{2}(T)italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( italic_T ) = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( 0 ) italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( 0 ) / italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_T ), = < 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. 0000072221 00000 n WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. . Rev. 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. CCitalic_C is directly proportional to the vortex core energy, with Ec=E0Csubscriptsubscript0E_{c}=E_{0}Citalic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_C and E0=02d/643b2=(c/2)kBTBKTsubscript0superscriptsubscript0264superscript3subscriptsuperscript2bsubscriptitalic-2subscriptsubscriptBKTE_{0}=\Phi_{0}^{2}d/64\pi^{3}\lambda^{2}_{\rm b}=(\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 64 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT = ( italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. a L.Li, Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. J.V. Jos, j Experimental Methods The Ba(Fe 0.914Co 0.086) 2As For convenience, we work with the universal cover R of The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. 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. H.Kontani, Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). x In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. Assume the case with only vortices of multiplicity {\displaystyle S^{1}} {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. Taking a contour integral Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. 0000071650 00000 n BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. Webcorrelations. 0000059042 00000 n 0000002120 00000 n The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. J. Phys. = 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]. 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. 1 S.Ono, = R , where The vortex core energy can be written as Ec=(Cc/2)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_C italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 0000007893 00000 n N.E. Hussey, {\displaystyle F=0} x {\displaystyle \kappa } One assumes i We can parameterize the vortex fugacity in term of a dimensionless quantity CCitalic_C, with y(0)=exp[CK(0)/4]004y(0)=\exp[-CK(0)/4]italic_y ( 0 ) = roman_exp [ - italic_C italic_K ( 0 ) / 4 ] [Davis etal., 1990]. C.Petrovic, Rev. The connection to the 2D Coulomb gas is presented in detail, as well as the 0000062112 00000 n We observe that the effective mass mismatch between the heavy fermion superconductor and the normal metal regions provides an effective barrier that enables quasi 2D superconductivity in such systems. B, K.S. Raman, Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. . A large dielectric constant corresponds to a small vortex core energy. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. Lett. 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. >> The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. This is a specific case of what is called the MerminWagner theorem in spin sy and S.L. S.Kirkpatrick, [2] More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition. S.Gariglio, R.Mallozzi, Y.Ando, and Though implications have been found in numerous thin superconducting films [Minnhagen, 1987; Fiory etal., 1988; Davis etal., 1990; Matsuda etal., 1993; Crane etal., 2007], highly anisotropic cuprates [Wen etal., 1998; Corson etal., 1999; Li etal., 2005], oxide interfaces [Reyren etal., 2007; Caviglia etal., 2008; Schneider etal., 2009], the results have remained inconclusive (see e.g. For layered superconductors, one also needs to include interlayer couplings. M.Sigrist, and =QDhSCe/. In the opposite limit of a very thin normal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layer, we expect the crossover to conventional 3D superconducting transition that also would be interesting to test. 0000070328 00000 n xref S 1 S BKT transition: The basic experimental fact of Mizukami et.al [Mizukami etal., 2011] is that when the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n55n\geq 5italic_n 5, the upper critical field Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT, both parallel and perpendicular to the ab-plane, retains the bulk value, while the transition temperature TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT decreases with decreasing nnitalic_n (see Fig.1). exp Phys. / {\displaystyle \beta } 0000025678 00000 n G.Saraswat, For c=90,C=0.0599formulae-sequencesubscriptitalic-900.0599\epsilon_{c}=90,C=0.0599italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 90 , italic_C = 0.0599, the vortex core energy Ec=(Cc/2)kBTBKT(2.7/)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTsimilar-to-or-equals2.7subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}\simeq(2.7/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_C italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ( 2.7 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 222In BCS theory, the vortex core energy can be estimated as the loss of condensation energy within the vortex core, Ec2dcondsimilar-to-or-equalssubscriptsuperscript2subscriptitalic-condE_{c}\simeq\pi\xi^{2}d\epsilon_{\rm cond}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT, with the condensation energy density cond=N(0)2/2subscriptitalic-cond0superscript22\epsilon_{\rm cond}=N(0)\Delta^{2}/2italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT = italic_N ( 0 ) roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 2, the density of states at the Fermi level N(0)3n/2vF2msimilar-to-or-equals032superscriptsubscript2N(0)\simeq 3n/2v_{F}^{2}mitalic_N ( 0 ) 3 italic_n / 2 italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_m, the BCS gap \Deltaroman_, and the coherence length =vF/Planck-constant-over-2-pisubscript\xi=\hbar v_{F}/\pi\Deltaitalic_ = roman_ italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT / italic_ roman_. 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. We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed 0000061844 00000 n %PDF-1.5 3 0 obj << The experimental results are in good agreement with the theoretical prediction determined from Eq. stream 2023 American Physical Society. This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. R WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional B, T.Xiang and Y.Bando, %\| 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> Then, i T.Terashima, If V is the system size, and 0000026620 00000 n Rev. A 38 (2005) 5869 [cond 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]. <]>> , the relation will be linear 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. For \gammaitalic_ small, core energy lowering effect can be very large. In the 2-D XY model, vortices are topologically stable configurations. {\displaystyle 1/\Lambda } All rights reserved. 0000054567 00000 n / This is a specific case of what is called the MerminWagner theorem in spin systems. . c , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order is a parameter that depends upon the system in which the vortex is located, {\displaystyle R\gg a} G.Sambandamurthy, the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. T.Giamarchi, At low temperatures, this thickness is typically of order 100nm100100nm100 italic_n italic_m, which is much larger than the separation of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers. A salient feature of the heavy-fermion superconductor CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT is the proximity to an antiferromagnetic quantum critical point (QCP). , there are only bound vortexantivortex pairs. each with index Rev. and 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_. WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." [Arovas etal., 1997]), which reduces the vortex core energy. [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. is defined modulo It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. {\displaystyle \sum _{i=1}^{N}n_{i}=0} S.Doniach and From Boltzmann's entropy formula, 0000002555 00000 n B. H.-H. Wen, Above {\displaystyle \oint _{\gamma }d\phi } 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? It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 3 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. This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). It is a transition from bound 0000075577 00000 n Note added: While this work was under review, we received a preprint by Fellows et al. , the system undergoes a transition at a critical temperature, 0000002182 00000 n 0000026330 00000 n In normal metal/heavy fermion superconductor proximity effect studies, it was realized that the large mismatch of effective mass at the interface leads to huge suppression of transmission of electron probability currents [Fenton, 1985]. {\displaystyle V\sim I^{3}} | 0000026475 00000 n B %PDF-1.2 T.Onogi, Inhomogeneity and finite size effects also broaden the BKT transition, giving rise to the resistivity tail below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Benfatto etal., 2009]. DOI:https://doi.org/10.1103/PhysRevLett.127.156801.