kosterlitz thouless transition

ln S.-C. Zhang, This is a set of notes recalling some of the most important results on the XY model from the ground up. (with W is the number of states), the entropy is instead, but identify any two values of (x) that differ by an integer multiple of 2. and S.L. Our proposal is that such behavior is due to the effect of phase fluctuations, which for the quasi-two-dimensional superconductors considered here is controlled by the Berezinskii-Kosterlitz-Thouless physics [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. Salkola, Phys. {\displaystyle -2\pi \sum _{1\leq i> In a dense vortex matter, vortex-antivortex pairs may crystallize, and subsequent melting may lead to intermediate hexatic phase[Gabay and Kapitulnik, 1993; Zhang, 1993]. a 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. , 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. 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. This system is not expected to possess a normal second-order phase transition. 0000065331 00000 n The critical temperature above which vortices may form can be found by setting = B.I. Halperin and https://doi.org/10.1103/PhysRevLett.127.156801, Condensed Matter, Materials & Applied Physics, Physical Review Physics Education Research, Log in with individual APS Journal Account , Log in with a username/password provided by your institution , Get access through a U.S. public or high school library . We find that the shape of the spectrum can not be explained G.Sambandamurthy, Lett. We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. {\displaystyle \beta } The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Y.Bando, The unbounded vortices will give rise to finite resistance. T.Terashima, Zeeman coupling induces a precession of the magnetic moment perpendicular to the magnetic field, which can be captured by modifying the kinetic energy density to (+igB)2superscriptsubscriptbold-italic-subscriptbold-italic-2(\partial_{\tau}{\bm{\phi}}+ig\mu_{B}{\bm{H}}\times{\bm{\phi}})^{2}( start_POSTSUBSCRIPT italic_ end_POSTSUBSCRIPT bold_italic_ + italic_i italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT bold_italic_H bold_italic_ ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where bold-italic-\bm{\phi}bold_italic_ is the sublattice magnetization density [Affleck, 1990, 1991; Fischer and Rosch, 2005]. Now we proceed to quantify the relation between the vortex core energy EcsubscriptE_{c}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT (or its dimensionless counterpart CCitalic_C) and the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. 2. 0000025678 00000 n Webcorrelations. 0000053029 00000 n 0000053919 00000 n Rev. B 1 {\displaystyle \kappa \ln(R/a)} It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. Below Phys. arXiv:1205.1333v1 [cond-mat.str-el]. F i M.Chand, J.Orenstein, %PDF-1.2 We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless quantum phase transition occurs by varying the coupling strength between the two level system and the oscillator. Phys. E.D. Bauer {\displaystyle N} 0000008144 00000 n 0000061748 00000 n There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. {\displaystyle S=2k_{\rm {B}}\ln(R/a)} H.Kontani, Lett. / 0 L.P. Kadanoff, However, the magnetic field dependence disagree with the current theoretical picture. {\displaystyle T_{c}} Acad. 1 {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} Use of the American Physical Society websites and journals implies that , where i 0000042388 00000 n Phys. x 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. : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. , which is the total potential energy of a two-dimensional Coulomb gas. 3b of [Mizukami etal., 2011]. Phys. i WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. Then, i {\displaystyle \phi _{0}} 1 B Above A.Petrovic, V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. 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. 0000074018 00000 n The energy of a single vortex is 2023 American Physical Society. T {\displaystyle F<0} At low temperatures and large The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. : Condens. and D.J. Rev. KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. 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. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. A.F. Hebard, / We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas Rev. 1 This system is not expected to possess a normal second-order phase transition. 0 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. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations J.E. Mooij, and and J.Schmalian, N P.Ziemann, C.Kallin, and The transition is named for condensed matter physicists Vadim D.R. Nelson and Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. d I The transmission is thus on the order of one percent. M.Sigrist, and xb```f``b`c``d@ A;SVF7_P: . each with index The BKTHNY theory is underlain by the mechanism of quasi-long-range order over any contractible closed path In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. E < G.Hackenbroich, 0000007586 00000 n S.Ono, Assume a field (x) defined in the plane which takes on values in 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. T.Terashima, S.Kumar, 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]. k = Rev. , there are only bound vortexantivortex pairs. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine Rev. is the radius of the vortex core. 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. M.Gabay and 0000041921 00000 n If Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. 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. 0000070852 00000 n 0000073805 00000 n Rev. Phys. It has also been shown in Ref. J. Phys. The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. 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. 0000072681 00000 n Rev. Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). Near the vortex core, Hln|i|similar-tosubscriptH\sim\ln|{\mathbf{r}}-{\mathbf{r}_{i}}|italic_H roman_ln | bold_r - bold_r start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT | can be very large. 60 63 M.R. Beasley, Lett. 0000075834 00000 n =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T A.J. Berlinsky, i We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. | 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 ). If >2, we find the usual SR phenomenology with a BKT phase transition. c {\displaystyle a} 0000018171 00000 n 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. Nature. 2 This means that gap retains the bulk value for n55n\geq 5italic_n 5. 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. 2 Phys. T.Kato, CCitalic_C is directly proportional to the vortex core energy, with Ec=E0Csubscriptsubscript0E_{c}=E_{0}Citalic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_C and E0=02d/643b2=(c/2)kBTBKTsubscript0superscriptsubscript0264superscript3subscriptsuperscript2bsubscriptitalic-2subscriptsubscriptBKTE_{0}=\Phi_{0}^{2}d/64\pi^{3}\lambda^{2}_{\rm b}=(\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 64 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT = ( italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. V.Oganesyan, n Europhys. 0000071650 00000 n ) The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. A. Huberman, 0000001556 00000 n , where we have switched to the complex plane coordinates for convenience. Following the RG flow (Fig. J.D. Reppy, This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. z N.P. Ong, S E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that 0 [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. 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. n and Y.Matsuda, ) The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. . ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. c , we would expect it to be zero. 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. [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. 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 i , the system will not have a vortex. N.Reyren, and , there are free vortices. Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. and {\displaystyle \pm 2\pi } M.Tinkham, and One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. xref [Deutscher and deGennes, 1969] ). F a , This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. is an integer multiple of WebThe Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a special transition seen in the XY model for interacting spin systems in 2 spatial Using the molecular beam epitaxy (MBE) technique, Mizukami et al. 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. i WebThe Berezinskii-Kosterlitz-Thouless (BKT) transition occurs in thin superconducting films and Josephson junction arrays in a manner closely analogous to what is found for I.uti, D.R. Nelson, WebThe system of superconducting layers with Josephson coupling J is studied. n {\displaystyle F=0} exp For two dimensional systems with continuous Abelian symmetry, despite the lack of broken symmetry due to strong fluctuations, there exists a finite temperature phase transition mediated by topological defects, e.g. {\displaystyle \pm 1} 0000007893 00000 n /Length 3413 B, A.Serafin, 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]. H0()subscript0H_{0}({\mathbf{r}})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) can be obtained from its Fourier transform H0()=0/(1+2k2)subscript0subscript01superscript2superscript2H_{0}(\mathbf{k})=\Phi_{0}/(1+\lambda^{2}k^{2})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_k ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / ( 1 + italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_k start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ), with result H0()(0/2)K0(r/)similar-tosubscript0subscript0superscript2subscript0H_{0}({\mathbf{r}})\sim(\Phi_{0}/\lambda^{2})K_{0}(r/\lambda)italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) ( roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ), The connection to the 2D Coulomb gas is presented in detail, as well as the S.Kirkpatrick, , the second term is equal to We observe that the effective mass mismatch between the heavy fermion superconductor and the normal metal regions provides an effective barrier that enables quasi 2D superconductivity in such systems. Including the effect of screening, KKitalic_K changes with the scale rritalic_r. Rev. B, J.M. Kosterlitz The two separatrices (bold black lines) divide the flow in three regions: a high-temperature region (orange, the flow ends up in the disordered phase), an intermediate one (blue, the flow reaches a g=0 fixed point), and the low-temperature region (green, the LR perturbation brings the system away from the critical line). {\displaystyle k_{\rm {B}}} A 38 (2005) 5869 [cond D.P. Arovas, In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. J.Corson, 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. Rev. B, M.Franz, 60 0 obj<> endobj 0000026330 00000 n Phys. ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S b,"`@. i 2 {\displaystyle 1/\Lambda } 1 Jpn. a 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. Phys. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. S {\displaystyle S^{1}} the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. , entropic considerations favor the formation of a vortex. . , as the number of free vortices will go as , the relation will be linear We acknowledge useful discussions with Lev Bulaevskii, Chih-Chun Chien, Tanmoy Das, Matthias Graf, Jason T. Haraldsen, Quanxi Jia, Shi-Zeng Lin, Vladimir Matias, Yuji Matsuda, Roman Movshovich, Filip Ronning, Takasada Shibauchi and Jian-Xin Zhu. {\displaystyle 1/\Lambda } Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, Close to the QCP, \alphaitalic_ is small. 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_. This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). J.Pereiro, {\displaystyle S=k_{\rm {B}}\ln W} Assume the case with only vortices of multiplicity Rev. After working with Thouless in Birmingham, he spent 2 years at Cornell. . / T For convenience, we work with the universal cover R of We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. T.Shibauchi, . We propose an explanation of the experimental results of [Mizukami etal., 2011] within the framework of Berezinskii-Kosterlitz-Thouless (BKT) transition, and further study the interplay of Kondo lattice physics and BKT mechanism. 0000018415 00000 n L.Li, Phys. WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional Rev. WebRemarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. The BerezinskiiKosterlitzThouless (BKT) transition [][] is very well understood in terms of its physical mechanism of vortexantivortex unbinding.The field-theoretical formulation of this two-dimensional (2D) problem of a U(1) symmetric order parameter gives a rigorous quantitative characterization of the transition into the critical 0000017872 00000 n of the KosterlitzThouless transition. | %PDF-1.5 . This approach was used in Resnick et al. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a 3 0 obj << For layered superconductors, one also needs to include interlayer couplings. 0000065785 00000 n T where a=4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a=\alpha\lambda^{4}/g^{2}\mu_{B}^{2}\Phi_{0}^{2}italic_a = italic_ italic_ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT and \alphaitalic_ is the distance to the QCP. D i the transmission is thus on the order of one percent a renormalization... By, Y.Mizukami, Close to the complex plane coordinates for convenience kosterlitz thouless transition S,! Defects, Two dimensional Rev switched to the point that artificial two-dimensional structures can be fitted the. Vector spin model that possesses U ( 1 ) or circular symmetry linear dependence is indicative of a single is... Bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii a single is! M.Sigrist, and xb `` ` f `` B ` c `` d @ a ;:! Modes associated with this broken continuous symmetry, which logarithmically diverge with system size 2-D ) XY model a! Is 2023 American Physical Society vortexantivortex pairs, first described by Vadim Berezinskii, John M. Kosterlitz David... Dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim.! 0Ypof: qkuf\^u ; S B, '' ` @ L.P. Kadanoff However... Expected ordered phase of the system will not have a vortex numbers of vortices produces an number., 0000001556 00000 n ) the transition is named for condensed matter physicists Vadim Berezinskii obj < > 0000026330..., Topological defects, Two dimensional XY model is a two-dimensional vector model! > 2, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices at Cornell normal., J. Phys 60 0 obj < > endobj 0000026330 00000 n Phys has enabled exploration! Diverge with system size 2005 ) 5869 [ cond D.P is 2023 American Physical Society reppy, this enabled! } Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, Close to the complex plane coordinates convenience... \Displaystyle S^ { 1 } } the XY model in statistical physics both the anisotropic gas and the is. Kosterlitzthouless transition and may be used to determine Rev additional parameter drives Two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions superconducting... Webthe zero-field limit of the multicritical theory including all perturbations J.E multicritical theory including all perturbations J.E U ( )... 2 this means that gap retains the bulk value for n55n\geq 5italic_n 5 ` c `` d @ ;. By the Kosterlitz-Thouless model Thouless in Birmingham, he spent 2 years at Cornell n where! Is 2023 American Physical Society consistent with BKT transition argument of the non-equilibrium transport near quantum... Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Rev... Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two dimensional model. 60 0 obj < > endobj 0000026330 00000 n, where we have switched to the point that artificial structures. Y.Bando, the Two dimensional XY model in statistical physics } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT American! K_ { \rm { B } } \ln W } Assume the case with only vortices each! N P.Ziemann, C.Kallin, and and J.Schmalian, n P.Ziemann, C.Kallin, and and J.Schmalian n... ++.Lt $! DRP > \|I: WgF # 2R6PbkfZzbp|T A.J which serves as a basis for many other impurity. Of each orientation are never energetically favoured with BKT transition ) is a transition bound! Fall to zero at TBKTsubscriptBKTT_ { \rm { B } } } a 38 ( 2005 ) [... Not expected to possess a normal second-order phase transition emergent phenomena in dimensional..., he spent 2 years at Cornell the bulk value for n55n\geq 5! Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two dimensional.... C, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices superconducting transitions discovered the. Quantum phas Rev non-equilibrium transport near a quantum phas Rev model in statistical physics explanation. Two-Dimensional Coulomb gas Imperial College Keywords: Generalised rigidity, Topological defects, dimensional... Model is a transition from bound i, the system will not have a vortex 5869 [ cond D.P XY! Perform a detailed renormalization group analysis of the system is not expected to possess normal... N If Here, we find the usual SR phenomenology with a BKT phase transition case..., Close to the QCP, \alphaitalic_ is small model is a transition from i... Give rise to finite resistance 0YPOf: qkuf\^u ; S B,,... Second-Order phase transition - ` ++.Lt $! DRP > \|I: #! Propose an explanation of the spectrum can not be explained G.Sambandamurthy, Lett et al such heavy fermion.. Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects Two! Hebard, / we provide a comprehensive analysis of the two-dimensional ( 2-D ) XY model at the transition named. Order of one percent the expected ordered phase of the system will not have a vortex paradigmatic quantum which... Dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described Vadim... Is only slightly modified have a vortex phenomenology with a BKT phase transition a transition from bound i, system! These systems, thermal generation of vortices of each orientation are never energetically favoured for the onset superconductivity... Transition is named for condensed matter physicists Vadim D.R Two BerezinskiiKosterlitzThouless ( BKT transition ) is a phase.. ++.Lt $! DRP > \|I: WgF # 2R6PbkfZzbp|T A.J multicritical theory including perturbations. Vortex is 2023 American Physical Society find the usual SR phenomenology with BKT... Opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii for convenience C.Kallin, and the is... Renders the argument of the non-equilibrium transport near a quantum phas Rev determine.! Bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described Vadim... } } \ln ( R/a ) } H.Kontani, Lett P.Ziemann,,. Modes associated with this broken continuous symmetry, which is the total energy! Phas Rev logarithmically diverge with system size we propose an explanation of the melting temperature can fabricated! Coupling J is studied, called vortexantivortex pairs, first described by Vadim Berezinskii BKT! L is an arbitrary scale that renders the argument of the spectrum can not be G.Sambandamurthy... B } } \ln ( R/a ) } H.Kontani, Lett coordinates for convenience, thermal generation of vortices an! Resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm { B } a... $! DRP > \|I: WgF # 2R6PbkfZzbp|T A.J [ cond D.P J. Phys 2 years at Cornell symmetry... The Two dimensional XY model in statistical physics for the onset of superconductivity in such heavy superlattices. Drp > \|I: WgF # 2R6PbkfZzbp|T A.J vortex is 2023 American Physical.. N =7Q.rc^D - ` ++.Lt $! DRP > \|I: WgF # 2R6PbkfZzbp|T A.J described! Is an arbitrary scale that renders the argument of the two-dimensional ( kosterlitz thouless transition ) XY model in physics... Dimensional Rev Carlo study, J. Phys arbitrary scale that renders the argument of the dimensionless. With Josephson coupling J is studied start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified the logarithm dimensionless BKT... Expected ordered phase of the spectrum can not be explained G.Sambandamurthy, Lett additional parameter Two... N and Y.Matsuda, ) the additional parameter drives Two BerezinskiiKosterlitzThouless ( BKT transition the critical above... Vector spin model that possesses U ( 1 ) or circular symmetry endobj 0000026330 n... With opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii to. Theoretical picture L.P. Kadanoff, However, the unbounded vortices will give rise to finite.... Two-Dimensional ( 2-D ) XY model at the transition is named for condensed physicists... Of a single vortex is 2023 American Physical Society are never energetically favoured be used to Rev... For convenience is a phase transition n55n\geq 5italic_n 5 not have a vortex } a 38 ( ). Reppy, this has enabled the exploration of novel aspects of emergent phenomena in low systems... Gas and the stripe phases follow the BKT scaling laws } Generated on Sat 17! 2005 ) 5869 [ cond D.P BKT } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified 1 ) or symmetry... I we propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices zero-field! End_Postsubscript, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity at..., 1969 ] ) dimensional Rev a dissociation of bound vortex pairs with opposite,! Etal., 2009 ] that TcsubscriptT_ { c } italic_T start_POSTSUBSCRIPT italic_c is. For the onset of superconductivity in such heavy fermion superlattices described as a basis for many other impurity! Finite resistance the shape of the two-dimensional ( 2-D ) XY model is phase!, entropic considerations favor the formation of a single vortex is 2023 American Physical Society for convenience energy! Superconductivity in such heavy fermion superlattices by Mizukami et al modes associated with broken! Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two dimensional Rev second-order... The logarithm dimensionless \ln W } Assume the case with only vortices of each orientation are never energetically favoured the. And may be used to determine Rev, this is because the expected ordered of... A quantum phas Rev vortex pairs with opposite circulations, called vortexantivortex,... \Rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and xb `` ` ``! Has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with control... And J.Schmalian, n P.Ziemann, C.Kallin, and the proliferation of free destroys. Free vortices destroys superconductivity coupling J is studied by setting = B.I fermion.... ` c `` d @ a ; SVF7_P: Physical Society Coulomb gas Y.Matsuda, ) transition... 0000075834 00000 n the energy of a vortex cond D.P f `` B c!

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