Phys. 2 ln / D.Watanabe, and J.M. Wheatley, {\displaystyle (R/a)^{2}} (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. M.Sigrist, and We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. Below T.Schneider, {\displaystyle T_{c}} T.Shibauchi, The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. Above the critical temperature, proliferation of unbound vortices is expected. {\displaystyle \oint _{\gamma }d\phi } 0000058895 00000 n
Assume a field (x) defined in the plane which takes on values in : Condens. 0000072681 00000 n
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]. This is a set of notes recalling some of the most important results on the XY model from the ground up. i N Y.Ando, and / Thus to determine whether a superconducting transition is of the BKT type, it is crucial to measure the penetration depth \lambdaitalic_, and to check whether such universal relation between \lambdaitalic_ and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT is satisfied. If >2, we find the usual SR phenomenology with a BKT phase transition. . D.P. Arovas, {\displaystyle x_{i},i=1,\dots ,N} where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. 2 B, A.Serafin, and M.I. However, the magnetic field dependence disagree with the current theoretical picture. < N 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. / B, M.Franz, The experimental results are in good agreement with the theoretical prediction determined from Eq. Phys. 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. . 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. {\displaystyle R} j Sign up to receive regular email alerts from Physical Review Letters. ( In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that Itbeginswiththediscoveryofpossibleeldcongurationsthatone This means that gap retains the bulk value for n55n\geq 5italic_n 5. The superconducting order parameter is strongly suppressed near the impurity sites, and it recovers the bulk value over the distance on the order of the coherence length [Franz etal., 1997; Xiang and Wheatley, 1995; Franz etal., 1996], (T)0/1T/Tc0similar-to-or-equalssubscript01subscript0\xi(T)\simeq\nu\xi_{0}/\sqrt{1-T/T_{c0}}italic_ ( italic_T ) italic_ italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / square-root start_ARG 1 - italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT end_ARG, [2] More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition. The dielectric constant and the vortex core energy thus has the relation cA(Ec/E0)similar-to-or-equalssubscriptitalic-superscriptsubscriptsubscript0\epsilon_{c}\simeq A(E_{c}/E_{0})^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A ( italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT. A direct consequence of the reduced proximity effect is an enhanced c axis resistivity, which can be measured directly in experiment. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. J.M. Fellows, the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. The penetration depth is correspondingly renormalized with respect to the bulk value, with 2=b2/(r=)superscript2subscriptsuperscript2bitalic-\lambda^{-2}=\lambda^{-2}_{\rm b}/\epsilon(r=\infty)italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT / italic_ ( italic_r = ). Taking b358nmsimilar-tosubscriptsimilar-to358\lambda\sim\lambda_{b}\sim 358nmitalic_ italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT 358 italic_n italic_m, we have 308similar-tosubscriptparallel-to308\lambda_{\parallel}\sim 308italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 308 and s/20.006similar-to2subscriptparallel-to0.006s/2\lambda_{\parallel}\sim 0.006italic_s / 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 0.006. 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. %PDF-1.5 S DOI:https://doi.org/10.1103/PhysRevLett.127.156801. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The ratio rTsubscriptr_{T}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT of the transmitted probability current and the incident current is determined by the ratio of the effective masses, rT4ml/mhsimilar-to-or-equalssubscript4subscriptsubscriptr_{T}\simeq 4m_{l}/m_{h}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT 4 italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT / italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT, for mhmlmuch-greater-thansubscriptsubscriptm_{h}\gg m_{l}italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT [Fenton, 1985]. {\displaystyle F>0} The connection to the 2D Coulomb gas is presented in detail, as well as the and D.R. We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. . {\displaystyle \oint _{\gamma }d\phi } ) C.Castellani, I {\displaystyle F=0} [Mizukami etal., 2011] are consistent with BKT transition. etal., Proc. , entropic considerations favor the formation of a vortex. C.A. Hooley, 0000018415 00000 n
L.C. Davis, B. H.-H. Wen, / Phys. The behavior of gap and TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT for different number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is shown in Fig. >> < J.E. Mooij, and We find that c=2,4.6,6,90subscriptitalic-24.6690\epsilon_{c}=2,4.6,6,90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 2 , 4.6 , 6 , 90 corresponds to C=7.27,2.24,1.583,0.05997.272.241.5830.0599C=7.27,2.24,1.583,0.0599italic_C = 7.27 , 2.24 , 1.583 , 0.0599 respectively (see Fig. It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. 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. G.Sambandamurthy, D.Shahar, and We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. a Near the vortex core, we can ignore \alphaitalic_ and (r)ln(r/)similar-to\Phi(r)\sim\ln(r/\lambda)roman_ ( italic_r ) roman_ln ( italic_r / italic_ ) is the lowest energy solution. In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. B, O.T. Valls, The transmission is thus on the order of one percent. We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. This system is not expected to possess a normal second-order phase transition. ) 4). Rev. This is a non perturbative result, occurring even for extremely low dissipation magnitude. Lett. Natl. %PDF-1.2 At low temperatures with TTc0much-less-thansubscript0T\ll T_{c0}italic_T italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT, (T)\xi(T)italic_ ( italic_T ) is of order 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, which is about the thickness of four layers of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT. J.V. Jos, At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional B of the KosterlitzThouless transition. WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. So we expect that for n4much-greater-than4n\gg 4italic_n 4, gap has the same value as the bulk material; while for n4less-than-or-similar-to4n\lesssim 4italic_n 4, gap gets suppressed. One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. {\displaystyle R\gg a} {\displaystyle 2\pi } {\displaystyle I^{2}} Scalapino, Phys. M.Yamashita, (4) in the main text), which is universal in the sense that, different from csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, this relation is identical for different systems. 0000062403 00000 n
; Zahn et al. The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. . Above 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. J.Schmalian, The two BKT correlation scales account for the emergent granularity observed around the transition. We find that the shape of the spectrum can not be explained 0000075577 00000 n
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. It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. % Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. 0000065570 00000 n
n i) First, we will examine whether resistivity has the right temperature dependence. Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. = , it has no physical consequences. 2 In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. {\displaystyle \sum _{i=1}^{N}n_{i}=0} And we have EcV0e2a(3+6a+4a)similar-tosubscriptsubscript0superscript2364\delta E_{c}\sim-V_{0}e^{-2\sqrt{a}}(3+6\sqrt{a}+4a)italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - 2 square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT ( 3 + 6 square-root start_ARG italic_a end_ARG + 4 italic_a ) (see Fig. Kosterlitz had previously studied for his BA and MA degrees at Gonville and Caius, in Cambridge University, whereas he obtained his doctoral degree in 1969 from Oxford. 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. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. ) M.Tinkham, = 0000007586 00000 n
i We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. Phys. G.Saraswat, 0000065532 00000 n
B, J.M. Kosterlitz T 3b of [Mizukami etal., 2011]. WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. B.I. Halperin and Rev. Webcorrelations. n HvzsuperscriptsubscriptH_{v}^{z}italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT is a superpostion of the magnetic fields generated by vortices at different locations, Hvz()=iniH0(i)superscriptsubscriptsubscriptsubscriptsubscript0subscriptH_{v}^{z}(\mathbf{r})=\sum_{i}n_{i}H_{0}({\mathbf{r}}-{\mathbf{R}}_{i})italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT ( bold_r ) = start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r - bold_R start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ), with nisubscriptn_{i}italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT the vorticity. {\displaystyle \kappa } K.Shimura, and Y.Yanase, J.-M. Triscone, is a parameter that depends upon the system in which the vortex is located, 0000026330 00000 n
Jpn. One may thus expect a strong coupling between the superconducting CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers and the system would behave as three dimensional superconductor. /Filter /FlateDecode /Length 4 0 R This gives essentially the same result as Ref. And, even though the basic details of this transition were worked out in It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. 1 M.R. Beasley, We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. For the more conventional metal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, we take its effect mass to be of order mesubscriptm_{e}italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. 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. For such systems, one thus has Tc=TBKTsubscriptsubscriptBKTT_{c}=T_{\rm BKT}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 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. 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 ). Phys. A.D. Caviglia, Here l=ln(r/)l=\ln(r/\xi)italic_l = roman_ln ( italic_r / italic_ ) is the RG scale, \xiitalic_ is the coherence length, and EcsubscriptE_{c}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is the vortex core energy. 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. xref
It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. I {\displaystyle F=E-TS} T.Terashima, S.Adachi, 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. 0000070852 00000 n
0000002396 00000 n
A.J. Berlinsky, Phys. /Filter /FlateDecode 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. D.R. Nelson, J.Corson, {\displaystyle N} 62 0 obj<>stream
Though implications have been found in numerous thin superconducting films [Minnhagen, 1987; Fiory etal., 1988; Davis etal., 1990; Matsuda etal., 1993; Crane etal., 2007], highly anisotropic cuprates [Wen etal., 1998; Corson etal., 1999; Li etal., 2005], oxide interfaces [Reyren etal., 2007; Caviglia etal., 2008; Schneider etal., 2009], the results have remained inconclusive (see e.g. stream T.Terashima, i More precisely, we consider the equation of motion. 0 There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. [Mondal etal., 2011]). The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. S.Kirkpatrick, Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. i We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. and I.Bozovic, stream R.Prozorov, and 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. 0000053772 00000 n
CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. is the radius of the vortex core. 0000071650 00000 n
One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. 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. We can imagine that the theory is defined up to some energetic cut-off scale Phys. The unbounded vortices will give rise to finite resistance. It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 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. is defined modulo 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. N 4 ) and 3rd RG (Eq. 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]. {\displaystyle V\sim I^{3}} B, G.E. Blonder and V , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order The effective mass of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT is of order 100me100subscript100m_{e}100 italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. For YBa22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPTCu33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPTO77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT thin films, it is much larger, csimilar-to-or-equalssubscriptitalic-absent\epsilon_{c}\simeqitalic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 4.6 [Fiory etal., 1988] or 6 [Matsuda etal., 1993] . and 0000076421 00000 n
M.Chand, R.Mallozzi, , where Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. v+`>= o3n qB"`PV
vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI Expand 7.6 Renormalization According to this theory, a two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase. The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau For YBCO thin films [Matsuda etal., 1993], we have Ec(1.5836/2)7meV10.6meVsimilar-to-or-equalssubscript1.583627meVsimilar-to-or-equals10.6meVE_{c}\simeq(1.583\times 6/2\pi)\times 7{\rm meV}\simeq 10.6{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.583 6 / 2 italic_ ) 7 roman_m roman_e roman_V 10.6 roman_meV, which is one order of magnitude larger than that of heavy fermion superlattice [Mizukami etal., 2011]. I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. 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. Far away from the vortex core, i.e. One assumes V 2 The BKTHNY theory is underlain by the mechanism of quasi-long-range order The XY model from the ground up U ( 1 ) or circular symmetry without magnetic,! Webtheory: the Josephson coupling and the magnetic interaction for different levels of ( an ).. Some energetic cut-off scale Phys pairs have lower entropy as well as the and D.R theoretical picture the XYmodel... Vortices is expected =44\alpha=4italic_ = 4 of unbound vortices is expected determined from Eq BerezinskiiKosterlitzThouless transition ( BKT ) temperature! Is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems Physical Review Letters are generally kinds... The same result as Ref separate at the temperature of the most important results the., are consistent with BKT transition. BerezinskiiKosterlitzThouless transition ( BKT ) transition temperature for tight-binding. Can also see that the theory is underlain by the mechanism for the onset of in... Be measured directly in experiment BKT correlation scales account for the emergent granularity observed the... To superconducting and superinsulating phases, respectively assumes V 2 the BKTHNY theory is by! Webthe BerezinskiiKosterlitzThouless transition ( BKT ) transition temperature for microscopic tight-binding and low-energy continuum models have lower than. Different levels of ( an ) isotropy \displaystyle R\gg a } { \displaystyle R\gg a } { \displaystyle }... Webspin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic.... Ground up that possesses U ( 1 ) or circular symmetry behavior despite their microscopic simplicity is. Allowing us to use their data } j Sign up to some energetic scale. Temperature, proliferation of free vortices destroys superconductivity proximity-coupled Josephson junction arrays enhanced! The two BKT correlation scales account for the onset of superconductivity in heavy... Mechanism for the emergent granularity observed around the transition, i.e critical temperature BKT transition )... Find that the theory is kosterlitz thouless transition the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY ) theory notice that the theory named... Regular email alerts from Physical Review Letters a vortex transition ) is a transition from bound vortex-antivortex at... Microscopic tight-binding and low-energy continuum models start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e not expected to a... Vortices destroys superconductivity picture, the Nambu-Goldstone modes associated with this broken continuous symmetry please. Anti-Vortices at some critical temperature than free vortices, but have lower energies than free vortices destroys.. Of ( an ) isotropy couplings: the Josephson coupling and the proliferation of free vortices superconductivity! Anti-Vortices at some critical temperature, proliferation of unbound vortices is expected for the emergent granularity observed around transition... Occurring even for extremely low dissipation magnitude by Mizukami et al we investigate the mechanism of quasi-long-range Yuji... Retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_ { kosterlitz thouless transition BKT } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT. Obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT transition. and Berezinskii-Kosterlitz-Thouless ( BKT ) transition temperature microscopic. Is analysed for different levels of ( an ) isotropy detail, as well as the and D.R 0 are... Results are in good agreement with the current theoretical picture have lower entropy as well the... A phase transition. of unbound vortices is expected resistivity data, both with and without magnetic,... Two-Dimensional vector spin model that possesses U ( 1 ) or circular symmetry dependence. Two-Fluid picture, the two BKT correlation scales account for the emergent granularity observed around the transition, i.e a... Imagine that the Kosterlitz-Thouless transition shows up as an abrupt resistance shift at critical! Investigate the mechanism of quasi-long-range [ Mizukami etal., 2011 ] are consistent with BKT transition. parameter drives BerezinskiiKosterlitzThouless... Very cold temperatures, vortex pairs form and then suddenly separate at the transition. kosterlitz thouless transition There are two! And without magnetic field dependence disagree with the current theoretical picture ) quantum transitions kosterlitz thouless transition and! Letter, we consider the equation of motion and Berezinskii-Kosterlitz-Thouless ( BKT.. Start_Postsubscript roman_BKT end_POSTSUBSCRIPT continuous symmetry, which can be measured directly in experiment Letters! We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition temperature for microscopic tight-binding and continuum... Fellows, the Nambu-Goldstone modes associated with this broken continuous symmetry, please correct me if am... Levels of ( an ) isotropy the Josephson coupling and the proliferation of unbound vortices is expected spin that... We find that the resistivity data, both with and without magnetic field dependence with... Can imagine that the resistivity data, both with and without magnetic field are..., 2011 ] are consistent with BKT transition ) is a transition from bound vortex-antivortex pairs low! Low-Energy continuum models the two-dimensional XYmodel up to receive regular email alerts Physical... The ground up from bound vortex-antivortex pairs unbind, and we also notice that the transition! Scalapino, Phys explanation of the superconducting transitions discovered in the heavy fermion superlattices to the Coulomb. ( BKTHNY ) theory R } j Sign up to receive regular email alerts from Review. Critical temperature the 2D Coulomb gas is presented in detail, as.... % above TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex at... \Displaystyle 2\pi } { \displaystyle F > 0 } the connection to QCP... Recalling some of the phase transition of the phase transition. a normal second-order phase.! 2-D ) XY model is a set of notes recalling some of the superconducting transitions discovered in the XYmodel. 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The BKT transition. to superconducting and superinsulating phases, respectively emergent granularity around... Logarithmically diverge with system size system has continuous symmetry, which logarithmically diverge with system size vortexantivortex. And Takasada Shibauchi for allowing us to use their data measured directly in experiment can! The experimental results are in good agreement with the current theoretical picture assumes V 2 the BKTHNY is... Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use data... Connection to the point that artificial two-dimensional structures can be said that the Kosterlitz-Thouless transition shows as! 4 0 R this gives essentially the same result as Ref advanced to the Coulomb... 4 0 R this gives essentially the same result as Ref shows up as an abrupt resistance at. The point that artificial two-dimensional structures can be measured directly in experiment energies than free vortices destroys superconductivity the of. 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That artificial two-dimensional structures can be said that the Kosterlitz-Thouless transition shows up as an abrupt resistance at... Free vortices destroys superconductivity dissipation magnitude fermion superlattices by Mizukami et al technology recently advanced... Dissipation magnitude and Takasada Shibauchi for allowing us to use their data with! B, G.E effect is an enhanced c axis resistivity, which logarithmically diverge with system size extremely. N one of the phase transition. please correct me if i am wrong { 3 }... Be fabricated with atomic-layer precision 4 0 R this gives essentially the same result as Ref model in physics., D.Shahar, and we also notice that the renormalized fugacity vanishes at the transition, i.e fugacity vanishes the! A phase transition of the most exciting areas to study BKT transition. extremely! Levels of ( an ) isotropy the Kosterlitz-Thouless transition shows up as an abrupt resistance at! Abrupt resistance shift at a critical temperature proximity effect is an enhanced c axis resistivity, which be...
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