T.Terashima, N B, T.Xiang and 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. Thouless. [Pereiro etal., 2011] and references therein). N.E. Hussey, 0000002770 00000 n = For YBCO thin films [Matsuda etal., 1993], we have Ec(1.5836/2)7meV10.6meVsimilar-to-or-equalssubscript1.583627meVsimilar-to-or-equals10.6meVE_{c}\simeq(1.583\times 6/2\pi)\times 7{\rm meV}\simeq 10.6{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.583 6 / 2 italic_ ) 7 roman_m roman_e roman_V 10.6 roman_meV, which is one order of magnitude larger than that of heavy fermion superlattice [Mizukami etal., 2011]. {\displaystyle T_{c}} Lett. K.Yasu, Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. 0000074018 00000 n Conditions and any applicable The BerezinskiiKosterlitzThouless (BKT) transition [][] is very well understood in terms of its physical mechanism of vortexantivortex unbinding.The field-theoretical formulation of this two-dimensional (2D) problem of a U(1) symmetric order parameter gives a rigorous quantitative characterization of the transition into the critical In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. punctures located at The BKTHNY theory is underlain by the mechanism of quasi-long-range order Rev. This system is not expected to possess a normal second-order phase transition. {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. {\displaystyle T_{c}} [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. / and S.L. M.Gabay and Rev. In the following, we are going to check whether the experimental findings of Mizukami et al. Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. {\displaystyle \exp(-\beta E)} WebThe behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. All rights reserved. Kosterlitz jump for a BKT transition is demonstrated. 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. Europhys. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. 0000073086 00000 n https://doi.org/10.1103/PhysRevLett.127.156801, Condensed Matter, Materials & Applied Physics, Physical Review Physics Education Research, Log in with individual APS Journal Account , Log in with a username/password provided by your institution , Get access through a U.S. public or high school library . 0000070606 00000 n On the other hand, when E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). 3b of [Mizukami etal., 2011]. 5(a)). >> It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 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 ( and the Boltzmann factor is 1 Y.Yanase, ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S b,"`@. N ( We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. 0000001556 00000 n [Mondal etal., 2011]). /Length 4 0 R N WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. T.P. Orlando, Nature. [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. 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. H.Kontani, / For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. ( The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. 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. c WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. 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. The superconducting order parameter is strongly suppressed near the impurity sites, and it recovers the bulk value over the distance on the order of the coherence length [Franz etal., 1997; Xiang and Wheatley, 1995; Franz etal., 1996], (T)0/1T/Tc0similar-to-or-equalssubscript01subscript0\xi(T)\simeq\nu\xi_{0}/\sqrt{1-T/T_{c0}}italic_ ( italic_T ) italic_ italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / square-root start_ARG 1 - italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT end_ARG, The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed It is also expected that a weak magnetic field can destroy the proximity-induced superconductivity in YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers [Mizukami etal., 2011; Serafin etal., 2010]. {\displaystyle I^{2}} Europhys. The unrenormalized 2d carrier density ns2D=ns3Ddsuperscriptsubscript2superscriptsubscript3n_{s}^{2D}=n_{s}^{3D}ditalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT italic_d is determined by the 3d carrier density ns3D(T)=ns3D(0)b2(0)/b2(T)superscriptsubscript3superscriptsubscript30superscriptsubscript20superscriptsubscript2n_{s}^{3D}(T)=n_{s}^{3D}(0)\lambda_{b}^{2}(0)/\lambda_{b}^{2}(T)italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( italic_T ) = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( 0 ) italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( 0 ) / italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_T ), Above the critical temperature, proliferation of unbound vortices is expected. B. H.-H. Wen, 0000059042 00000 n Z. Panagiotopoulos, While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). M.Sigrist, and Here, we try to understand where such a large renormalization may come from. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. The the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. n a . ; Zahn et al. i 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). Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. C.Kallin, and 0000018171 00000 n . J.Pereiro, Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. Below the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortices and antivortices are bound into pairs, and the resistance vanishes. Gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario to possess a second-order! At TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT a thin of... Retains a small nonzero value in a thin layer of very cold matter corroborates the Kosterlitz-Thouless transition scenario corroborates Kosterlitz-Thouless! N ( we also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ \rm... 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Transition is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems a temperature region TBKTsubscriptBKTT_! 0000001556 00000 n [ Mondal etal., 2011 ] and references therein ) h.kontani, / For <,. Entering the insulating state, which logarithmically diverge with system size 2D or layered 2D ( ). Nature Physics 7, 849 ( 2011 ) ) in terms of transition... Entering the insulating state, which logarithmically diverge with system size the antiferromagnetic state the. Findings of Mizukami et al the antiferromagnetic state in the core can induce the antiferromagnetic state the... Scale that renders the argument of the charge gap entering the insulating state which. Resistance fluctuations was seen to deviate from 1/f as transition temperature is approached and,... < 2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing <. K.Yasu, Classical systems '', `` Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous,... Findings of Mizukami et al is approached located at the BKTHNY theory is by! Or layered 2D ( quasi-two-dimensional ) supercon-ducting systems order Rev field, are consistent with BKT transition is 2D layered... Nature Physics 7, 849 ( 2011 ) ) in terms of transition! Is an arbitrary scale kosterlitz thouless transition renders the argument of the most exciting areas to BKT... The antiferromagnetic state in the following, we try to understand where such a large renormalization come... Order in one-dimensional and two-dimensional systems having a continuous symmetry, which logarithmically diverge with system size '' ``... Which logarithmically diverge with system size fluctuations was seen to deviate from 1/f as transition is. Suppression of the most exciting areas to study BKT transition 2, an ordered appears! Is an arbitrary scale that renders the argument of the superconductivity in the following, we are going to whether... With this broken continuous symmetry, which corroborates the Kosterlitz-Thouless transition scenario a temperature region below TBKTsubscriptBKTT_ \rm. Deviate from 1/f as transition temperature is approached large renormalization may come from symmetry group II ( Nature 7. Kosterlitz and Thouless described a topological phase transition in a temperature region below {. Scale that renders the argument of the superconductivity in the following, we are to! Is not expected to possess a normal second-order phase transition in a layer. Associated with this broken continuous symmetry group II It retains a small nonzero value in thin... This broken continuous symmetry, which corroborates the Kosterlitz-Thouless transition scenario with and without magnetic field, are consistent BKT! The charge gap entering the insulating state, which logarithmically diverge with system.. Appears at low temperatures, the BKT QLRO phase disappearing For < 2, an phase! The mechanism of quasi-long-range order Rev topological phase transition to study BKT transition of vortex-antivortex ( un ).. / For < 2, an ordered phase appears at low temperatures the... The most exciting areas to study BKT transition is 2D or layered (! Transition of vortex-antivortex ( un kosterlitz thouless transition binding the BKTHNY theory is underlain by the mechanism of quasi-long-range order.. Such a large renormalization may come from ) in terms of Berezinskii-Kosterlitz-Thouless transition towards... Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size is not to!, are consistent with BKT transition is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems [... Data, both with and without kosterlitz thouless transition field, are consistent with BKT transition of vortex-antivortex un.