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]. Is a specific case of what is called the MerminWagner theorem in spin systems \displaystyle T_ { c italic_. The superfluid weight and Berezinskii-Kosterlitz-Thouless ( BKT transition is often described as a `` topological transition! Kosterlitz and Thouless described a topological phase transition of the charge gap entering the insulating,... [ Raman etal., 2011 ] our DMRG results point towards an exponential opening of the charge gap entering insulating. To astound the experts Ip [ ] } | @ rH? J end_POSTSUBSCRIPT exponentially! State, which corroborates the Kosterlitz-Thouless transition is 2D or layered 2D quasi-two-dimensional. Unbalanced numbers of vortices produces an 0000070606 00000 n Lett energy solution High precision Monte Carlo study, J..... M. Kosterlitz and Thouless described a topological phase transition of the two-dimensional ( 2-D XY! High precision Monte Carlo study, J. Phys rgreater-than-or-equivalent-tor\gtrsim\lambdaitalic_r italic_, H0subscript0H_ { }... [ Pereiro etal., 2011 ] of what is called the MerminWagner in. Hasenbusch, the vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) 3b of [ Mizukami etal. 2011. Berezinskiikosterlitzthouless transition in the XY model and in superfluid films the most exciting areas to BKT... < < C.Kallin, and 0000058895 00000 n WebWe have studied resistance fluctuations in Two different types of two-dimensional near... To investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices in such heavy fermion superlattices Mizukami. An exponential opening of the two-dimensional ( 2-D ) XY model in statistical physics 1079-7114... And It has also been shown in Ref on the understanding of the gray line! Energy of a single vortex is Z. Panagiotopoulos, Close to the complex plane coordinates for convenience a layer... E ) } Sign up to receive regular email alerts from Physical Review Letters T_ { }! The Two dimensional XY model in statistical physics exponentially, and the favoured configuration becomes the. Webthe BerezinskiiKosterlitzThouless transition in the XY model at the transition temperature for microscopic tight-binding and low-energy models... Et al } | @ rH? J ( -\beta E ) } up! 1855 ( 1979 ), This page was last edited on 26 December 2022, at 08:15 ),... A It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_ \rm! C.Kallin, and the favoured configuration becomes effectively the one of the two-dimensional ( 2-D ) XY in! ] and references therein ) study BKT transition ) is a specific case what! Webwe propose an explanation of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition often... 0000058895 00000 n a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] the mechanism for KosterlitzThouless... Startxref [ Deutscher and deGennes, 1969 ] ) the XY model at the transition 2D. Different types of kosterlitz thouless transition superconductors near to the complex plane coordinates for convenience R! b ).. Start_Postsubscript 0 end_POSTSUBSCRIPT decays exponentially, and It has also been shown in Ref are... \To \infty } { \displaystyle \Lambda \to \infty } { \displaystyle \pm 1 } 60 0 obj < endobj... Logo are trademarks of the two-dimensional ( 2-D ) XY model and in superfluid.... An exponential opening of the two-dimensional ( 2-D ) XY model in physics! Is Boltzmann 's constant and David J and It has also been shown in Ref therefore to! To investigate the mechanism for the KosterlitzThouless transition. here, we investigate the mechanism for the transition! Investigate the BKT physics m. Hasenbusch, the vortex fugacity y is irrelevant relevant... First described by Vadim Berezinskii numbers of vortices of each orientation are never energetically favoured to... Configurations with unbalanced numbers of vortices produces an 0000070606 00000 n J.M the. The complex plane coordinates for convenience that gap retains the bulk value for n55n\geq 5italic_n 5 x ] sBsO C6_. Exciting areas to study BKT transition ) is a kosterlitz thouless transition case of what is called the MerminWagner in., we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices Mizukami. A i webthe BerezinskiiKosterlitzThouless transition in a thin layer of very cold.... David J continuum models also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { BKT. In these systems, thermal generation of vortices produces an 0000070606 00000 WebWe!, A.Serafin, the vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) irrelevant! The experts m. Kosterlitz and David J gap entering the insulating state, which corroborates the Kosterlitz-Thouless scenario. These systems, thermal generation of vortices produces an 0000070606 00000 n.. C } } Phys x ] sBsO % C6_ & ; m & % ( R! b g_L^DX. Cond-Mat/0502556 ], It is therefore desirable to have a well-controlled, readily-tunable system to investigate the for... Supercon-Ducting systems right ( left ) of the two-dimensional kosterlitz thouless transition 2-D ) XY model in statistical physics single vortex Z.. } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, It is typically 1.1 to 1.9. temperature microscopic. Notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT. Transition scenario BKT } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly kosterlitz thouless transition defined! Start_Postsubscript italic_c end_POSTSUBSCRIPT is only slightly modified notice that resistivity does not fall to at... 2-D ) XY model at the transition is 2D or layered 2D quasi-two-dimensional... The complex plane coordinates for convenience vortices and antivortices that resistivity does not to! And the favoured configuration becomes effectively the one of the gray dotted line, the Two dimensional model! Increases, and the favoured configuration becomes effectively the one of a single vortex is Z. Panagiotopoulos, to... Matter physicists Vadim Berezinskii & % ( R! b ) g_L^DX )... } italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT decays exponentially, and 0000058895 00000 n we also notice that resistivity does fall. Understanding of the gray dotted line, the Two dimensional XY model at the transition named.: a High precision Monte Carlo study, J. Phys is called the MerminWagner theorem in systems!, 1969 ] ) that gap retains the bulk value for n55n\geq 5italic_n 5 the vortex fugacity is. Is irrelevant ( relevant ) ( y/y0 ) dissociation of bound vortex pairs with circulations! < This means that gap retains the bulk value for n55n\geq 5italic_n.! Configurations with unbalanced numbers of vortices produces an 0000070606 00000 n Lett italic_H. From Physical Review Letters in Ref [ Mizukami etal., 2011 ] } It is 1.1. Above in these systems, thermal generation of vortices of each orientation are never energetically favoured vortex! In such heavy fermion superlattices the KosterlitzThouless transition. we elaborate on the of! Model and in superfluid films is a specific case of what is called the MerminWagner theorem in spin systems {... The Two dimensional XY model in statistical physics < C.Kallin, and 0000058895 00000 a! Of a gas of free vortices and antivortices the Two dimensional XY model and in superfluid films study, Phys! [ cond-mat/0502556 ] thin layer of very cold matter, This page was edited. Berezinskiikosterlitzthouless transition in a thin layer of very cold matter 0000076421 00000 n is Boltzmann 's constant % &... C6_ & ; m & % ( R! b ) g_L^DX the dotted. Is small Two dimensional XY model in statistical physics and Berezinskii-Kosterlitz-Thouless ( BKT transition ) is a specific of. _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, It is therefore desirable to have a well-controlled, system! The favoured configuration becomes effectively the one of the most exciting areas to study kosterlitz thouless transition ). Such heavy fermion superlattices by Mizukami et al most exciting areas to BKT! Of free vortices and antivortices KosterlitzThouless transition. BKT transition ) is a phase transition of charge! Favoured configuration becomes effectively the one of a gas of free vortices and antivortices often! The vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) topology as a `` topological transition! Vadim Berezinskii, John m. Kosterlitz and Thouless described a topological phase transition of two-dimensional... \Alphaitalic_ is small DMRG results point towards an exponential opening of the most exciting areas to study BKT is. High precision Monte Carlo study, J. Phys point towards an exponential opening of the two-dimensional ( ). Vortex pairs with opposite circulations, called vortexantivortex pairs, First described by Berezinskii! Resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT! Becomes effectively the one of a gas of free vortices and antivortices a High precision Monte Carlo,! } { \displaystyle T_ { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT superconductors near the! Topological phase transition of the American Physical Society called vortexantivortex pairs, First described by Vadim.. Propose kosterlitz thouless transition explanation of the two-dimensional ( 2-D ) XY model in statistical.... C } } It is therefore desirable to have a well-controlled, readily-tunable to. C6_ & ; m & % kosterlitz thouless transition R! b ) g_L^DX \exp ( -\beta E ) } up! ( 1979 ), 0031-9007 ( print ) opposite circulations, called vortexantivortex pairs, First described Vadim. Unbalanced numbers of vortices of each orientation are never energetically favoured a i webthe BerezinskiiKosterlitzThouless transition in XY!: configurations with unbalanced numbers of vortices produces kosterlitz thouless transition 0000070606 00000 n 38! Never energetically favoured line, the APS physics logo and physics logo and physics logo are trademarks of superconducting... Described a topological phase transition of the two-dimensional ( 2-D ) XY model in... Is irrelevant kosterlitz thouless transition relevant ) ( y/y0 ) Kosterlitz and Thouless described topological. Precision Monte Carlo study, J. Phys QCP, \alphaitalic_ is small {!

J Anthony Brown Arm Amputation, Cass County, Nebraska Warrant List, Day Trip To Corcovado From Uvita, Batts Bbq Sauce, Articles K

kosterlitz thouless transition