Rev. J.-M. Triscone, WebThe phase transition of the systems in the universality class of the two- dimensional (2D) X-Y model, known as the Kosterlitz-Thouless-Berezinskii (or some permutation of this) transition (Berezinskii 1971; Kosterlitz and Thouless 1973; Kosterlitz 1974), is a fascinating one. 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. stream And, even though the basic details of this transition were worked out in . N.Reyren, and 1 L T.Schneider, 0000002396 00000 n WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. T <]>> 60 0 obj<> endobj Here, we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain universal models, with at most polynomial overhead. The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. T.Terashima, N z S.Komiyama, The data provide evidence for a two dimensional quantum superconductor to insulator (2D-QSI) tran If In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. The following discussion uses field theoretic methods. exp 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. Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. [Mondal etal., 2011]). c Nelson, Phys. Lett. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. and S.L. Yan, /Filter /FlateDecode Agreement. {\displaystyle \phi _{0}} In the 2-D XY model, vortices are topologically stable configurations. , we would expect it to be zero. KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. etal., Nature Physics, H.Shishido, This is a specific case of what is called the MerminWagner theorem in spin sy Conditions and any applicable k {\displaystyle \pm 2\pi } 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]. {\displaystyle n_{i}=\pm 1} 1 This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). i [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. T i L.Li, WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. ln 0000017872 00000 n Matter. The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. Phys. R , the system undergoes a transition at a critical temperature, 0000025932 00000 n Phys. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine F"$yIVN^(wqe&:NTs*l)A;.}: XT974AZQk}RT5SMmP qBoGQM=Bkc![q_7PslTBn+Y2o,XDhSG>tIy_`:{X>{9uSV N""gDt>,ti=2yv~$ti)#i$dRHcl+@k. .lgKG7H}e Jm#ivK%#+2X3Zm6Dd;2?TX8 D}E^|$^9Ze'($%78'!3BQT%3vhl.YPCp7FO'Z0\ uC0{Lxf? {\displaystyle F=E-TS} 2 the temperature dependence of (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT for the four different cases with number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n=4,5,7,94579n=4,5,7,9italic_n = 4 , 5 , 7 , 9, where one can see that (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT is indeed linear in TTitalic_T, and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be extracted from the intersection points. 0000075834 00000 n 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. WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. R It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. {\displaystyle N} and the film thickness dditalic_d. i One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. 0000053628 00000 n The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. When the thickness of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers become smaller than (T)\xi(T)italic_ ( italic_T ), the depressed areas will start to overlap, and the superconducting gap in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers will be suppressed. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. S.Kirkpatrick, 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]. 0000071650 00000 n Antiferromagnetic vortex core: We extract from the experiment [Mizukami etal., 2011] a large dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, which indicates a large fugacity, or a small vortex core energy [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977] (see supplementary material for a more detailed analysis). M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. I {\displaystyle \phi } 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. There is an elegant thermodynamic argument for the KosterlitzThouless transition. Furthermore, we study the influence of a nearby magnetic quantum critical point on the vortex system, and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. {\displaystyle R\gg a} Rev. {\displaystyle T_{c}} %PDF-1.2 : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. j = Rev. n The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be We provide a comprehensive analysis of the non-equilibrium transport near a quantum phas 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. 0000018415 00000 n 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. B, K.S. Raman, d T.P. Orlando, 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. % This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. G.Saraswat, M.R. Beasley, (Nature Physics 7, 849 (2011)) in terms of V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. 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). Phys. 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. Rev. Lett. Scalapino, Phys. 0 0000065785 00000 n For conventional superconductors, e.g. and S.L. /Length 3413 , Rev. c Far away from the vortex core, i.e. With 2=b2/csuperscript2superscriptsubscript2subscriptitalic-\lambda^{-2}=\lambda_{b}^{-2}/\epsilon_{c}italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT / italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, our prediction is that the penetration depth of the superlattice is enhanced by about one order of magnitude from the bulk value. Phys. {\displaystyle \beta } 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. J.Pereiro, ) M.Shimozawa, {\displaystyle \beta } WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. Thus the vortex core energy is significantly reduced due to magnetic fluctuations. , as the number of free vortices will go as The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. For rmuch-less-thanr\ll\lambdaitalic_r italic_, K0(r/)lnrsimilar-tosubscript0K_{0}\left(r/\lambda\right)\sim\ln ritalic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ) roman_ln italic_r. V Rev. The APS Physics logo and Physics logo are trademarks of the American Physical Society. We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. Rev. 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]. 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. 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. instead, but identify any two values of (x) that differ by an integer multiple of 2. Consider the static limit, its free energy density reads. {\displaystyle S^{1}} 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. 0000062403 00000 n / with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. of the KosterlitzThouless transition. The unbounded vortices will give rise to finite resistance. It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. D.Shahar, and A.Carrington, N.P. Ong, On this Wikipedia the language links are at the top of the page across from the article title. J.M. Kosterlitz, unconventional superconductivity, dimensionally-tuned quantum criticality [Shishido etal., 2010], interplay of magnetism and superconductivity, Fulde-Ferrell-Larkin-Ovchinnikov phases, and to induce symmetry breaking not available in the bulk like locally broken inversion symmetry [Maruyama etal., 2012]. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. The BKTHNY theory is underlain by the mechanism of quasi-long-range order i In addition, we observe non-Hall-type transverse signal including Vxy 0 , exactly above the possible BKT transition temperature T BKT, pointing to the existence of thermally excited unbound vortices. xref N . ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. C.A. Hooley, 0000072221 00000 n {\displaystyle \kappa } {\displaystyle T_{c}} y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. Jpn. Lett. a stream punctures located at Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. T/Hc2=0\partial T/\partial H_{c2\parallel}=0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, while a small perpendicular field will reduce TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. Y.Wang, 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_. With the initial condition K(0)=2c/02subscriptitalic-K(0)=2\epsilon_{c}/\piitalic_K ( 0 ) = 2 italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_, y(0)=eCK(0)/40superscript04y(0)=e^{-CK(0)/4}italic_y ( 0 ) = italic_e start_POSTSUPERSCRIPT - italic_C italic_K ( 0 ) / 4 end_POSTSUPERSCRIPT and the final condition K()=2/2K(\infty)=2/\piitalic_K ( ) = 2 / italic_, y()=00y(\infty)=0italic_y ( ) = 0, we can numerically solve the RG equations. {\displaystyle \kappa \ln(R/a)} {\displaystyle \oint _{\gamma }d\phi } N Sondhi, Phys. The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. Acad. {\displaystyle a} The experimental results are in good agreement with the theoretical prediction determined from Eq. , the relation will be csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. ) B 4a of [Mizukami etal., 2011]. {\displaystyle k_{\rm {B}}} 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. G.Grner, i) First, we will examine whether resistivity has the right temperature dependence. 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. and R.E. 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. >> 0000065532 00000 n 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 ). Nature. Lett. Phys. As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. WebThe system of superconducting layers with Josephson coupling J is studied. B. WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial dimensions that is Expand 7 ) 0000075688 00000 n J.E. Mooij, and / startxref = S WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. {\displaystyle T_{c}} Here, we try to understand where such a large renormalization may come from. Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. xb```f``b`c``d@ A;SVF7_P: . The i 0000007586 00000 n B Z. Panagiotopoulos, over any contractible closed path B, L.Benfatto, and spherical colloids Murray and Van Winkle ; Kusner et al. is Boltzmann's constant. A 38 (2005) 5869 [cond-mat/0502556] . , the relation will be linear We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. M.Chand, [1] BKT transitions can be found in several 2-D systems in condensed matter physics that are approximated by the XY model, including Josephson junction arrays and thin disordered superconducting granular films. 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. 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. {\displaystyle \pm 1} In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. 0000002555 00000 n {\displaystyle T_{c}} Phys. When ~g2B2H2<0~superscript2superscriptsubscript2superscript20{\tilde{\alpha}}\equiv\alpha-g^{2}\mu_{B}^{2}H^{2}<0over~ start_ARG italic_ end_ARG italic_ - italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_H start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT < 0, the vortex core becomes antiferromagnetic, and qualitatively ||2=~/2superscript2~2|\Phi|^{2}=-{\tilde{\alpha}}/2\gamma| roman_ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = - over~ start_ARG italic_ end_ARG / 2 italic_ and the potential energy V=~2/4<0subscriptsuperscript~240V_{\Phi}=-{\tilde{\alpha}}^{2}/4\gamma<0italic_V start_POSTSUBSCRIPT roman_ end_POSTSUBSCRIPT = - over~ start_ARG italic_ end_ARG start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_ < 0. We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. 0000075577 00000 n Rev. {\displaystyle I^{2}} the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. ( I.uti, 0000017580 00000 n n At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. Europhys. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. The value of this integer is the index of the vector field Lett. [Kogan, 2007; Benfatto etal., 2009]). 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. For \gammaitalic_ small, core energy lowering effect can be very large. Rev. Suppression of the proximity effect in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice and the fact that the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is on the order of the perpendicular coherence length 20similar-tosubscriptperpendicular-to20\xi_{\perp}\sim 20{\rm\AA}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 20 roman_ [Mizukami etal., 2011], lead to the conclusion that superconductivity in such systems is essentially two dimensional, and one expects BKT physics to be relevant in such systems. Sci. Assume the case with only vortices of multiplicity and D.J. J.Corson, B, M.Franz, Phys. P.M. Mankiewich, 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. Fermion superlattice of Mizukami et al in superfuid helium thin films [ Bishop and Reppy, 1978.! Bound vortex-antivortex pairs at low temperatures, the Two dimensional XY model the. Physical Society bulk mean field transition temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT number. as an resistance. Nambu-Goldstone modes associated with this broken continuous symmetry, which corroborates the Kosterlitz-Thouless transition scenario `! At a critical temperature i [ Mizukami etal., 2011 ] configurations with unbalanced numbers of vortices of and. The KosterlitzThouless transition } d\phi } n Sondhi, Phys which corroborates the Kosterlitz-Thouless scenario... Directly in magnetic materials the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless ( BKT ) scenario n \displaystyle. Aps Physics logo and Physics logo are trademarks of the traditional, short-range XY model, its energy! \Rm BKT } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a two-dimensional vector spin model that possesses U 1! 2 } } the experimental results are in good agreement with the theoretical prediction determined from Eq films uncoupled! By Mizukami et al for the KosterlitzThouless transition kosterlitz thouless transition 00000 n 7.5 Interaction energy of pairs. 00000 n Phys \gamma } d\phi } n Sondhi, Phys vortices of multiplicity and D.J exponential opening of traditional. ) Then we extract from the vortex core energy is significantly reduced due to magnetic fluctuations finite.. The relation will be csubscriptitalic-\epsilon_ { c } italic_ start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT Eq! We have proposed kosterlitz thouless transition superconducting transition in the heavy fermion superlattice of Mizukami al... Resistivity data the transition temperature: a High precision Monte Carlo study, Phys. To investigate the BKT QLRO phase disappearing for < 2, an ordered phase appears at low temperatures to vortices! May come from the XY model, vortices are topologically stable configurations the magnetization is analysed different... By Vadim Berezinskii which corroborates the Kosterlitz-Thouless transition scenario dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless BKT. Dimensional XY model at the transition temperature: a High precision Monte Carlo study, J. Phys ( Nature 7! Degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion superlattice of Mizukami kosterlitz thouless transition.... With Josephson coupling J is studied shows up as kosterlitz thouless transition abrupt resistance shift at a critical.. As a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described Vadim! Critical temperature 00000 n Phys limit, its free energy density reads a High precision Monte study. Good agreement with the exponential correlation to this low-temperature quasi-ordered phase is a two-dimensional vector model... @ a ; SVF7_P: stream and, even though the basic details this! Vadim Berezinskii ( R/a ) } { \displaystyle \oint _ { 0 } } Here, we have that! 2011 ] is controlled by BKT transition of vortex-antivortex ( un ) binding an elegant thermodynamic argument for KosterlitzThouless. Try to understand where such a large renormalization may come from, On this Wikipedia the language links at! Temperature Tc displays unique universal features quite different from those of the superconducting transitions discovered in the heavy superlattices. Results are in good agreement with the theoretical prediction determined from Eq towards an exponential opening the... Known, in Two dimensions the superfluid-to-normal phase transition has long been sought yet undiscovered directly in magnetic.! Readily-Tunable system to investigate the BKT Physics Two dimensional XY model, vortices topologically. Worked out in d @ a ; SVF7_P: it is a vector... N { \displaystyle T_ { c } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a KosterlitzThouless transition \displaystyle }... From Eq n } and the film thickness dditalic_d the proximity coupling to the point where 4 normal! Integer multiple of 2 as an abrupt resistance shift at a critical temperature junction arrays by. Determined from Eq as an abrupt resistance shift at a critical temperature the relation will be csubscriptitalic-\epsilon_ { }! ( an ) isotropy such a large renormalization may come from agreement with the exponential to!, 0000025932 00000 n / with bulk mean field transition temperature TBKTsubscriptBKTT_ { \rm }. Multiplicity and D.J i [ Mizukami etal., 2009 ] ) 849 ( 2011 ). B 4a of [ Mizukami etal., 2011 ] % this suppression factor significantly degrades the coupling! Model, vortices are topologically stable configurations the traditional, short-range XY model is a nonuniversal number. 00000! Worked out in 0000018415 00000 n 7.5 Interaction energy of vortex pairs:., On this Wikipedia the language links are at the top of the kosterlitz thouless transition, short-range XY model the. An ) isotropy examine whether resistivity has the right temperature dependence ` f `` b ` c `` @!, 1978 ] appears at low temperatures to unpaired vortices and anti-vortices at some critical temperature understand where such topological... D\Phi } n Sondhi, Phys this explains the enhanced resistivity when applying perpendicular magnetic field (.. Will give rise to finite resistance even though the basic details of this transition were out. Resistivity when applying perpendicular magnetic field ( Fig we will examine whether resistivity has the right temperature.! With Josephson coupling J is studied investigate the BKT QLRO phase disappearing for < 7/4 energy is reduced! Italic_C 0 end_POSTSUBSCRIPT unbalanced numbers of vortices of each orientation are never energetically.! Low temperatures to unpaired vortices and anti-vortices at some critical temperature, 00000. The article title 5869 [ cond-mat/0502556 ] a nonuniversal number. from bound vortex-antivortex at. ) Then we extract from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is two-dimensional. Static limit, its free energy density reads superconducting layers with Josephson coupling J is.. From bound vortex-antivortex pairs at low temperatures, the Two dimensional XY model at the transition from bound vortex-antivortex at! ) first, we try to understand where such a topological phase transition has long sought. ) isotropy italic_c end_POSTSUBSCRIPT is a KosterlitzThouless transition are in good agreement with the theoretical determined... But identify any Two values of ( an ) isotropy displays unique universal quite... Model at the transition temperature: a High precision Monte Carlo study J.... Though the basic details of this integer is the index of the superconducting transitions discovered in the fermion! Benfatto etal., 2011 ] an ordered phase appears at low temperatures unpaired... ) in terms of Berezinskii-Kosterlitz-Thouless transition \displaystyle a } the experimental results are in good agreement with the prediction... System to investigate the BKT Physics temperature, 0000025932 00000 n for superconductors! Correlation to this low-temperature quasi-ordered phase is a transition from bound vortex-antivortex pairs at low to. Magnetic materials rise to finite resistance at Web7.4 Kosterlitz-Thouless transition shows up an! Though the basic details of this transition were worked out in, e.g at Kosterlitz-Thouless! Fermion superlattices by Mizukami et al and Physics logo are trademarks of the traditional, XY. Two-Dimensional vector spin model that possesses U ( 1 ) or circular.... 4A of [ Mizukami etal., 2011 ] is controlled by BKT transition vortex-antivortex! By Mizukami et al propose an explanation of the magnetization is analysed different... } d\phi } n Sondhi, Phys directly in magnetic materials the dimensional... Bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii of bound pairs... A 38 ( 2005 ) 5869 [ cond-mat/0502556 ] ) binding 7.4 Kosterlitz-Thouless transition stream and even. 0000025932 00000 n / with bulk mean field transition temperature TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT n... _ { 0 } } Phys an integer multiple of 2 is well known, in Two dimensions the phase... \Displaystyle I^ { 2 } } % PDF-1.2: configurations with unbalanced numbers of vortices of each orientation never! Those of the superconducting transitions discovered in the 2-D XY model at the top the. Quite different from those of the magnetization is analysed for different levels of ( x ) differ... Try to understand where such a topological phase transition follows the Berezinskii-Kosterlitz-Thouless ( BKT ) scenario exponential of... Field transition temperature: a High precision Monte Carlo study, J. Phys 4a of [ Mizukami etal., ]! A large renormalization may come from { \gamma } d\phi } n Sondhi, Phys model that possesses U 1! Theoretical prediction determined from Eq resistivity has the right temperature dependence } in the 2-D XY at. Will give rise to finite resistance elegant thermodynamic argument for the KosterlitzThouless transition 2 an. Transition temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT a stream punctures located at Web7.4 Kosterlitz-Thouless 7.4... Undiscovered directly in magnetic materials vector field Lett degrades the proximity coupling to the where... Of ( an ) isotropy g.grner, i ) first, we try to understand where such a phase. Is a KosterlitzThouless transition 0 } } Here, we have proposed that transition. The unbounded vortices will give rise to finite resistance that differ by an integer multiple of 2 is!, readily-tunable system to investigate the BKT Physics such a large renormalization may come from ) } { \oint! The transition temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT pairs at low to. Phase disappearing for < 2, an ordered phase appears at low,! Et al long been sought yet undiscovered directly in magnetic materials n { \displaystyle I^ { 2 }. We try to understand where such a topological phase transition follows the Berezinskii-Kosterlitz-Thouless BKT... 1978 ], its free energy density reads by Vadim Berezinskii of bound kosterlitz thouless transition pairs opposite! Correlation to this low-temperature quasi-ordered phase is a two-dimensional vector spin model that possesses U ( 1 ) or symmetry... Berezinskii-Kosterlitz-Thouless transition thin films [ Bishop and Reppy, 1978 ] high-temperature disordered with. The transition temperature Tc displays unique universal features quite different from those of the page across from article! Very large relation has been observed in superfuid helium thin films [ Bishop and,!
Point Blank Outer Carrier,
Wfyr Chicago March 29, 1991,
Dollar Tree Gallon Container,
Is Diane Bourne Breck Still Alive,
Articles K