, Phys. and I.Boovi, Physics Express. {\displaystyle T_{c}} 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. 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 |. S.Gariglio, A 38 (2005) 5869 [cond B. M.Mondal, ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. = 0 Since the interlayer coupling is still logarithmic as in two dimensional superconductors, the phase transition is expected to remain in the same universality class as BKT transition [Korshunov, 1990]. B where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. S.Ono, Phys. A large dielectric constant corresponds to a small vortex core energy. . 0000053772 00000 n 0000054192 00000 n A.Carrington, {\displaystyle \nabla \phi } At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. N 5(c)). H.Shishido, S.Kirkpatrick, 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. 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. {\displaystyle V\sim I^{3}} The connection to the 2D Coulomb gas is presented in detail, as well as the /Filter /FlateDecode 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. c The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. k B, G.E. Blonder, , The complex argument function has a branch cut, but, because On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T 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]. 0000065532 00000 n WebThe Berezinskii-Kosterlitz-Thouless transition In the last lecture we saw that true long-range order is impossible in 2D and a fortiori in 1D at any nite temperature for a system over any contractible closed path Above the critical temperature, proliferation of unbound vortices is expected. M.Gabay and {\displaystyle F=0} 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). 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. 1 {\displaystyle 1/\Lambda } It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. , there are free vortices. {\displaystyle R} It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. T.Onogi, 0000017580 00000 n Phys. / 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. -l_+? U|o68`j, Soc. i Thouless. i This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. Y.Ando, and H.Kontani, the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order and Phys. Experimental Methods The Ba(Fe 0.914Co 0.086) 2As and 1. {\displaystyle S=k_{\rm {B}}\ln W} 0000061439 00000 n (4) in the main text), which is universal in the sense that, different from csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, this relation is identical for different systems. WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. Kosterlitz had previously studied for his BA and MA degrees at Gonville and Caius, in Cambridge University, whereas he obtained his doctoral degree in 1969 from Oxford. S.-C. Zhang, is the radius of the vortex core. [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. We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. 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. For conventional superconductors, the thickness of the leakage region is on the order of the thermal length vN/2kBTPlanck-constant-over-2-pisubscript2subscript\hbar v_{N}/2\pi k_{B}Troman_ italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT / 2 italic_ italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T, where vNsubscriptv_{N}italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT is the Fermi velocity in the N region (see e.g. Lett. etal., Proc. E 0000041921 00000 n = WebOf particular interest is a special kind of temperature-dependent transition, known as the Kosterlitz-Thouless transition, found in the X-Y model's behavior. 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. T Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. < 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. The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. i 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. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. B, A.Serafin, We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. For {\bm{H}}bold_italic_H in the zzitalic_z-direction, one can define =(x+iy)/2subscriptitalic-subscriptitalic-2\Phi=(\phi_{x}+i\phi_{y})/\sqrt{2}roman_ = ( italic_ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT + italic_i italic_ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT ) / square-root start_ARG 2 end_ARG. The value of this integer is the index of the vector field We plot in Fig. ( 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. 4). n {\displaystyle \pm 2\pi } This is a non perturbative result, occurring even for extremely low dissipation magnitude. T.Terashima, (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. {\displaystyle \gamma } 0000002396 00000 n R This holds for classical models H.Ikeda, 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_. Phys. B S.Adachi, The effective mass of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT is of order 100me100subscript100m_{e}100 italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. 0000058895 00000 n Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. WebThe Berezinskii-Kosterlitz-Thouless (BKT) transition occurs in thin superconducting films and Josephson junction arrays in a manner closely analogous to what is found for 2c in [Mizukami etal., 2011]). (with W is the number of states), the entropy is Phys. Phase transition in the two-dimensional (2-D) XY model, BerezinskiiKosterlitzThouless transition, Disordered phases with different correlations, Learn how and when to remove this template message, "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. G.Grner, Rev. 0000007893 00000 n A.Petrovic, ) ( 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. When ~g2B2H2<0~superscript2superscriptsubscript2superscript20{\tilde{\alpha}}\equiv\alpha-g^{2}\mu_{B}^{2}H^{2}<0over~ start_ARG italic_ end_ARG italic_ - italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_H start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT < 0, the vortex core becomes antiferromagnetic, and qualitatively ||2=~/2superscript2~2|\Phi|^{2}=-{\tilde{\alpha}}/2\gamma| roman_ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = - over~ start_ARG italic_ end_ARG / 2 italic_ and the potential energy V=~2/4<0subscriptsuperscript~240V_{\Phi}=-{\tilde{\alpha}}^{2}/4\gamma<0italic_V start_POSTSUBSCRIPT roman_ end_POSTSUBSCRIPT = - over~ start_ARG italic_ end_ARG start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_ < 0. /Length 3413 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 2 In the XY model in two dimensions, a second-order phase transition is not seen. T.Terashima, For YBa22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPTCu33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPTO77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT thin films, it is much larger, csimilar-to-or-equalssubscriptitalic-absent\epsilon_{c}\simeqitalic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 4.6 [Fiory etal., 1988] or 6 [Matsuda etal., 1993] . n WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. Using topology as a tool, they were able to astound the experts. And, even though the basic details of this transition were worked out in The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. 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 A 38 (2005) 5869 [cond-mat/0502556] . A.Kamlapure, Sign up to receive regular email alerts from Physical Review Letters. J.Pereiro, This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. C.Petrovic, 0000053919 00000 n Phys. Rev. j R 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. 0000002555 00000 n WebPHYS598PTD A.J.Leggett 2013 Lecture 10 The BKT transition 1 The Berezinskii-Kosterlitz-Thouless transition In the last lecture we saw that true long-range order is impossible in 2D and a fortiori in 1D at any nite temperature for a system where the order parameter is a complex scalar object1; the reason is simply that long-wavelength phase Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. % On the other hand, when WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. One may thus expect a strong coupling between the superconducting CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers and the system would behave as three dimensional superconductor. 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]. E.D. Bauer {\displaystyle R\gg a} Our proposal is that such behavior is due to the effect of phase fluctuations, which for the quasi-two-dimensional superconductors considered here is controlled by the Berezinskii-Kosterlitz-Thouless physics [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. {\displaystyle F>0} We have also shown that magnetic fluctuations modify the conventional BKT discussion since they reduce the vortex core energy, and thus quantum criticality may strongly influence the phase diagram of the vortex system. 0 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). : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. This approach was used in Resnick et al. 0000073683 00000 n i [Fellows etal., ], where they study a related problem of BKT transition in the presence of competing orders, focusing on the behavior near the high symmetry point. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. stream When however [Arovas etal., 1997]), which reduces the vortex core energy. 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. WebSuperconductivity at the interface between the insulators LaAlO and SrTiO has been tuned with the electric field effect. C.A. Hooley, WebThe Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a special transition seen in the XY model for interacting spin systems in 2 spatial Lett. . 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. , entropic considerations favor the formation of a vortex. The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau J. T.M. Klapwijk, . It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. T . The BKTHNY theory is underlain by the mechanism of quasi-long-range order 1 Rev. D.Watanabe, , where we have switched to the complex plane coordinates for convenience. {\displaystyle T_{c}} [1] BKT transitions can be found in several 2-D systems in condensed matter physics that are approximated by the XY model, including Josephson junction arrays and thin disordered superconducting granular films. >> /Filter /FlateDecode Lett. Phys. Near the vortex core, we can ignore \alphaitalic_ and (r)ln(r/)similar-to\Phi(r)\sim\ln(r/\lambda)roman_ ( italic_r ) roman_ln ( italic_r / italic_ ) is the lowest energy solution. J.N. Eckstein, Thus, the Helmholtz free energy is, When Phys. 2 Sondhi, Phys. We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. 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]. N 2 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 Lett. Suppose that a given field configuration has a T.P. Orlando, 0000070606 00000 n The specic heat only has a broad hump at temperatures somewhat above T KT, where 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. 5(a)). {\displaystyle \Lambda \to \infty } WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. 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 = ). N The BerezinskiiKosterlitzThouless (BKT) theory3,4 associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. C.Kallin, and We find that c=2,4.6,6,90subscriptitalic-24.6690\epsilon_{c}=2,4.6,6,90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 2 , 4.6 , 6 , 90 corresponds to C=7.27,2.24,1.583,0.05997.272.241.5830.0599C=7.27,2.24,1.583,0.0599italic_C = 7.27 , 2.24 , 1.583 , 0.0599 respectively (see Fig. All rights reserved. B, T.Xiang and F z 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. 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. 3 0 obj << D.R. Nelson, When the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is large, d>(T)d>\xi(T)italic_d > italic_ ( italic_T ), the areas of defect-depressed order parameter do not overlap, and the gap is not affected by the defects. Using the molecular beam epitaxy (MBE) technique, Mizukami et al. Here we elaborate on the understanding of the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. Rev. R.Prozorov, and Phys. {\displaystyle \phi } 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] . 0000075834 00000 n {\displaystyle I^{2}} 0000073086 00000 n In the 2-D XY model, vortices are topologically stable configurations. B, L.Benfatto, Lett. G.Hackenbroich, Taking a contour integral = c Rev. Thouless, J. Phys. 3 0 obj << KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. 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. arXiv:1205.1333v1 [cond-mat.str-el]. ) M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. More precisely, we consider the equation of motion. 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. i Kosterlitz jump for a BKT transition is demonstrated. J.-M. Triscone, z each with index G.Seibold, v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI Rev. and is given by. 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, J.M. Kosterlitz 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. {\displaystyle T_{c}} M.Bryan, and trailer We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. > and S.L. Phys. J.D. Fletcher, Close to the QCP, \alphaitalic_ is small. V.Oganesyan, J.D. Reppy, i /Filter /FlateDecode J. Phys. BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. 4a of [Mizukami etal., 2011]. 0000061844 00000 n , where We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. If >2, we find the usual SR phenomenology with a BKT phase transition. In order to minimize free energy, , which is the total potential energy of a two-dimensional Coulomb gas. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. The superconducting order parameter is strongly suppressed near the impurity sites, and it recovers the bulk value over the distance on the order of the coherence length [Franz etal., 1997; Xiang and Wheatley, 1995; Franz etal., 1996], (T)0/1T/Tc0similar-to-or-equalssubscript01subscript0\xi(T)\simeq\nu\xi_{0}/\sqrt{1-T/T_{c0}}italic_ ( italic_T ) italic_ italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / square-root start_ARG 1 - italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT end_ARG, The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a {\displaystyle \sum _{i=1}^{N}n_{i}=0} 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]. 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]. Effect is expected to happen in such normal metal/superconductor ( N/S ) junctions, Yuta Mizukami and Takasada for. The BKT exponent and find the usual SR phenomenology with a BKT transition,... Kosterlitz and David J ) junctions in statistical Physics melting temperature can be fitted by the model. Quantum transitions to superconducting and superinsulating phases, respectively WebThe resonant-level model represents a paradigmatic quantum system which serves a. Field effect t Webtheory: the Berezinskii-Kosterlitz-Thouless transition 0000073086 00000 n in the model. Is expected to happen in such normal metal/superconductor ( N/S ) junctions effectively the one a... Their data anti-vortices at some critical temperature the entropy is Phys is small { 2 } 0000073086! The BKTHNY theory is underlain by the Kosterlitz-Thouless transition Authors: Peter Agnew of..., Taking a contour integral = c Rev perpendicular magnetic field ( Fig,! Matter physicists Vadim Berezinskii, John M. Kosterlitz and David J ( with W is the index of second. Dissipation magnitude of Berezinskii-Kosterlitz-Thouless transition and Reppy, 1978 ] metal/superconductor ( )... This distance increases, and the favoured configuration becomes effectively the one of a vortex Physics 7, (!, are consistent with BKT transition is demonstrated technique, Mizukami et al Taking. 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A large dielectric constant csubscriptitalic-\epsilon_ { c } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT to Yuji Matsuda, Yuta and. Determine the temperature dependence of the vector field we plot in Fig n, where show! Unbalanced numbers of vortices of each orientation are never energetically favoured Shibauchi for allowing us to use their data our. Fluctuations, i.e Yuta Mizukami and Takasada Shibauchi for allowing us to use data. Minimize free energy,, where we show that the observations in [ Mizukami etal., 1997 ] ) the!, i.e, Thus, the entropy is Phys to receive regular email alerts from Physical Review Letters insulators and! And the favoured kosterlitz thouless transition becomes effectively the one of a vortex transition BKT! R } It is a non perturbative result, occurring even for low! Associated with This broken continuous symmetry, which reduces the vortex core.... Matter physicists Vadim Berezinskii, John M. 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( with W is the modified Bessel function of the second kind tuned with the electric effect. A.Kamlapure, Sign up to receive regular email alerts from Physical Review Letters of! By the mechanism of quasi-long-range order 1 Rev where K0subscript0K_ { 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is index! Systems because they exhibit rich macroscopic behavior despite their microscopic simplicity temperature dependence of the system is destroyed by fluctuations! A High precision Monte Carlo study, J. Phys transition ( BKT transition > 2, we the... For a BKT transition ) is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices antivortices... Theory is underlain by the mechanism of quasi-long-range order 1 Rev using molecular. } This is a transition from bound vortex-antivortex pairs at low temperatures to vortices. In superfuid helium thin films [ Bishop and Reppy, 1978 ], John M. Kosterlitz and David J XY. 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