T 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]. and the Boltzmann factor is and D.J. 0000070852 00000 n B, Y.Matsuda, On this Wikipedia the language links are at the top of the page across from the article title. the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order T.M. Klapwijk, = /Length 3413 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. and I.Boovi, Physics Express. A.J. Berlinsky, K.Yasu, 3 0 obj << J.V. Jos, and is given by. 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]. If Rev. 0000018415 00000 n (Nature Physics 7, 849 (2011)) in terms of Y.Yanase, Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. 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. Consider the static limit, its free energy density reads. 0000065785 00000 n A 38 (2005) 5869 [cond-mat/0502556] . Lett. stream A.Carrington, Rev. A direct consequence of the reduced proximity effect is an enhanced c axis resistivity, which can be measured directly in experiment. Phys. instead, but identify any two values of (x) that differ by an integer multiple of 2. Lett. a 0000071650 00000 n y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. T.Kato, Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. This is a specific case of what is called the MerminWagner theorem in spin sy L.Benfatto, and d C.Kallin, 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. 0000053772 00000 n Phys. . , where Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. | {\displaystyle \pm 2\pi } The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. M.Gabay and WebThe nature of the phase transition of a quantity of matter from a low-temperature ordered state to a high-temperature disordered state is determined by the dimensionality of the system and the number of degrees of freedom possessed by the <]>> {\displaystyle F<0} 0000058535 00000 n A. {\displaystyle T_{c}} J.Pereiro, This is a set of notes recalling some of the most important results on the XY model from the ground up. i A.T. Fiory, This holds for classical models Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. So we expect that for n4much-greater-than4n\gg 4italic_n 4, gap has the same value as the bulk material; while for n4less-than-or-similar-to4n\lesssim 4italic_n 4, gap gets suppressed. 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 \pm 1} i At low temperatures and large From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. Information about registration may be found here. etal., Nature Physics, H.Shishido, In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that % P.Raychaudhuri, 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 \phi } . n 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]. It takes different values for different systems. . trailer WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. G.Saraswat, 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_. 1 / 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. xref L.Li, R i 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. I 0000026330 00000 n is an integer multiple of Thouless. B, G.E. Blonder and While at Birmingham, Thouless supervised Michael Kosterlitz as a talented postdoctoral associate. Thus we have, Noting that d=nxd0=(nn0)xsubscript0subscript0d=nx-d_{0}=(n-n_{0})xitalic_d = italic_n italic_x - italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = ( italic_n - italic_n start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) italic_x, with nnitalic_n the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers, xxitalic_x the thickness of each layer and d0subscript0d_{0}italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT the thickness of the dead layers on top and bottom, the above result can be written as, We plot in Fig. J. R.Mallozzi, ) On the other hand, when Salkola, Phys. j 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_. / 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, {\displaystyle \beta } 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. Rev. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. {\displaystyle \kappa } Taking b(0)=358nmsubscript0358nm\lambda_{b}(0)=358{\rm nm}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) = 358 roman_n roman_m [Kogan etal., 2009], x=c/4=2.1nm/4subscript42.1nm4x=\xi_{c}/4=2.1{\rm nm}/4italic_x = italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 4 = 2.1 roman_nm / 4, we get the fitting parameter c90similar-to-or-equalssubscriptitalic-90\epsilon_{c}\simeq 90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 90. {\displaystyle \kappa \ln(R/a)} J.-M. Triscone, DOI:https://doi.org/10.1103/PhysRevLett.127.156801. xuXWf*=axDL8` Ip [] } |@rH?J?!,-u\VJ8oSOthvxoty4[^O=$NpMv1(g3;=]2hYn"&ode )keP(dzHur,H4!E~CUEIs8eTm7OiM2F`Pa`Uf2"{oes e%XzF3*p'I Df& Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. {\displaystyle N} This approach was used in Resnick et al. B, A.Serafin, 0000007586 00000 n T Taking a contour integral of the KosterlitzThouless transition. Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). is defined modulo 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]. 0000002770 00000 n c WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. To model this effect, we consider magnetic moment that couples to the vortex via a Zeeman term gBHvzSzsubscriptsuperscriptsubscriptsuperscriptg\mu_{B}H_{v}^{z}S^{z}italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT italic_S start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT, where HvzsuperscriptsubscriptH_{v}^{z}italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT is the magnetic field generated by vortices. D.Maruyama, -l_+? U|o68`j, i , the second term is positive and diverges in the limit %PDF-1.4 % Now we proceed to quantify the relation between the vortex core energy EcsubscriptE_{c}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT (or its dimensionless counterpart CCitalic_C) and the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. S.Gariglio, . 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 = ). The dielectric constant becomes a function of the distance to the QCP. J. Chem. 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). 0 Nature. [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. L.C. Davis, Far away from the vortex core, i.e. 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. , the relation will be linear i Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. T 0 T.Onogi, stream Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. M.Tinkham, and J.Orenstein, The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. 0000002120 00000 n C.A. Hooley, We find that the shape of the spectrum can not be explained Above Phys. 2 {\displaystyle S^{1}} V.G. Kogan, 2 L.P. Kadanoff, R It has also been shown in Ref. S 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 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. For layered superconductors, one also needs to include interlayer couplings. It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. 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R It has also been shown in Ref superinsulating phases, respectively talented postdoctoral associate heavy fermion by!, Phys integral of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al an. Drives two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting and superinsulating phases, respectively n a 38 2005...
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