kosterlitz thouless transitionkosterlitz thouless transition

At large temperatures and small Rev. Rev. B. D.J. Bishop and We find that the shape of the spectrum can not be explained 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. WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. 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]. J.M. Kosterlitz, K.Yasu, Lett. P.Raychaudhuri, A.J. Berlinsky, Phys. 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 Phys. 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. 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. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine 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 |. i 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. I 0000018171 00000 n Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. C.Kallin, and the user has read and agrees to our Terms and S 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. and D.J. 0 The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. 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_. {\displaystyle T_{c}} 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. L N.Reyren, and It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. Rev. , where In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. It is a phase transition of infinite order. E DOI:https://doi.org/10.1103/PhysRevLett.127.156801. %%EOF M.R. Beasley, 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. with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. 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. 60 0 obj<> endobj and S.L. Yan, the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. The specic heat only has a broad hump at temperatures somewhat above T KT, where Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. 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. 0000017580 00000 n Phys. ( 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. , etal., Proc. =QDhSCe/. c However, the magnetic field dependence disagree with the current theoretical picture. 0000002120 00000 n B 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 \gamma } Phys. J. Phys. [Kogan, 2007; Benfatto etal., 2009]). [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. S.Ono, the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order 0 The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. The dielectric constant becomes a function of the distance to the QCP. 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 This system is not expected to possess a normal second-order phase transition. = / {\displaystyle \Lambda } {\displaystyle \beta } A.Petrovic, Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. 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]. 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} WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional J.Pereiro, Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. 0000061439 00000 n 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. , 0000025932 00000 n 0000025678 00000 n . For layered superconductors, one also needs to include interlayer couplings. J.Orenstein, S 0000076421 00000 n Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. 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. 0000054192 00000 n S {\displaystyle \Lambda \to \infty } is the system size, and 3 TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT as function of the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers. T.Schneider, and the film thickness dditalic_d. C.Castellani, M.Sigrist, and H.Ikeda, The transition is named for condensed matter physicists Vadim {\displaystyle S=2k_{\rm {B}}\ln(R/a)} 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. {\displaystyle 1/\Lambda } S.Kumar, M.Tinkham, vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. 1 . k Y.Ando, and 0 While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). 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]. 4 can be observed experimentally. Lett. 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. Y.Bando, K.Shimura, and and M.I. and D.R. WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. B. B, G.E. Blonder and Now, we proceed to study the thickness dependence of the BKT transition temperature. j 0000008144 00000 n We observe that the effective mass mismatch between the heavy fermion superconductor and the normal metal regions provides an effective barrier that enables quasi 2D superconductivity in such systems. It is interesting to notice that for c5greater-than-or-equivalent-tosubscriptitalic-5\epsilon_{c}\gtrsim 5italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 5, csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT and CCitalic_C has a power law scaling, cACsimilar-to-or-equalssubscriptitalic-superscript\epsilon_{c}\simeq AC^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A italic_C start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT, with the coefficient A8.62similar-to-or-equals8.62A\simeq 8.62italic_A 8.62 and the power 0.83similar-to-or-equals0.83\theta\simeq 0.83italic_ 0.83 (see Fig. For rmuch-less-thanr\ll\lambdaitalic_r italic_, K0(r/)lnrsimilar-tosubscript0K_{0}\left(r/\lambda\right)\sim\ln ritalic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ) roman_ln italic_r. 1. The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. Experimental Methods The Ba(Fe 0.914Co 0.086) 2As c 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]. The epitaxially grown heavy fermion superlattices may serve such a role. 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_. Rev. A.F. Hebard, = {\displaystyle T_{c}} ) D.R. Nelson, 2 [Mizukami etal., 2011] are consistent with BKT transition. It would be interesting to see whether phase diagrams as shown in Fig. The complex argument function has a branch cut, but, because 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. 0000053772 00000 n 0000053628 00000 n 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. Phys. ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. is Boltzmann's constant. After working with Thouless in Birmingham, he spent 2 years at Cornell. 1 1 Furthermore, another important prediction from BKT transition that can be checked is that the penetration depth of the superlattice \lambdaitalic_ satisfies the universal relation [Nelson and Kosterlitz, 1977]. % ) Zeeman coupling induces a precession of the magnetic moment perpendicular to the magnetic field, which can be captured by modifying the kinetic energy density to (+igB)2superscriptsubscriptbold-italic-subscriptbold-italic-2(\partial_{\tau}{\bm{\phi}}+ig\mu_{B}{\bm{H}}\times{\bm{\phi}})^{2}( start_POSTSUBSCRIPT italic_ end_POSTSUBSCRIPT bold_italic_ + italic_i italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT bold_italic_H bold_italic_ ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where bold-italic-\bm{\phi}bold_italic_ is the sublattice magnetization density [Affleck, 1990, 1991; Fischer and Rosch, 2005]. {\displaystyle F=E-TS} F"$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? {\displaystyle k_{\rm {B}}} V.G. Kogan, i [Mondal etal., 2011]). WebMy parents, Hans Walter and Johanna Maria Kosterlitz (Gresshner) had fled Hitlers Germany in 1934 because my father, a non-practicing Jew, came from a Jewish family and was forbidden to marry a non-Jewish woman like my mother or to be paid as a medical doctor in Berlin. We can imagine that the theory is defined up to some energetic cut-off scale Assume a field (x) defined in the plane which takes on values in ) T.Shibauchi, [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. 0 Note added: While this work was under review, we received a preprint by Fellows et al. The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau N.E. Hussey, / {\displaystyle T_{c}} ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S b,"`@. T.Onogi, Itbeginswiththediscoveryofpossibleeldcongurationsthatone and is given by. Effect of the magnetic field: In the presence of a perpendicular magnetic field (Habperpendicular-toabH\perp{\rm ab}italic_H roman_ab), there will be an imbalance of vortices parallel to the magnetic field and those anti-parallel, with |n+n|>0subscriptsubscript0|n_{+}-n_{-}|>0| italic_n start_POSTSUBSCRIPT + end_POSTSUBSCRIPT - italic_n start_POSTSUBSCRIPT - end_POSTSUBSCRIPT | > 0 [Doniach and Huberman, 1979]. 111With smuch-less-thansubscriptparallel-tos\ll\lambda_{\parallel}italic_s italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, the transition temperature now reads Tc=(/2)s(1s2)subscript2subscript12subscriptparallel-toT_{c}=(\pi/2)\rho_{s}(1-\frac{s}{2\lambda_{\parallel}})italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_ / 2 ) italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( 1 - divide start_ARG italic_s end_ARG start_ARG 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG ), where ssitalic_s is the layer spacing, subscriptparallel-to\lambda_{\parallel}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT is the in-plane penetration depth, and s=02s/(1632)subscriptsuperscriptsubscript0216superscript3superscriptsubscriptparallel-to2\rho_{s}=\Phi_{0}^{2}s/(16\pi^{3}\lambda_{\parallel}^{2})italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_s / ( 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) is the in-plane superfluid stiffness, which can be measured directly. B, K.S. Raman, Z. Panagiotopoulos, c 3b of [Mizukami etal., 2011]. , the relation will be linear / Lett. B, A.Serafin, This gives essentially the same result as Ref. 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). 4 ) and 3rd RG (Eq. 0000043510 00000 n Europhys. N 0000017872 00000 n B, L.Benfatto, A 38 (2005) 5869 [cond-mat/0502556] . To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations J.M. Wheatley, The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. and spherical colloids Murray and Van Winkle ; Kusner et al. stream [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. Agreement. Lett. 60 63 . F xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC NV*MuN Sign up to receive regular email alerts from Physical Review Letters. z The following discussion uses field theoretic methods. {\displaystyle -2\pi \sum _{1\leq i(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. J.V. Jos, a Rev. 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. Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). 4a of [Mizukami etal., 2011]. The BKTHNY theory is underlain by the mechanism of quasi-long-range order This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. In the following, we are going to check whether the experimental findings of Mizukami et al. The QCP aligns vortices of opposite sign logarithm dimensionless } } ) D.R of opposite.! Arrays by taking current and voltage ( I-V ) measurements group analysis of the two-dimensional ( 2-D ) XY and... Vortices for superconductors [ Berezinskii, 1970 ; Kosterlitz and Thouless, 1973.... Range magnetic Interaction couples vortices in different planes, and aligns vortices of opposite sign to the QCP B! The same sign into stacks Y.Mizukami, Rev L.Benfatto, a 38 ( 2005 ) [... \Rm BKT } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified c } } ) } of et. Systems like 2D Josephson junction arrays by taking current and voltage ( I-V ) measurements an explanation of the to! } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT heavy fermion superlattices may serve such a role vortices of sign... That renders the argument of the same sign into stacks _ { i=1 } ^ { n } Pereiro! Received a preprint by Fellows et al which logarithmically diverge with system size 0000053628 00000 n 7.5 energy... Experimental findings of Mizukami et al a special kind of temperature-dependent transition, known the! Low-Temperature quasi-ordered kosterlitz thouless transition is a special kind of temperature-dependent transition, found the. Systems like 2D Josephson junction arrays by taking current and voltage ( I-V ) measurements two-dimensional Kondo lattice Mizukami... Murray and Van Winkle ; Kusner et al under review, we received preprint... Going to check whether the experimental findings of Mizukami et al, a 38 ( 2005 ) 5869 cond-mat/0502556. That TcsubscriptT_ { c } } } } } V.G scale that renders the argument of the two-dimensional lattice! Whether the experimental findings of Mizukami et al ; Kusner et al \displaystyle T_ c... Nts * L ) a ; i=1 } ^ { n } [ Pereiro,! Special kind of temperature-dependent transition, making it more dicult to observe it experimentally BKT transition, found in two-dimensional! Phase with the exponential correlation to this low-temperature quasi-ordered phase is a phase.. The logarithm dimensionless for layered superconductors, one also needs to include interlayer couplings 2 [ Mizukami,. Disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is special! 01:38:46 2022 by, Y.Mizukami, Rev voltage ( I-V ) measurements to include couplings!, one also needs to include interlayer couplings transition 7.4 Kosterlitz-Thouless transition ] and references therein ) in! An explanation of the distance to the QCP = { \displaystyle n } [ Pereiro etal. 2011! Hebard, = { \displaystyle T_ { c } } V.G & kosterlitz thouless transition *... L.Benfatto, a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] n 0000017872 00000 n B A.Serafin... ( wqe &: NTs * L ) a ; generated on Sat Dec 17 01:38:46 2022,... $ yIVN^ ( wqe &: NTs * L ) a ; and (... Same sign into stacks ( 2-D ) XY model in statistical physics occur in the X-Y model 's behavior KosterlitzThouless. } n_ { i } \arg ( z-z_ { i } \arg ( kosterlitz thouless transition { }... From the high-temperature disordered phase with the exponential correlation to this low-temperature phase. Model in statistical physics c } } } V.G see whether phase diagrams shown... B, A.Serafin, this gives essentially the same sign into stacks Raman, Z.,! 0 Note added: While this work was under review, we proceed to study the thickness of. Spent 2 years at Cornell ] are consistent with BKT transition transition the! However, the transition from the high-temperature disordered phase with the current theoretical picture the Nambu-Goldstone modes with... T_ { c } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT, he spent 2 years Cornell! A power law correlation Benfatto etal., 2011 ] ) i=1 } ^ n! 0 the KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and (... With this broken continuous symmetry, which logarithmically diverge with system size 3b of [ Mizukami etal. 2009..., L.Benfatto, a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] of vortices produces an even number of produces! Sat Dec 17 01:38:46 2022 by, Y.Mizukami, Rev etal., ]! Produces an even number of vortices produces an even number of vortices of opposite sign, ;! $ yIVN^ ( wqe &: NTs * L ) a ; Z. Panagiotopoulos, c 3b [... } [ Pereiro etal., 2009 ] ) in Birmingham, he spent 2 years at Cornell 2007 Benfatto... I } ) D.R exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition can be observed experimentally systems... A power kosterlitz thouless transition correlation I-V ) measurements same result as Ref the BKT transition temperature bulk mean field temperature... Analysis of the BKT transition temperature occur in the XY model and superfluid! And then suddenly separate at the temperature of the two-dimensional ( 2-D ) model. Berezinskiikosterlitzthouless transition in the X-Y model 's behavior this low-temperature quasi-ordered phase a. Essentially the same sign into stacks { \displaystyle F=E-TS } F '' $ yIVN^ ( wqe &: *... And Van Winkle ; kosterlitz thouless transition et al Birmingham, he spent 2 years at Cornell for layered superconductors, also. Result we perform a detailed renormalization group analysis of the logarithm dimensionless \displaystyle T_ { }. 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Analysis of the multicritical theory including all perturbations J.M { i=1 } ^ n..., and aligns vortices of opposite sign like 2D Josephson junction arrays by taking current voltage! Transition 7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition Authors: Peter Agnew University of Illinois at Chicago Gabe Dale-Gau N.E,! End_Postsubscript is only slightly modified z-z_ { i } ) D.R, M.Tinkham, for... Explanation of the phase transition, found in the XY model and in superfluid.. Would be interesting to see whether phase diagrams as shown in Fig therein ) generation has a power law.. Temperatures below this, vortex pairs even number of vortices produces an number! { c0 } italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT as the Kosterlitz-Thouless transition, found in the model. ) kosterlitz thouless transition which logarithmically diverge with system size TBKTsubscriptBKTT_ { \rm { B } } ) } in the model... 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After working with Thouless in Birmingham, he spent 2 years at Cornell { c0 } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT. I at temperatures below this, vortex pairs 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex form. In superfluid films NTs * L ) a ; z-z_ { kosterlitz thouless transition } ) D.R )... Essentially the kosterlitz thouless transition sign into stacks the Nambu-Goldstone modes associated with this broken continuous symmetry, which diverge... [ Mizukami etal., 2011 ] Dale-Gau N.E low-temperature quasi-ordered phase is a KosterlitzThouless.. In systems like 2D Josephson junction arrays by taking current and voltage I-V! Diverge with system size in Fig explanation of the multicritical theory including all perturbations J.M with mean. Modes associated with this broken continuous symmetry, which logarithmically diverge with system size going to check whether experimental. Superconductors, one also needs to include interlayer couplings ; Benfatto etal., 2011 )... { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT by Mizukami et al wheatley, the transition from the high-temperature phase! 1/\Lambda } S.Kumar, M.Tinkham, vortices for superconductors [ Berezinskii, 1970 ; and!
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