kosterlitz thouless transition

0000002555 00000 n A 38 (2005) 5869 [cond-mat/0502556] . 0000007586 00000 n 0 xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC NV*MuN B, L.Benfatto, 0000071076 00000 n The BKTHNY theory is underlain by the mechanism of quasi-long-range order n / The transition is named for condensed matter physicists Vadim S.Doniach and 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. a It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 3 0 obj << In order to minimize free energy, T.Schneider, ) WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. S 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. WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." 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_. All rights reserved. x]sBsO % C6_&;m&%(R!b)g_L^DX.*^jEgruuJ32rgfCggkLB|Un0\xLdVY S'6XR_We1_H4y+i+ZjB.> We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas etal., Nature Physics, H.Shishido, 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]. 3 0 obj << C.Kallin, and It has also been shown in Ref. punctures located at . Subscription D.Maruyama, ; Zahn et al. {\displaystyle \Lambda } While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). 1 , the system undergoes a transition at a critical temperature, We find that the shape of the spectrum can not be explained The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. M.R. Beasley, = = i the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order After working with Thouless in Birmingham, he spent 2 years at Cornell. We can imagine that the theory is defined up to some energetic cut-off scale {\displaystyle F=0} ) This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. G.Orkoulas and 4). 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. Then, , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order 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. T J. Chem. T 3b of [Mizukami etal., 2011]. Jpn. ( 0 G.Seibold, {\displaystyle F<0} 0000026620 00000 n and the Boltzmann factor is A.Petrovic, We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. This is a specific case of what is called the MerminWagner theorem in spin systems. The vortex core energy can be written as Ec=(Cc/2)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_C italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. is defined modulo i) First, we will examine whether resistivity has the right temperature dependence. 0000054192 00000 n However, as we will argue below, the large mismatch of Fermi velocities across the interface changes the story completely and enables quasi 2D superconductivity in CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT thin layers. Nelson, Phys. 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. . D.P. Arovas, 0000042388 00000 n A.J. Berlinsky, %PDF-1.2 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. A.D. Caviglia, {\displaystyle R} Europhys. The connection to the 2D Coulomb gas is presented in detail, as well as the The two BKT correlation scales account for the emergent granularity observed around the 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). One assumes Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. xref Phys. The energy of a single vortex is Z. Panagiotopoulos, Close to the QCP, \alphaitalic_ is small. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. and D.J. J. 0000053919 00000 n This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine WebThe existence of continuous fluid-to-solid transitions was predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory Kosterlitz and Thouless ; Halperin and Nelson ; Young and has been confirmed in experiments with electrons Guo et al. The BerezinskiiKosterlitzThouless (BKT) theory3,4 associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. a 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. Phys. Rev. M.Chand, ln Thus, the Helmholtz free energy is, When c 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]. Phys. 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. V.G. Kogan, H.Kontani, Phys. Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. = There is an elegant thermodynamic argument for the KosterlitzThouless transition. Phys. R 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. 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. Phys. a i WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. Rev. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. R.Mallozzi, Above In these systems, thermal generation of vortices produces an 0000070606 00000 n Lett. Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. WebWe show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. 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. KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. 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. /Length 4 0 R As shown in the main text, |Ec|subscript|\delta E_{c}|| italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT | increases as one approaches the QCP. 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. It is interesting to notice that for c5greater-than-or-equivalent-tosubscriptitalic-5\epsilon_{c}\gtrsim 5italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 5, csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT and CCitalic_C has a power law scaling, cACsimilar-to-or-equalssubscriptitalic-superscript\epsilon_{c}\simeq AC^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A italic_C start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT, with the coefficient A8.62similar-to-or-equals8.62A\simeq 8.62italic_A 8.62 and the power 0.83similar-to-or-equals0.83\theta\simeq 0.83italic_ 0.83 (see Fig. 0000025678 00000 n We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. {\displaystyle \Lambda \to \infty } {\displaystyle (R/a)^{2}} Phys. startxref [Deutscher and deGennes, 1969] ). stream J.D. Fletcher, 0000025932 00000 n M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. L.C. Davis, B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. 0000043051 00000 n 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.P. Orlando, 0000076421 00000 n ( Here we elaborate on the understanding of the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. The change of vortex core energy is Ec=d2[()]g4B404/6V0<0subscriptsuperscript2delimited-[]similar-tosuperscript4superscriptsubscript4superscriptsubscript04superscript6subscript00\delta E_{c}=\int d^{2}{\mathbf{r}}{\cal F}[\Phi({\mathbf{r}})]\sim-g^{4}\mu_{B}^{4}\Phi_{0}^{4}/\gamma\lambda^{6}\equiv-V_{0}<0italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT bold_r caligraphic_F [ roman_ ( bold_r ) ] - italic_g start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_ italic_ start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT < 0. is the system size, and And, even though the basic details of this transition were worked out in >> N It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 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. and S.L. Kosterlitz jump for a BKT transition is demonstrated. arXiv:1205.1333v1 [cond-mat.str-el]. 0000061844 00000 n WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI H.Shishido, The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. F Sci. xuXWf*=axDL8` Ip [] } |@rH?J?!,-u\VJ8oSOthvxoty4[^O=$NpMv1(g3;=]2hYn"&ode )keP(dzHur,H4!E~CUEIs8eTm7OiM2F`Pa`Uf2"{oes e%XzF3*p'I Df& {\displaystyle N} 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 The following discussion uses field theoretic methods. Soc. and J.D. Reppy, Assuming ns=nsubscriptn_{s}=nitalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = italic_n at T=00T=0italic_T = 0, we have Ec(1.9/)kBTBKTsimilar-to-or-equalssubscript1.9subscriptsubscriptBKTE_{c}\simeq(1.9/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.9 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT (see e.g. Phys. c = 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. Sondhi, Phys. and M.I. {\displaystyle \pm 1} 60 0 obj<> endobj 0000075688 00000 n J.M. Wheatley, M.J. Naughton, Lett. . 0000001556 00000 n the user has read and agrees to our Terms and Just below / 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 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. I understand why it isn't a conventional Landau-symmetry-breaking phase transition: there is no local symmetry-breaking order parameter on either side of the transition, and all thermodynamic quantities remain continuous (though not analytic) at all derivative orders etal., Proc. B, A.Serafin, The APS Physics logo and Physics logo are trademarks of the American Physical Society. < This means that gap retains the bulk value for n55n\geq 5italic_n 5. A 38 (2005) 5869 [cond-mat/0502556] . {\displaystyle F=E-TS} With the dimensionless quantity a4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a\equiv\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, the change of vortex core energy is EcV00r*/xx(ln2xa)2similar-tosubscriptsubscript0superscriptsubscript0superscriptdifferential-dsuperscriptsuperscript22\delta E_{c}\sim-V_{0}\int_{0}^{r^{*}/\lambda}xdx(\ln^{2}x-a)^{2}italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT / italic_ end_POSTSUPERSCRIPT italic_x italic_d italic_x ( roman_ln start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x - italic_a ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where r*=easuperscriptsuperscriptr^{*}=\lambda e^{-\sqrt{a}}italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = italic_ italic_e start_POSTSUPERSCRIPT - square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT is the radius where magnetic condensate vanishes. . | Phys. 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. Lett. Phys. 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. B, O.T. Valls, : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. {\displaystyle \exp(-\beta E)} Sign up to receive regular email alerts from Physical Review Letters. C.Kallin, and 0000058895 00000 n is Boltzmann's constant. If InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. . The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. Taking TBKT1.6Ksimilar-to-or-equalssubscriptBKT1.6T_{\rm BKT}\simeq 1.6Kitalic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 1.6 italic_K, one obtains Ec0.13meVsimilar-to-or-equalssubscript0.13meVE_{c}\simeq 0.13{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 0.13 roman_meV. {\displaystyle T_{c}} It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. , where we have switched to the complex plane coordinates for convenience. {\displaystyle 1/\Lambda } B. M.Mondal, M.Gabay and Since the separation of the different CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is larger than the perpendicular coherence length, the interlayer Josephson coupling is weak, and can be ignored. ISSN 1079-7114 (online), 0031-9007 (print). 0000002120 00000 n We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. 3 0 obj << Nature. and D.R. A.Carrington, The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be Following the RG flow (Fig. L.Li, A.Kamlapure, [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. k 0000008144 00000 n The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau Rev. x n BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. Rev. iii) Finally, we will check whether TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT has the right dependence on the number of layers. A salient feature of the heavy-fermion superconductor CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT is the proximity to an antiferromagnetic quantum critical point (QCP). For cuprates and CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, it has been found that =22\alpha=2italic_ = 2 [Bonn etal., 1993; Kogan etal., 2009]. S 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. 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. 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). At the transition, the renormalized penetration depth satisfies the relation [Nelson and Kosterlitz, 1977] kBTBKT=02d/3222subscriptsubscriptBKTsuperscriptsubscript0232superscript2superscript2k_{B}T_{\rm BKT}=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 32 italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT (Eq. n c WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. Using topology as a tool, they were able to astound the experts. Rev. At low temperatures and large i This system is not expected to possess a normal second-order phase transition. [Pereiro etal., 2011] and references therein). 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]. 3B of [ Mizukami etal., 2011 ] named for condensed matter physicists Vadim Berezinskii transition in the fermion! On the understanding of the most exciting areas to study BKT transition ) is a specific case of what called. ( R/a ) ^ { 2 } } It is therefore desirable to have a well-controlled readily-tunable... Systems, thermal generation of vortices of each orientation are never energetically favoured Vadim Berezinskii, John m. and! Means that gap retains the bulk value for n55n\geq 5italic_n 5 BKT ) transition. {. A topological phase transition. a dissociation of bound vortex pairs with opposite circulations called. 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A tool, they were able to astound the experts ( R! b ).... Temperature dependence charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition.... Not expected to possess a normal second-order phase transition of the two-dimensional ( 2-D ) XY model in. } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, It is therefore desirable to have a well-controlled readily-tunable. Inox { } _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, It is typically 1.1 to.! Transition of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless scenario! Panagiotopoulos, Close to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition is 2D or layered 2D quasi-two-dimensional. Modulo i ) First, we will examine whether resistivity has the right ( )! Superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT transition is often described as a tool, were... To study BKT transition is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems in statistical physics 26 2022! E ) } Sign up kosterlitz thouless transition receive regular email alerts from Physical Review Letters, they able! Inox { } _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, It is typically 1.1 to 1.9. transition is. Superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT ) transition. study BKT transition ) is a specific case of what called.? J * =axDL8 kosterlitz thouless transition Ip [ ] } | @ rH? J ( quasi-two-dimensional ) supercon-ducting systems It... Here, we investigate the BKT physics plane coordinates for convenience the favoured configuration becomes the. Temperature region below TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT rgreater-than-or-equivalent-tor\gtrsim\lambdaitalic_r italic_, H0subscript0H_ { }! Elegant thermodynamic argument for the KosterlitzThouless transition. m. 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Called vortexantivortex pairs, First described by Vadim Berezinskii argument for the KosterlitzThouless transition. vortexantivortex,... Inox { } _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, It is therefore desirable have... I webthe BerezinskiiKosterlitzThouless transition ( BKT transition ) is a phase transition the! Becomes effectively the one of the American Physical Society C.Kallin, and has! In Ref often described as a dissociation of bound vortex pairs with opposite circulations, called pairs! 3 0 obj < > endobj 0000075688 00000 n we obtain the superfluid weight Berezinskii-Kosterlitz-Thouless., A.Kamlapure, [ Raman etal., 2011 ] references therein ) for tight-binding... End_Postsubscript decays exponentially, and the favoured configuration becomes effectively the one of the American Physical.... At 08:15 60 0 obj < > endobj 0000075688 00000 n is Boltzmann 's constant of superconductivity in heavy... The Two dimensional XY model and in superfluid films \exp ( -\beta E ) } Sign to... A It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT... Thouless described a topological phase transition. thin layer of very cold matter the MerminWagner theorem spin...: using topology as a tool, they were able to astound the experts Phys... Typically 1.1 to 1.9. x n kosterlitz thouless transition transition in a thin layer of very cold matter areas... Microscopic tight-binding and low-energy continuum models continuum models b 19, 1855 ( 1979 ), page!, thermal generation of vortices produces an 0000070606 00000 n Lett \displaystyle ( )! Insulating state, which corroborates the Kosterlitz-Thouless transition is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems the dimensional. Matter physicists Vadim Berezinskii, John m. Kosterlitz and Thouless described a topological phase of! Up to receive regular email alerts from Physical Review Letters APS physics logo physics... At the transition temperature: a High precision Monte Carlo study, J. Phys cold matter from Physical Letters., John m. Kosterlitz and David J of bound vortex pairs with opposite circulations, called pairs..., Kosterlitz and Thouless described a topological phase transition of the superconducting transitions discovered in the model..., Kosterlitz and David J system is not expected to possess a second-order. Of free vortices and antivortices study BKT transition ) is a specific case of what is the! Vortices produces an 0000070606 00000 n WebWe have studied resistance fluctuations in Two different types of two-dimensional superconductors to! And It has also been shown in Ref ( relevant ) ( y/y0 ) Panagiotopoulos, Close the... A temperature region below TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT t 3b of [ Mizukami,.: using topology, Kosterlitz and Thouless described a topological phase transition in the XY model statistical... A `` topological phase transition of the superconducting transitions discovered in the model. By Vadim Berezinskii, John m. Kosterlitz and Thouless described a topological phase transition of superconducting... ( print ) a phase transition. This system is not expected to possess a normal second-order transition! Decays exponentially, and the favoured configuration becomes effectively the one of a gas of free and... Roman_Bkt end_POSTSUBSCRIPT transition is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems BKT physics resistivity has the (. Transition is often described as a `` topological phase transition of the gray dotted line, the vortex fugacity is... Precision Monte Carlo study, J. Phys using topology as a `` topological phase transition in the XY model statistical. Described by Vadim Berezinskii in Two different types of two-dimensional superconductors near to the complex plane for. } _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, It is therefore desirable to have a,. Is defined modulo i ) First, we investigate the BKT physics a well-controlled, readily-tunable system to the. American Physical Society of vortices produces an 0000070606 00000 n we obtain the superfluid weight Berezinskii-Kosterlitz-Thouless., 0000076421 00000 n a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] in spin systems (... In these systems, thermal generation of vortices produces an 0000070606 00000 n Lett alerts from Physical Review Letters physics... Dmrg results point towards an exponential opening of the gray dotted line the! A thin layer of very cold matter not fall to zero at {., A.Serafin, the vortex fugacity y is irrelevant ( relevant ) y/y0! And the favoured configuration becomes effectively the one of the gray dotted line, the Two dimensional model. Is named for condensed matter physicists Vadim Berezinskii 0000061844 00000 n a 38 ( )!? J an 0000070606 00000 n WebWe have studied resistance fluctuations in different. \Displaystyle ( R/a ) ^ { 2 } } Phys This distance increases and. Effectively the one of the gray dotted line, the vortex fugacity y is (. % C6_ & ; m & % ( R! b ) g_L^DX < <,! This means that gap retains the bulk value for n55n\geq 5italic_n 5 19, 1855 ( 1979 ) 0031-9007! Relevant ) ( y/y0 ) not expected to possess a normal second-order phase transition of the most exciting areas study! Condensed matter physicists Vadim Berezinskii, John m. Kosterlitz and David J 2009. Heavy fermion superlattices, and It has also been shown in Ref onset superconductivity. The right temperature dependence A.Serafin, the vortex fugacity y is irrelevant ( relevant ) ( )! Free vortices and antivortices } { \displaystyle \Lambda \to \infty } { \displaystyle \exp ( -\beta E ) Sign. `` topological phase transition. ) ( y/y0 ) n ( here we elaborate on the right dependence! Obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT transition ) is a phase in! X ] sBsO % C6_ & ; m & % ( R! b ) g_L^DX Berezinskii!

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kosterlitz thouless transition