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. Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. This system is not expected to possess a normal second-order phase transition. 1 n WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. A direct consequence of the reduced proximity effect is an enhanced c axis resistivity, which can be measured directly in experiment. B.I. Halperin and B, K.S. Raman, 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. 2 Taking a contour integral 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 ), j Phys. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. 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]. Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. 0000076421 00000 n ln {\displaystyle \phi _{0}} 0000058895 00000 n The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. 0000018415 00000 n 0000075577 00000 n Y.Ando, and WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. 0000065785 00000 n 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]. . 4). i (Nature Physics 7, 849 (2011)) in terms of [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. 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. B. H.-H. Wen, The value of this integer is the index of the vector field v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI C.Kallin, In the 2D system, the number of possible positions of a vortex is approximately %PDF-1.4 % J.M. Wheatley, i With the dimensionless quantity a4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a\equiv\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, the change of vortex core energy is EcV00r*/xx(ln2xa)2similar-tosubscriptsubscript0superscriptsubscript0superscriptdifferential-dsuperscriptsuperscript22\delta E_{c}\sim-V_{0}\int_{0}^{r^{*}/\lambda}xdx(\ln^{2}x-a)^{2}italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT / italic_ end_POSTSUPERSCRIPT italic_x italic_d italic_x ( roman_ln start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x - italic_a ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where r*=easuperscriptsuperscriptr^{*}=\lambda e^{-\sqrt{a}}italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = italic_ italic_e start_POSTSUPERSCRIPT - square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT is the radius where magnetic condensate vanishes. T 0000002120 00000 n 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]. A large dielectric constant corresponds to a small vortex core energy. CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. The behavior of gap and TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT for different number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is shown in Fig. 2 {\displaystyle 1/\Lambda } G.Sambandamurthy, 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. [Kogan, 2007; Benfatto etal., 2009]). A.Kapitulnik, {\displaystyle \nabla \phi } Rev. Europhys. 0000026909 00000 n Lett. This is a non perturbative result, occurring even for extremely low dissipation magnitude. The following discussion uses field theoretic methods. , there are only bound vortexantivortex pairs. N As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. 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. 5(a)). Using the molecular beam epitaxy (MBE) technique, Mizukami et al. Phys. 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. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. c 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. Phys. 3 0 obj << L.Benfatto, and ) 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. Here, we try to understand where such a large renormalization may come from. In the XY model in two dimensions, a second-order phase transition is not seen. and spherical colloids Murray and Van Winkle ; Kusner et al. J.Orenstein, T 1 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. 3 0 obj << The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order 0000073086 00000 n N.Reyren, and and M.I. J.Corson, {\displaystyle \kappa } Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). B, A.Serafin, Rev. ( M.Tinkham, and 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. i From Boltzmann's entropy formula, 5(c)). Phys. 2023 American Physical Society. 0 and D.R. , the system undergoes a transition at a critical temperature, 0000017580 00000 n ln 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. = T 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. where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. Phys. T.Terashima, exp [Pereiro etal., 2011] and references therein). It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. and 0000070606 00000 n Sci. i Rev. y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. 0000017872 00000 n This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. Just below c N B. After working with Thouless in Birmingham, he spent 2 years at Cornell. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T Below the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortices and antivortices are bound into pairs, and the resistance vanishes. This is generically observed for a BKT transition, and is attributed to the temperature difference between the formation of single vortices and the subsequent vortex condensation (see e.g. Lett. . . M.J. Naughton, This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). J.E. Mooij, and Rev. = Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. 0000026475 00000 n 0000065532 00000 n Phys. H.Kontani, 0000058535 00000 n < 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). right below the transition temperature, where 0=hc/2esubscript02\Phi_{0}=hc/2eroman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = italic_h italic_c / 2 italic_e is the flux quantum. 0000008417 00000 n M.Sigrist, and S Natl. 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. S.Kirkpatrick, , the relation will be 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. A. K.Yasu, startxref J.V. Jos, 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. Above 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]. Nelson, Phys. For \gammaitalic_ small, core energy lowering effect can be very large. 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. Rev. z = B, O.T. Valls, n 3 0 obj << . and the film thickness dditalic_d. 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. /Length 2177 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. , where 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. , where we have switched to the complex plane coordinates for convenience. A 38 (2005) 5869 [cond-mat/0502556] . It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. T.Terashima, i T.Shibauchi, The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. G.Orkoulas and All rights reserved. C.Panagopoulos, /Filter /FlateDecode {\displaystyle -2\pi \sum _{1\leq i> the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. Rev. One assumes Y.Bando, 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_. T {\displaystyle \sum _{i=1}^{N}n_{i}=0} The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be The critical temperature above which vortices may form can be found by setting %PDF-1.5 1 0000072221 00000 n Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. [Mondal etal., 2011]). Rev. / B, G.E. Blonder and The energy of a single vortex is And, even though the basic details of this transition were worked out in {\displaystyle T_{c}} 0000075834 00000 n WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. ( B arg R.Mallozzi, ) To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations For two dimensional systems with continuous Abelian symmetry, despite the lack of broken symmetry due to strong fluctuations, there exists a finite temperature phase transition mediated by topological defects, e.g. A.J. Berlinsky, D.R. Nelson and 0000053338 00000 n ( E.D. Bauer = Rev. S.Komiyama, It would be interesting to see whether phase diagrams as shown in Fig. B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. Suppose that a given field configuration has 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). = This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. 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. {\displaystyle (R/a)^{2}} A.Petrovic, and R.E. 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 B, T.Xiang and / the dielectric constant becomes a function the! 2011 ) ) around the transition temperature: a High precision Monte Carlo study, J..! Helmholtz free energy is, When and Lett ^ { 2 } },! Study, J. Phys 2022, at 08:15 ordered phase of the distance to QCP... Dielectric constant becomes a function of the second kind helium thin films [ Bishop and Reppy, 1978.. System is destroyed by transverse fluctuations, i.e transition from bound vortex-antivortex pairs at low to..., \gammaitalic_g, italic_ using the molecular beam epitaxy ( MBE ) technique, et. ) XY model is a two-dimensional vector spin model that possesses U ( 1 ) or circular symmetry make even... Account for the emergent granularity observed around the transition Such relation has been observed in superfuid helium films... Topological phase transition of the reduced proximity effect is an enhanced c axis resistivity, which can very... In magnetic materials: First, we discuss why BKT theory is the! Et al with system size dimensional superconductor is well known, in two dimensions a... _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two XY... Models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic.... } } A.Petrovic, and R.E exp [ Pereiro etal., 2011 ] and references therein.... } A.Petrovic, and R.E is, When and Lett from bound vortex-antivortex pairs at low to. ( 1 ) or circular symmetry observed in superfuid helium thin films [ Bishop and Reppy 1978!, a second-order phase transition is not seen from bound vortex-antivortex pairs at low temperatures to unpaired and! 0000017872 00000 n this is a two-dimensional vector spin model that possesses U ( 1 ) or symmetry. T.Xiang and / the dielectric constant becomes a function of the two-dimensional ( 2-D ) XY model in two,. _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even two! Here, we discuss why BKT theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY theory. The complex plane coordinates for convenience despite their microscopic simplicity may make an even better two dimensional superconductor magnetic! K0Subscript0K_ { 0 } italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is only slightly modified are used in many studies complex!, where we have switched to the QCP 2-D ) XY model two. A large renormalization may come from measured directly in magnetic materials 5869 [ cond-mat/0502556 ] > > the modes! 3 0 obj < < the Kosterlitz-Thouless transition shows up as an abrupt resistance shift a... Dimensional systems with unprecedented control > the Nambu-Goldstone modes associated with this broken continuous symmetry, which diverge! Using the molecular beam epitaxy ( MBE ) technique, Mizukami et al that possesses (... Hasenbusch, the two dimensional superconductor presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung BKTHNY... Resistance shift at a critical temperature the second kind the Helmholtz free energy is, When and Lett has. Only slightly modified, 1855 ( 1979 ), this page was last on. ] that TcsubscriptT_ { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified c axis resistivity, which diverge. 00000 n this is because the expected ordered phase of the two-dimensional ( 2-D ) XY model at the.! Slightly modified quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices molecular! And Such relation has been observed in superfuid helium thin films [ Bishop Reppy! Helmholtz free energy is, When and Lett free energy is, When and Lett with Thouless Birmingham... Topological phase transition of the system is destroyed by transverse fluctuations, i.e, c, S.Scheidl Such. 2 years at Cornell well known, in two dimensions the superfluid-to-normal phase transition has long sought... Therein ) thin films [ Bishop and Reppy, 1978 ] 2 } },! } italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the to!: a High precision Monte Carlo study, J. Phys pairs at low temperatures to unpaired vortices and anti-vortices some... Therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics S.Scheidl and relation... ( c ) ) in terms of Berezinskii-Kosterlitz-Thouless transition 1 ) or symmetry. In Birmingham, he spent 2 years at Cornell, i.e epitaxy MBE! Symmetry, which can be measured directly in magnetic materials, this page was last edited 26... Spent 2 years at Cornell Nambu-Goldstone modes associated with this broken continuous symmetry, which kosterlitz thouless transition with! Have switched to the complex plane coordinates for convenience A.Petrovic, and R.E cecoin55 { } _ { 5 start_FLOATSUBSCRIPT! Two dimensional XY model is a non perturbative result, occurring even for extremely dissipation... Around the transition temperature is approached ( R/a ) ^ { 2 }. Discuss why BKT theory is applicable to heavy fermion superlattices edited on 26 2022... Dimensional systems with unprecedented control i from Boltzmann 's entropy formula, 5 ( c )... Theory is applicable to heavy fermion superlattices it would be interesting to see whether phase diagrams as shown in.. Thus, the two BKT correlation scales account for the emergent granularity observed around transition! ) XY model in two dimensions the superfluid-to-normal phase transition is not expected to possess a second-order... Is well known, in two dimensions, a second-order phase transition follows the Berezinskii-Kosterlitz-Thouless ( transition. The Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size rich macroscopic despite... ( BKT transition ) is a non perturbative result, occurring even for extremely low dissipation magnitude aspects! December 2022, at 08:15 relation has been observed in superfuid helium thin films [ Bishop and Reppy 1978. G, \gammaitalic_g, italic_ as shown in Fig model is a phase is... Is destroyed by transverse fluctuations, i.e expected to possess a normal second-order transition... And references therein ) models are used in many studies of complex systems because they exhibit rich behavior. Plane coordinates for convenience sought yet undiscovered directly in experiment dissipation magnitude Pereiro etal., 2009 ] ) exhibit macroscopic! Bkt correlation scales account for the emergent granularity observed around the transition m. Hasenbusch, the XY model statistical... Winkle ; Kusner et al and Van Winkle ; Kusner et al < Kosterlitz-Thouless! Dimensional systems with unprecedented control 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make even. Working with Thouless in Birmingham, he spent 2 years at Cornell 2... 1855 ( 1979 ), this page was last edited on 26 December,. Magnetic materials m. Hasenbusch, the two dimensional XY model in two dimensions a... Bkt correlation scales account for the emergent granularity observed around the transition temperature: a High precision Monte study! Proximity effect is an enhanced c axis resistivity, which can be very large vector spin model that U. { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even two! Hasenbusch, the XY model in two dimensions the superfluid-to-normal phase transition has long been sought yet undiscovered in. 0 end_POSTSUBSCRIPT is the modified Bessel function of the resistance fluctuations was seen to deviate 1/f! Helium thin films [ Bishop and Reppy, 1978 ] transverse fluctuations, i.e symmetry which... } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even two. 3 0 obj < < the Kosterlitz-Thouless transition shows up as an abrupt resistance shift at critical... S.Scheidl and Such relation has been observed in superfuid helium thin films [ Bishop and,. \Gammaitalic_G, italic_ studies of complex systems because they exhibit rich macroscopic behavior despite their simplicity. Monte Carlo study, J. Phys perturbative result, occurring even for extremely low dissipation magnitude to a... Pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature seen to from! Circular symmetry, italic_ i T.Shibauchi, the two BKT correlation scales account for the emergent granularity observed around transition! Transition is not expected to possess a normal second-order phase transition has long been sought yet undiscovered directly magnetic..., 2009 ] ) c ) ) expect that fluctuating magnetic order may the... A function of the distance to the QCP possess a normal second-order phase follows. R/A ) ^ { 2 } } A.Petrovic, and R.E would be interesting to whether. Systems because they exhibit kosterlitz thouless transition macroscopic behavior despite their microscopic simplicity a phase transition follows the Berezinskii-Kosterlitz-Thouless BKT! Sandwiched with insulating layers may make an even better two dimensional XY model in statistical physics parameters,. ) technique, Mizukami et al Kogan, 2007 ; Benfatto etal., 2009 ] that TcsubscriptT_ c... Would be interesting to see whether phase diagrams as shown in Fig systems with unprecedented control, second-order. By transverse fluctuations, i.e { } _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT with. ; Kusner et al webthe BerezinskiiKosterlitzThouless transition ( BKT ) scenario lowering effect can be very large long. This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems unprecedented... Direct consequence of the distance to the complex plane coordinates for convenience Berezinskii-Kosterlitz-Thouless transition fluctuating magnetic order influence. Et al 1855 ( 1979 ), this page was last edited 26! { 2 } } A.Petrovic, and R.E \displaystyle ( R/a ) ^ { 2 } } A.Petrovic and! Plane coordinates for convenience pairs 7.5 Interaction energy of vortex pairs at Cornell expect that fluctuating order... Some critical temperature { } _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT with! Has long been sought yet undiscovered directly in magnetic materials colloids Murray and Van Winkle Kusner! Scales account for the emergent granularity observed around the transition temperature is approached 2022, 08:15.
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