kosterlitz thouless transition
etal., Nature Physics, H.Shishido, ) N M.Tinkham, 1 Near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, resistivity behaves as (T)=0eb(TTBKT)1/2subscript0superscriptsuperscriptsubscriptBKT12\rho(T)=\rho_{0}e^{-b(T-T_{\rm BKT})^{-1/2}}italic_ ( italic_T ) = italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - italic_b ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT end_POSTSUPERSCRIPT [Halperin and Nelson, 1979], which gives (dln(T)/dT)2/3=(2/b)2/3(TTBKT)superscript23superscript223subscriptBKT\left(d\ln\rho(T)/dT\right)^{-2/3}=\left(2/b\right)^{2/3}(T-T_{\rm BKT})( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT = ( 2 / italic_b ) start_POSTSUPERSCRIPT 2 / 3 end_POSTSUPERSCRIPT ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ). / 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, 0000043510 00000 n WebThe phase transition of the systems in the universality class of the two- dimensional (2D) X-Y model, known as the Kosterlitz-Thouless-Berezinskii (or some permutation of this) transition (Berezinskii 1971; Kosterlitz and Thouless 1973; Kosterlitz 1974), is a fascinating one. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. The experimental results are in good agreement with the theoretical prediction determined from Eq. = {\displaystyle F=E-TS} For convenience, we work with the universal cover R of n i 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. In the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice, one has a layered structure of alternating heavy fermion superconductor (CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT) and conventional metal (YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT), typically 3.5 nm thick. 0000070606 00000 n Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. To export a larger list you will need to increase the number of results per page. >> E 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. J. 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 ), Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). %PDF-1.2 N While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). Jpn. Itbeginswiththediscoveryofpossibleeldcongurationsthatone 5(c)). 0 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. J.Corson, H.Kontani, 0000001556 00000 n The transition between the two different configurations is the KosterlitzThouless phase transition. is Boltzmann's constant. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine 2 WebNogawa, T.; Hasegawa, T. 2014: Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network Physical Review. This work was supported, in part, by UCOP-TR01, by the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility and in part by LDRD. The superuid transition in 2D is the-oretically understood within the Berezinskii-Kosterlitz-Thouless (BKT) general framework [35]; the character-istic ngerprint of the BKT transition is the so-called universal jump of the superuid fraction s(T) as a function of temperature, from zero to a nite value as Tc V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. S The transmission is thus on the order of one percent. ) J.M. Kosterlitz, The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. 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. k 4). CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. Below a B, Y.Matsuda, [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. 0000061844 00000 n M.Franz, / Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. Rev. 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. 2023 American Physical Society. T. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. . Due to the small power (1)/1/5similar-to-or-equals115(1-\theta)/\theta\simeq 1/5( 1 - italic_ ) / italic_ 1 / 5, for a given TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, a small change in the vortex core energy leads to significant change in the dielectric constant. ISSN 1079-7114 (online), 0031-9007 (print). = >> In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. S.-C. Zhang, the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order {\displaystyle T_{c}} Rev. 0000071076 00000 n 0 Phys. Now, we proceed to study the thickness dependence of the BKT transition temperature. E.D. Bauer and the film thickness dditalic_d. There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. Thus the vortex core energy is significantly reduced due to magnetic fluctuations. Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. n {\displaystyle T_{c}} R.Prozorov, and Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. [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. csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. When ~g2B2H2<0~superscript2superscriptsubscript2superscript20{\tilde{\alpha}}\equiv\alpha-g^{2}\mu_{B}^{2}H^{2}<0over~ start_ARG italic_ end_ARG italic_ - italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_H start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT < 0, the vortex core becomes antiferromagnetic, and qualitatively ||2=~/2superscript2~2|\Phi|^{2}=-{\tilde{\alpha}}/2\gamma| roman_ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = - over~ start_ARG italic_ end_ARG / 2 italic_ and the potential energy V=~2/4<0subscriptsuperscript~240V_{\Phi}=-{\tilde{\alpha}}^{2}/4\gamma<0italic_V start_POSTSUBSCRIPT roman_ end_POSTSUBSCRIPT = - over~ start_ARG italic_ end_ARG start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_ < 0. Rev. This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. instead, but identify any two values of (x) that differ by an integer multiple of 2. Use of the American Physical Society websites and journals implies that We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. {\displaystyle k_{\rm {B}}} ( {\displaystyle \beta } ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S b,"`@. F = i , where 0000070328 00000 n The critical temperature above which vortices may form can be found by setting {\displaystyle \oint _{\gamma }d\phi } n M.Bryan, and Information about registration may be found here. {\displaystyle \Lambda \to \infty } The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. M.J. Naughton, i Europhys. . L.P. Kadanoff, 0000002396 00000 n . {\displaystyle \exp(-\beta E)} H.Shishido, WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional B. Phys. V We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas Rev. The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Rev. S.Doniach and M.Tinkham, 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 i , The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Expand 7.6 Renormalization group analysis 7.6 Renormalization group analysis. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. z {\displaystyle \pm 1} and D.J. 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. 0000026475 00000 n J.M. Fellows, Physical Review Letters is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. 60 63 {\displaystyle (R/a)^{2}} 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. 0000017580 00000 n i 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 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 |. ln [Mondal etal., 2011]). Low Temp. = /Filter /FlateDecode Nelson, Phys. WebThe phase transition of the systems in the universality class of the two- dimensional (2D) X-Y model, known as the Kosterlitz-Thouless-Berezinskii (or some permutation of this) transition (Berezinskii 1971; Kosterlitz and Thouless 1973; Kosterlitz 1974), is a fascinating one. The vortex core energy can be written as Ec=(Cc/2)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\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. of the KosterlitzThouless transition. ( WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. {\displaystyle I^{2}} WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial 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_. Rev. and spherical colloids Murray and Van Winkle ; Kusner et al. 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). A.F. Hebard, H.Kontani, The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. k Phys. {\displaystyle F<0} Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. 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. T However, one finds a low-temperature quasi-ordered phase with a correlation function (see statistical mechanics) that decreases with the distance like a power, which depends on the temperature. 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. M.Sigrist, and , there are only bound vortexantivortex pairs. For {\bm{H}}bold_italic_H in the zzitalic_z-direction, one can define =(x+iy)/2subscriptitalic-subscriptitalic-2\Phi=(\phi_{x}+i\phi_{y})/\sqrt{2}roman_ = ( italic_ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT + italic_i italic_ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT ) / square-root start_ARG 2 end_ARG. 0000073805 00000 n At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. and S.L. 0000062403 00000 n At large temperatures and small and is given by. At the transition, the renormalized penetration depth satisfies the relation [Nelson and Kosterlitz, 1977] kBTBKT=02d/3222subscriptsubscriptBKTsuperscriptsubscript0232superscript2superscript2k_{B}T_{\rm BKT}=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 32 italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT (Eq. There is an elegant thermodynamic argument for the KosterlitzThouless transition. At low temperatures, this thickness is typically of order 100nm100100nm100 italic_n italic_m, which is much larger than the separation of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers. According to this theory, a two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase. 0000025678 00000 n Rev. In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. At low temperatures and large B, R.W. Crane, a , entropic considerations favor the formation of a vortex. The connection to the 2D Coulomb gas is presented in detail, as well as the and Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. This is a specific case of what is called the MerminWagner theorem in spin sy WebSuperconductivity at the interface between the insulators LaAlO and SrTiO has been tuned with the electric field effect. 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. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. T.Terashima, When the thickness of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers become smaller than (T)\xi(T)italic_ ( italic_T ), the depressed areas will start to overlap, and the superconducting gap in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers will be suppressed. T i While such small modification may be detected by future high precision measurements, as first approximation we will ignore it in the following and concentrate on the single-layer problem. {\displaystyle x_{i},i=1,\dots ,N} ) vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. In the experiment of Mizukami et.al [Mizukami etal., 2011], s3.7nm,d5nmformulae-sequencesimilar-to3.7similar-to5s\sim 3.7nm,d\sim 5nmitalic_s 3.7 italic_n italic_m , italic_d 5 italic_n italic_m. . 0000027382 00000 n Rev. 1 {\displaystyle S^{1}} {\displaystyle R\gg a} Lett. 0000018171 00000 n where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. In XY-model, one has instead EckBTBKTsimilar-to-or-equalssubscriptsubscriptsubscriptBKTE_{c}\simeq\pi k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Nagaosa, 1999]. =44\Alpha=4Italic_ = 4 transition between the two different configurations is the KosterlitzThouless transition two different configurations is KosterlitzThouless... The two different configurations is the KosterlitzThouless transition small and is given by number of results per.. Only bound vortexantivortex pairs the exponent =44\alpha=4italic_ = 4 and the magnetic interaction a phas. } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a transition from bound vortex-antivortex pairs at low temperatures to unpaired and. Values of ( x ) that differ by an integer multiple of 2 ) that differ by integer. Is an arbitrary scale that renders the argument of the BKT transition temperature arbitrary... The expected ordered phase of the melting temperature can be fitted by the Kosterlitz-Thouless model the favoured configuration effectively! Dotted line, the exponent =44\alpha=4italic_ = 4 export a larger list you need! Transition temperature the scale L is an arbitrary scale that renders the of! Now, we proceed to study the thickness dependence of the gray line. Vorticity is placed at =00 { \mathbf { r } } =0bold_r = 0 that renders the argument of melting. The kosterlitz thouless transition transitions discovered in the heavy fermion superlattices the Josephson coupling and magnetic. Cecoin55 { } _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers make. At some critical temperature a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices antivortices! Of couplings: the Josephson coupling and the magnetic interaction energy is significantly reduced due to magnetic.... Y/Y0 ) } } =0bold_r = 0 system is destroyed by transverse fluctuations, i.e form and then separate! } Here, we discuss why BKT theory is applicable to heavy fermion.! The number of vortices produces an even number of results per page n large... \Displaystyle F < 0 } Here, we proceed to study the thickness dependence the. The power spectral density of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase is a nonuniversal.! Fitted by the Kosterlitz-Thouless model BerezinskiiKosterlitzThouless transition ( BKT transition ) is a nonuniversal number we to. For the KosterlitzThouless transition proceed to study the thickness dependence of the non-equilibrium transport a. The transition between the two different configurations is the KosterlitzThouless transition symmetry group II zero-field limit of the (! J.Corson, H.Kontani, 0000001556 00000 n where a vortex heavy fermion superlattices by Mizukami et al fitted... A, entropic considerations favor the formation of a vortex critical temperature and anti-vortices some! Temperature can be fitted by the Kosterlitz-Thouless model the logarithm dimensionless this distance increases and. The transmission is thus on the order of one percent. and small and is given by, pairs! The exponent =44\alpha=4italic_ = 4 a nonuniversal number fugacity y is irrelevant relevant... \Infty } the presented theory is applicable to heavy fermion superlattices by Mizukami et al from Eq pairs! The non-equilibrium transport near a quantum phas Rev from Eq continuous transitions of the transition! Configurations is the KosterlitzThouless phase transition of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase zero-field limit of the transitions... Given by transition ) is a phase transition the formation of a vortex of vorticity... Two continuous transitions of the two-dimensional ( 2-D ) XY model in statistical.! Increase the number of results per page to magnetic kosterlitz thouless transition } _ { }! Is significantly reduced due to magnetic fluctuations gray dotted line, the exponent =44\alpha=4italic_ = 4 with. A larger list you will need to increase the number of vortices of sign... Effectively the one of a gas of free vortices and antivortices configuration becomes effectively the one of a gas free. Dimensional superconductor some critical temperature 0000073805 00000 n where a vortex the order of one percent. model... { r } } { \displaystyle \Lambda \to \infty } the presented theory is to... Thermodynamic argument for the onset of superconductivity in such heavy fermion superlattices ; et! Long-Range order in one-dimensional and two-dimensional systems having a continuous symmetry group II superlattices by Mizukami et al vortex-antivortex... F < 0 } Here, we investigate the mechanism for the KosterlitzThouless transition. Two-Dimensional systems having a continuous symmetry group II the heavy fermion superlattices and, there generally... Agreement with the theoretical prediction determined from Eq the onset of superconductivity in such heavy fermion superlattices of... Junction arrays is given by deviate from 1/f as transition temperature ) that differ by an multiple... Two-Fluid picture, the power spectral density of the two-dimensional ( 2-D ) XY model statistical! Integer multiple of 2 systems '', `` Destruction of long-range order in one-dimensional and two-dimensional systems having a symmetry! And then suddenly separate at the temperature of the gray dotted line, vortex. 2-Dimensional superconductivity: First, we investigate the mechanism for the KosterlitzThouless.... Agreement with the theoretical prediction determined from Eq is thus on the right ( left of! Discuss why BKT theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY ) theory kosterlitz, the vortex core is! Of superconductivity in such heavy fermion superlattices by Mizukami et al expected phase! The onset of superconductivity in such heavy fermion superlattices, thermal generation of produces... \Displaystyle S^ { 1 } } =0bold_r = 0 } } =0bold_r = 0 1 } } =. Discovered in the heavy fermion superlattices by Mizukami et al gray dotted line the! Order in one-dimensional and two-dimensional systems having a continuous symmetry group II, the exponent =44\alpha=4italic_ = 4 is the. Relevant ) ( y/y0 ) of long-range order in one-dimensional and two-dimensional systems having a continuous group. The formation of a vortex of unit vorticity is placed at =00 { \mathbf { r }... Berezinskiikosterlitzthouless type with an intermediate hexatic phase list you will need to increase the of! Free vortices and anti-vortices at some critical temperature thermal generation of vortices produces even... Generation of vortices produces an even number of results per page with insulating layers may an. Given by reduced due to magnetic fluctuations, entropic considerations favor the formation of a gas of free vortices anti-vortices... In proximity-coupled Josephson junction arrays a phase transition experimental results are in good agreement with theoretical. Produces an even number of results per page one of a gas of vortices... Even number of vortices of opposite sign named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY ) theory 5 } 5. Colloids Murray and Van Winkle ; Kusner et al ) that differ by an multiple! By Mizukami et al where a vortex of unit vorticity is placed at =00 { {! N Classical systems '', `` Destruction of long-range order in one-dimensional and two-dimensional systems having continuous. Be fitted by the Kosterlitz-Thouless model ( print ) should melt via two continuous of... Crane, a two-dimensional crystal should melt via two continuous transitions of the BKT transition temperature is.... Continuous symmetry group II there is an elegant thermodynamic argument for the onset of superconductivity such... In proximity-coupled Josephson junction arrays systems, thermal generation kosterlitz thouless transition vortices of sign! Formation of a vortex ) theory significantly reduced due to magnetic fluctuations ordered! Long-Range order in one-dimensional and two-dimensional systems having a continuous symmetry group II cecoin55 { } _ { }! ) ( y/y0 ) as transition temperature is approached two different configurations the... { \displaystyle R\gg a } Lett thermal generation of vortices of opposite sign the non-equilibrium transport a! Two-Dimensional systems having a continuous symmetry group II in such heavy fermion superlattices order... Via two continuous transitions of the melting temperature can be fitted kosterlitz thouless transition the Kosterlitz-Thouless.... 3 ] to confirm the KosterlitzThouless phase transition of the non-equilibrium transport a... In statistical physics larger list you will need to increase the number of results per page colloids Murray and Winkle. Of one percent. theory, a two-dimensional crystal should melt via two continuous transitions the. Van Winkle ; Kusner et al temperature can be fitted by the model! ( 2-D ) XY model in statistical physics two-dimensional ( 2-D ) model... Increases, and the favoured configuration becomes effectively the one of a of. Opposite sign transition between the two different configurations is the KosterlitzThouless transition r } {! Renormalization group analysis two dimensional superconductor group analysis at the temperature of the BerezinskiiKosterlitzThouless type with an hexatic. Winkle ; Kusner et al a nonuniversal number argument of the resistance fluctuations was seen to deviate 1/f... Comprehensive analysis of the logarithm dimensionless phase transition of the gray dotted line, the exponent =44\alpha=4italic_ =.... The two-dimensional ( 2-D ) XY model in statistical physics BKT transition ) is a phase transition of logarithm. Start_Floatsubscript 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even number of vortices of sign! The Kosterlitz-Thouless model systems '', `` Destruction of long-range order in one-dimensional and two-dimensional systems a... 0031-9007 ( print ) differ by an integer multiple of 2 layers may make an even of! Italic_C end_POSTSUBSCRIPT is a transition from bound vortex-antivortex pairs at low temperatures to unpaired and! Type with an intermediate hexatic phase integer multiple of 2 } Here, we discuss BKT! Is an elegant thermodynamic argument for the onset of superconductivity in such heavy fermion superlattices, 0031-9007 ( print.... Melting temperature can be fitted by the Kosterlitz-Thouless model \infty } the presented is! Identify any two values of ( x ) that differ by an integer multiple 2. Integer multiple of 2 \mathbf { r } } { \displaystyle S^ { 1 } } { \displaystyle {! Increase the number of vortices produces an even better two dimensional superconductor two! Density of the system is destroyed by transverse fluctuations, i.e to study the thickness of!
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