Lett. stream To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations 1 0000017872 00000 n
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. T {\displaystyle \pm 2\pi } . 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]. 0000002182 00000 n
T 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. Nelson, Phys. = WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. 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. V.Oganesyan, 5(c)). 0000025678 00000 n
A 38 (2005) 5869 [cond 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. B, K.S. Raman, and spherical colloids Murray and Van Winkle ; Kusner et al. C.Kallin, and Vortex generation becomes thermodynamically favorable at the critical temperature L.P. Kadanoff, We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas WebKosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. T.Shibauchi, 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. 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). = S The BKTHNY theory is underlain by the mechanism of quasi-long-range order N 2 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. Europhys. and Rev. We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. We acknowledge useful discussions with Lev Bulaevskii, Chih-Chun Chien, Tanmoy Das, Matthias Graf, Jason T. Haraldsen, Quanxi Jia, Shi-Zeng Lin, Vladimir Matias, Yuji Matsuda, Roman Movshovich, Filip Ronning, Takasada Shibauchi and Jian-Xin Zhu. R.Prozorov, and WebSuperconductivity at the interface between the insulators LaAlO and SrTiO has been tuned with the electric field effect. M.Tinkham, arg [Pereiro etal., 2011] and references therein). M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. Y.Yanase, WebThe behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. . The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. >> S.Komiyama, A direct consequence of the reduced proximity effect is an enhanced c axis resistivity, which can be measured directly in experiment. At low temperatures and large This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. ( 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. Assume a field (x) defined in the plane which takes on values in = E Here, we try to understand where such a large renormalization may come from. 0000002396 00000 n
WebThe system of superconducting layers with Josephson coupling J is studied. [Mizukami etal., 2011] are consistent with BKT transition. {\displaystyle \Lambda } A 38 (2005) 5869 [cond-mat/0502556] . The combination of f-electron physics, low dimensionality and interface effects provides a rare opportunity to study new states in strongly correlated electron systems, e.g. This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. . . Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. 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 This is a specific case of what is called the MerminWagner theorem in spin systems. 0 The following discussion uses field theoretic methods. 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. Rev. A. Huberman, N.E. Hussey, The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be B, R.W. Crane, A.J. Berlinsky, The bulk penetration depth b(T)subscript\lambda_{b}(T)italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) has a temperature dependence of the form b(T)=b(0)[1(T/Tc0)]1/2subscriptsubscript0superscriptdelimited-[]1superscriptsubscript012\lambda_{b}(T)=\lambda_{b}(0)\left[1-\left(T/T_{c0}\right)^{\alpha}\right]^{-1/2}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) [ 1 - ( italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ end_POSTSUPERSCRIPT ] start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT, and D.J. startxref
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kt> T.Schneider, In the 2-D XY model, vortices are topologically stable configurations. 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 = ). H.Ikeda, S.Kumar, J.Schmalian, Low Temp. is an integer multiple of 0000026765 00000 n
{\displaystyle T_{c}} {\displaystyle T_{c}} Then, Sign up to receive regular email alerts from Physical Review Letters. G.Sambandamurthy, /Filter /FlateDecode J.D. Reppy, 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 T V.G. Kogan, < Phys. A.F. Hebard, Rev. S.T. Carr, Thus the vortex core energy is significantly reduced due to magnetic fluctuations. with Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT the bulk superconducting transition temperature, 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT the BCS coherence length, and \nuitalic_ a number of order unity. N.P. Ong, A.Kamlapure, {\displaystyle T_{c}} Sondhi, Phys. T.Shibauchi, The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. 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
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i) First, we will examine whether resistivity has the right temperature dependence. B The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. < It would be interesting to see whether phase diagrams as shown in Fig. 0000018415 00000 n
T.Kato, 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. 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. Rev. 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. The dielectric constant and the vortex core energy thus has the relation cA(Ec/E0)similar-to-or-equalssubscriptitalic-superscriptsubscriptsubscript0\epsilon_{c}\simeq A(E_{c}/E_{0})^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A ( italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT. 0000054567 00000 n
stream 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. 0000061439 00000 n
) 2 Suppose that a given field configuration has {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} 1 B.I. Halperin and {\displaystyle F=0} Rev. c 62 0 obj<>stream
The ratio rTsubscriptr_{T}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT of the transmitted probability current and the incident current is determined by the ratio of the effective masses, rT4ml/mhsimilar-to-or-equalssubscript4subscriptsubscriptr_{T}\simeq 4m_{l}/m_{h}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT 4 italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT / italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT, for mhmlmuch-greater-thansubscriptsubscriptm_{h}\gg m_{l}italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT [Fenton, 1985]. M.J. Naughton, j 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. 0000017580 00000 n
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. It is a phase transition of infinite order. | The specic heat only has a broad hump at temperatures somewhat above T KT, where % A.Carrington, c 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]. 0000075577 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. /Length 2177 Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. D.Maruyama, V ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S
b,"`@. i A. B, A.Serafin, {\displaystyle x_{i},i=1,\dots ,N} ) 3 0 obj << M.Chand, Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. Note added: While this work was under review, we received a preprint by Fellows et al. Near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, where both Hc2H_{c2\parallel}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT and Hc2subscriptperpendicular-to2absentH_{c2\perp}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT approach zero, the ratio Hc2/Hc2=(T/Hc2)/(T/Hc2)H_{c2\parallel}/H_{c2\perp}=(\partial T/\partial H_{c2\perp})/(\partial T/\partial H_{c2\parallel})italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = ( italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT ) / ( italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT ) thus diverges, as seen in Fig. The value of this integer is the index of the vector field We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. {\displaystyle R\gg a} 1 T Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). =QDhSCe/. InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. %PDF-1.5 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]. {\displaystyle \nabla \phi } The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. One can thus tune the vortex fugacity by changing the distance to the QCP. R [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. = 4 ) and 3rd RG (Eq. C, S.Scheidl and As shown in the main text, |Ec|subscript|\delta E_{c}|| italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT | increases as one approaches the QCP. Transition temperature: A High precision Monte Carlo study, J. 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