Increasing csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT from 5 to 90, the vortex core energy only changes from 1.54kBTBKT1.54subscriptsubscriptBKT1.54k_{B}T_{\rm BKT}1.54 italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT to 0.85kBTBKT0.85subscriptsubscriptBKT0.85k_{B}T_{\rm BKT}0.85 italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. {\displaystyle I^{2}} 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. 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 5(a)). Sci. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. W Soc. 1 Above ( C, S.Scheidl and WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial ( 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. R 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 find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. Rev. Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. J. i We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. 2 the temperature dependence of (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT for the four different cases with number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n=4,5,7,94579n=4,5,7,9italic_n = 4 , 5 , 7 , 9, where one can see that (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT is indeed linear in TTitalic_T, and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be extracted from the intersection points. a Expand 7.6 Renormalization group analysis 7.6 Renormalization group analysis. . T.Terashima, ( i) First, we will examine whether resistivity has the right temperature dependence. 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. Phys. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. 0 (Nature Physics 7, 849 (2011)) in terms of The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a S.Adachi, 0000008417 00000 n {\displaystyle \Lambda \to \infty } and Y.Matsuda, The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. V [Deutscher and deGennes, 1969] ). A large dielectric constant corresponds to a small vortex core energy. On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). 0000074018 00000 n I C.Kallin, and F 0000054192 00000 n This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine C.Castellani, Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. In these systems, thermal generation of vortices produces an A 38 (2005) 5869 [cond-mat/0502556] . At the transition, the renormalized penetration depth satisfies the relation [Nelson and Kosterlitz, 1977] kBTBKT=02d/3222subscriptsubscriptBKTsuperscriptsubscript0232superscript2superscript2k_{B}T_{\rm BKT}=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 32 italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT (Eq. J.N. Eckstein, M.Franz, {\displaystyle \gamma } WebSuperconductivity at the interface between the insulators LaAlO and SrTiO has been tuned with the electric field effect. 2 M.Sigrist, and N.P. Ong, x G.Orkoulas and c Jpn. 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. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. Phys. Europhys. vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. {\displaystyle x_{i},i=1,\dots ,N} 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. Rev. Phys. 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? 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. 0000053029 00000 n Science. 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. Rev. With 2=b2/csuperscript2superscriptsubscript2subscriptitalic-\lambda^{-2}=\lambda_{b}^{-2}/\epsilon_{c}italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT / italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, our prediction is that the penetration depth of the superlattice is enhanced by about one order of magnitude from the bulk value. One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. . Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Itbeginswiththediscoveryofpossibleeldcongurationsthatone (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. 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]. The experimental results are in good agreement with the theoretical prediction determined from Eq. {\displaystyle S^{1}} each with index 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]. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 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. j For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. Rev. B.I. Halperin and This is a specific case of what is called the MerminWagner theorem in spin systems. Y.Yanase, 1 B, K.S. Raman, For large csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, we have Ec/kBTBKT(A1//2)c(1)/similar-to-or-equalssubscriptsubscriptsubscriptBKTsuperscript12superscriptsubscriptitalic-1E_{c}/k_{B}T_{\rm BKT}\simeq(A^{1/\theta}/2\pi)\epsilon_{c}^{-(1-\theta)/\theta}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ( italic_A start_POSTSUPERSCRIPT 1 / italic_ end_POSTSUPERSCRIPT / 2 italic_ ) italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - ( 1 - italic_ ) / italic_ end_POSTSUPERSCRIPT (see Fig. > [Pereiro etal., 2011] and references therein). 0000007893 00000 n and D.J. B, O.T. Valls, >> {\displaystyle \phi } k T i A.Petrovic, 0000054567 00000 n x Phys. = 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] . P.M. Mankiewich, S.Doniach and Phys. Rev. = = L Y.Ando, and Antiferromagnetic vortex core: We extract from the experiment [Mizukami etal., 2011] a large dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, which indicates a large fugacity, or a small vortex core energy [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977] (see supplementary material for a more detailed analysis). With and without magnetic field, are considered 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting.! 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Confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays, found in the XY model in... Generation of vortices produces an a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] j