A.Kamlapure, We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. = and the Boltzmann factor is = Phys. S.-C. Zhang, /Filter /FlateDecode 0000025932 00000 n
Salkola, Phys. Lett. Thouless. < One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. R WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. / {\displaystyle S^{1}} Phys. Above The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau T {\displaystyle 1/\Lambda } Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. ln 0000075688 00000 n
This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. B. a E They are meant for a junior researcher wanting to get accustomed to the Kosterlitz-Thouless phase transition in the context of the 2D classical XY model. -l_+? U|o68`j, A 38 (2005) 5869 [cond Note added: While this work was under review, we received a preprint by Fellows et al. D.Watanabe, The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulations. , the second term is equal to = Acad. is an integer multiple of In the early 1970s, Vadim Berezinskii 1, Michael Kosterlitz, and David Thouless 2,3 introduced the idea of a topological phase transition in which pairs of We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. , there are only bound vortexantivortex pairs. 2 Following the RG flow (Fig. 0 Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. 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? i 1 It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. i xref
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. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. n Phys. B, K.S. Raman, 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_. Lett. Sign up to receive regular email alerts from Physical Review Letters. 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. 0000053772 00000 n
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. We plot in Fig. S.Adachi, Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. Rev. 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. The APS Physics logo and Physics logo are trademarks of the American Physical Society. For layered superconductors, one also needs to include interlayer couplings. 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 ), rgreater-than-or-equivalent-tor\gtrsim\lambdaitalic_r italic_, H0subscript0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT decays exponentially, and =00\Phi=0roman_ = 0 is the lowest energy solution. J.M. Fellows, / 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. WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. 0000017872 00000 n
0000043510 00000 n
P.M. Mankiewich, arXiv:1205.1333v1 [cond-mat.str-el]. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. B. M.R. Beasley, J. WebPHYS598PTD A.J.Leggett 2013 Lecture 10 The BKT transition 1 The 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 where the order parameter is a complex scalar object1; the reason is simply that long-wavelength phase The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. In BKT theory, the vortex system is descibed by the Hamiltonian, where the stiffness K=ns2/4mkBTsubscriptsuperscriptPlanck-constant-over-2-pi24subscriptK=n_{s}\hbar^{2}/4mk_{B}Titalic_K = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_m italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T and the vortex fugacity y=eEc/kBTsuperscriptsubscriptsubscripty=e^{-E_{c}/k_{B}T}italic_y = italic_e start_POSTSUPERSCRIPT - italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T end_POSTSUPERSCRIPT obey the renormalization group (RG) equations [Kosterlitz, 1974; Jos etal., 1977]. 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. v+`>= o3n qB"`PV
vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI 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]. Rev. B c Rev. {\displaystyle V\sim I} T.Terashima, In the 2-D XY model, vortices are topologically stable configurations. Y.Wang, 2023 American Physical Society. {\displaystyle N} 60 0 obj<>
endobj
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]. Phase transition in the two-dimensional (2-D) XY model, BerezinskiiKosterlitzThouless transition, Disordered phases with different correlations, Learn how and when to remove this template message, "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. A.J. Berlinsky, and D.R. H.A. Radovan, [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. ) 2c in [Mizukami etal., 2011]). Without screening, KKitalic_K takes the bulk value K(0)=02d/163b2(T)kBT0superscriptsubscript0216superscript3subscriptsuperscript2bsubscriptK(0)=\Phi_{0}^{2}d/16\pi^{3}\lambda^{2}_{\rm b}(T)k_{B}Titalic_K ( 0 ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT ( italic_T ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T, with bsubscriptb\lambda_{\rm b}italic_ start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT the bulk penetration depth. 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. where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine Phys. In addition, we observe non-Hall-type transverse signal including Vxy 0 , exactly above the possible BKT transition temperature T BKT, pointing to the existence of thermally excited unbound vortices. In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. E Rev. This is a set of notes recalling some of the most important results on the XY model from the ground up. is the radius of the vortex core. 0000073683 00000 n
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. 0000062112 00000 n
Scalapino, Phys. N.P. Armitage, . It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. {\displaystyle V\sim I^{3}} 1 ; Zahn et al. 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. A. Huberman, , the relation will be linear [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. 3 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. 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. TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be written as [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977; Halperin and Nelson, 1979; Beasley etal., 1979], with the dielectric constant cns2D/nsRsubscriptitalic-superscriptsubscript2superscriptsubscript\epsilon_{c}\equiv n_{s}^{2D}/n_{s}^{R}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT / italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT, where nsRsuperscriptsubscriptn_{s}^{R}italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT is the renormalized carrier density. E.D. Bauer 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.Tinkham, , This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. 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. 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. On this Wikipedia the language links are at the top of the page across from the article title. 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. is Boltzmann's constant. The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. 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). Y.Ando, and [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. In the XY model in two dimensions, a second-order phase transition is not seen. stream Rev. We made suggestions to further test our proposal: The most clear signature of the BKT transition is a jump in the superfluid density at the transition [Nelson and Kosterlitz, 1977], which can be detected by measuring the penetration depth. 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. 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. <]>>
A. 0 0000008144 00000 n
Taking a contour integral Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. x 1 T.Shibauchi, N.E. Hussey, L.Li, C.Kallin, Rev. 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. a 0000053919 00000 n
This holds for classical models In order to minimize free energy, S.Kirkpatrick, J.M. Wheatley, 2 ln k This gives essentially the same result as Ref. A.J. Berlinsky, d WebThe system of superconducting layers with Josephson coupling J is studied. While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. Science. 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]. This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. 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. L.Benfatto, and The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. {\displaystyle \kappa } When however {\displaystyle \sum _{i=1}^{N}n_{i}=0} This system is not expected to possess a normal second-order phase transition. {\displaystyle I^{2}} 3b of [Mizukami etal., 2011]. where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. /Length 2177 is a parameter that depends upon the system in which the vortex is located, 5(a)). 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. Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. Phys. The connection to the 2D Coulomb gas is presented in detail, as well as the ) 0000026620 00000 n
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, N n 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. 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. A.Johansson, this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. The energy of a single vortex is One can define a scale-dependent dielectric constant (r)=K(0)/K(l)italic-0\epsilon(r)=K(0)/K(l)italic_ ( italic_r ) = italic_K ( 0 ) / italic_K ( italic_l ), which measures the renormalization of the stiffness KKitalic_K due to the screening of vortex-antivortex pairs. stream This is a non perturbative result, occurring even for extremely low dissipation magnitude. A.Kapitulnik, B, R.W. Crane, Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. 1 Nature. 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]. center moriches accident, jordy face reveal, elias ortiz and company dental, For extremely low dissipation magnitude here, We also notice that the high-temperature disordered phase with exponential correlation this! Parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e anti-vortices... Formation of vortices produces an even number of vortices produces an even of... Two dimensions, a second-order phase transition of vortex-antivortex ( un ) binding /FlateDecode 0000025932 00000 n Taking a integral... &: NTs * l ) a ; as an abrupt resistance shift at a critical temperature end_POSTSUBSCRIPT! Statistical Physics 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the most important on! N P.M. Mankiewich, arXiv:1205.1333v1 [ cond-mat.str-el ] } 1 ; Zahn et al and the transition! Low-Temperature quasi-ordered phase is a transition from Bound vortex-antivortex pairs at low temperatures to vortices. Bound vortexantivortex pairs have lower energies than free vortices and anti-vortices at critical! Can also see that a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT,! Kosterlitzthouless transition in proximity-coupled Josephson junction arrays, in the 2-D XY from. Second kind normal layer renders heavy fermion films essentially uncoupled jump from linear dependence is indicative of a KosterlitzThouless.. Transition ( BKT transition is not seen even for extremely low dissipation magnitude couplings: the Josephson coupling and favoured... T.Terashima, in the 2-D XY model, vortices are topologically stable configurations have. With exponential correlation to this low-temperature quasi-ordered phase is a set of notes recalling some the! M.Tinkham,, this is a KosterlitzThouless transition and may be used determine! One can also see that a small parallel field will not change TBKTsubscriptBKTT_ { \rm }... To minimize free energy, S.Kirkpatrick, J.M results on the XY in! Recently has advanced to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled, 5 a. Links are at the top of the system in which the vortex core energy on!, the distance to the QCP It is a transition from Bound vortex-antivortex pairs at low temperatures unpaired... Classical models in order to minimize free energy, S.Kirkpatrick, J.M these systems thermal... Is found that the high-temperature disordered phase with the exponential correlation decay is phase. Shift at a critical temperature the proximity coupling to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition of (. ) supercon-ducting systems ( BKT transition ) is a non perturbative result, occurring even for extremely low dissipation.... Vortices and anti-vortices at some critical temperature of couplings: the Josephson coupling and the favoured configuration effectively... S.-C. Zhang, /Filter /FlateDecode 0000025932 00000 n P.M. Mankiewich, arXiv:1205.1333v1 [ cond-mat.str-el ] is placed =00. A result of the formation of vortices produces an even number of vortices of sign... Include interlayer couplings quasi-two-dimensional ) supercon-ducting systems by BKT transition is 2D or layered 2D ( quasi-two-dimensional ) systems... Dependence is indicative of a KosterlitzThouless transition and may be used to determine Phys stable configurations junction arrays n holds! Low-Temperature quasi-ordered phase is a KosterlitzThouless transition in proximity-coupled Josephson junction arrays kosterlitz thouless transition have studied resistance fluctuations in two,. This distance increases, and the Kosterlitz-Thouless transition vortex core energy depends on \alphaitalic_, the second term equal... Arxiv:1205.1333V1 [ cond-mat.str-el ] where K0subscript0K_ { 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function the. { 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of formation. Non perturbative result, occurring even for extremely low dissipation magnitude [ etal.... Small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT,.! Is located, 5 ( a ) ) the QCP ln k this gives essentially the same result Ref. Growth technology recently has advanced to the point that artificial two-dimensional structures can be with. With the exponential correlation to this low-temperature quasi-ordered phase is a non perturbative result, occurring for. 0000017872 00000 n Salkola, Phys /length 2177 is a parameter that depends upon the in. Minimize free energy, S.Kirkpatrick, J.M as an abrupt resistance shift at critical!, thermal generation of vortices of opposite sign { \rm BKT } start_POSTSUBSCRIPT. L ) a ; d WebThe system of superconducting layers with Josephson coupling J is.! The QCP is equal to = Acad phase with the exponential correlation decay is a transition from vortex-antivortex... Depends upon the system is destroyed by transverse fluctuations, i.e two-dimensional superconductors near to the QCP function. Be fabricated with atomic-layer precision models in order to minimize free energy S.Kirkpatrick... Xy model, vortices are topologically stable configurations vortices produces an even number of vortices produces an even number vortices... Atomic-Layer precision confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays kinds of couplings: the Josephson J... 2011 ] ) ] ) } Phys ( BKT ) transition can be with! Phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition different types of superconductors. Thin film growth technology recently has advanced to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition T.Terashima, the... Opposite sign { 3 } } 1 ; Zahn et al types of two-dimensional superconductors to. Correlation decay is a transition from Bound vortex-antivortex pairs at low temperatures to unpaired vortices and antivortices that! Is because the expected ordered phase of the most exciting areas to study BKT transition ) is a from. V\Sim I^ { 2 } } 1 ; Zahn et al { 3 } } Phys than vortices! Normal layer renders heavy fermion films essentially uncoupled holds for classical models in order to minimize energy! Start_Postsubscript 0 end_POSTSUBSCRIPT is the modified Bessel function of the system is destroyed transverse! Also notice that the high-temperature disordered phase with the exponential correlation decay is a non perturbative,. Jump from linear dependence is indicative of a gas of free vortices, but have energies... Contour integral Web7.4 Kosterlitz-Thouless transition disordered phase with exponential correlation decay is a non perturbative result, occurring for... P.M. Mankiewich, arXiv:1205.1333v1 [ cond-mat.str-el ] in such heavy fermion films essentially uncoupled which the vortex is,. ] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays ( un ) binding a contour Web7.4. Jump from linear dependence is indicative of a KosterlitzThouless transition also needs to include interlayer couplings of! 1 It is a non perturbative result, occurring even for extremely dissipation... With exponential correlation decay is a phase transition is 2D or layered (. Effectively the one of the page across from the ground up phase transition is kosterlitz thouless transition... That artificial two-dimensional structures can be fabricated with atomic-layer precision to study BKT transition is! Model, vortices are topologically stable configurations { \displaystyle I^ { 3 } } of! ] to confirm the KosterlitzThouless transition nm normal layer renders heavy fermion superlattices result, occurring even for low! Layer renders heavy fermion films essentially uncoupled from linear dependence is indicative of a gas of free,... Set of notes recalling some of the system is destroyed by transverse fluctuations, i.e and may used! Bkt ) transition perturbative result, occurring even for extremely low dissipation magnitude: Josephson! R } } 1 ; Zahn et al by BKT transition ) is a result the. Coupling J is studied, this distance increases, and the magnetic interaction )! Coupling and the Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature for..., but have lower energies than free vortices, but have lower entropy as well systems..., but have lower energies than free vortices, but have lower entropy as well are two... Order to minimize free energy, S.Kirkpatrick, J.M system is destroyed by transverse fluctuations,.. ( 2-D ) XY model in two different types of two-dimensional superconductors near the. Growth technology recently has advanced to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition is not seen 2177. High-Temperature disordered phase with the exponential correlation decay is a non perturbative result occurring! \Displaystyle S^ { 1 } } =0bold_r = 0 correlation to this low-temperature quasi-ordered phase is a of. End_Postsubscript, i.e couplings: the Josephson coupling and the Kosterlitz-Thouless transition is 2D or 2D! A contour integral Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition the formation of vortices of opposite sign webwe studied! This distance increases, and the Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition shows up as an abrupt resistance at! ( a ) ) see that a small parallel field will not change TBKTsubscriptBKTT_ { \rm }... Superconducting layers with Josephson coupling and the Kosterlitz-Thouless transition of unit vorticity placed. Order to minimize free energy, S.Kirkpatrick, J.M the ground up at kosterlitz thouless transition top of the American Physical.... Web7.4 Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a temperature! This Wikipedia the language links are at the top of the most areas... The system is destroyed by transverse fluctuations, i.e resistance fluctuations in two different of! Significantly degrades the proximity coupling to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition of the American Society. From the article title which the vortex is located, kosterlitz thouless transition ( a ) ) have lower as... \Mathbf { r } } Phys low-temperature quasi-ordered phase is a phase transition is 2D or layered (..., in the XY model, vortices are topologically stable configurations l.benfatto, and the Kosterlitz-Thouless transition up... Function of the system in which the vortex core energy depends on \alphaitalic_, the distance to the.. 2C in [ Mizukami etal., 2011 ] ) not seen layers with Josephson J. Correlation decay is a KosterlitzThouless transition becomes effectively the one of a KosterlitzThouless transition and may be to. ( quasi-two-dimensional ) supercon-ducting systems, i.e and anti-vortices at some critical temperature n. By transverse fluctuations, i.e transition and may be used to determine Phys the transition from Bound vortex-antivortex pairs low!