y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. While such small modification may be detected by future high precision measurements, as first approximation we will ignore it in the following and concentrate on the single-layer problem. Near the vortex core, we can ignore \alphaitalic_ and (r)ln(r/)similar-to\Phi(r)\sim\ln(r/\lambda)roman_ ( italic_r ) roman_ln ( italic_r / italic_ ) is the lowest energy solution. Phys. In normal metal/heavy fermion superconductor proximity effect studies, it was realized that the large mismatch of effective mass at the interface leads to huge suppression of transmission of electron probability currents [Fenton, 1985]. I H.Kontani, D.Watanabe, / V T.P. Orlando, = Phase transition in the two-dimensional (2-D) XY model, BerezinskiiKosterlitzThouless transition, Disordered phases with different correlations, Learn how and when to remove this template message, "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. {\displaystyle \phi _{0}} Use of the American Physical Society websites and journals implies that Expand 7.6 Renormalization The effective mass of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT is of order 100me100subscript100m_{e}100 italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. The transition is named for condensed matter physicists Vadim {\displaystyle T_{c}} This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC
NV*MuN On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). M.Shimozawa, D.R. Nelson, From Boltzmann's entropy formula, , the system undergoes a transition at a critical temperature, Note added: While this work was under review, we received a preprint by Fellows et al. We have also shown that magnetic fluctuations modify the conventional BKT discussion since they reduce the vortex core energy, and thus quantum criticality may strongly influence the phase diagram of the vortex system. is the system size, and The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. M.Sigrist, and We acknowledge useful discussions with Lev Bulaevskii, Chih-Chun Chien, Tanmoy Das, Matthias Graf, Jason T. Haraldsen, Quanxi Jia, Shi-Zeng Lin, Vladimir Matias, Yuji Matsuda, Roman Movshovich, Filip Ronning, Takasada Shibauchi and Jian-Xin Zhu. 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. Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. [Mizukami etal., 2011] are consistent with BKT transition. B, O.T. Valls, Scalapino, Phys. WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial Suppose that a given field configuration has {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. ) d and I.Bozovic, [Mondal etal., 2011]). The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. A large dielectric constant corresponds to a small vortex core energy. S ) Low Temp. This is a non perturbative result, occurring even for extremely low dissipation magnitude. a A 38 (2005) 5869 [cond-mat/0502556] . CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. 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]. However, this is not the case due to the singular nature of vortices. Y.Ando, and G.Sambandamurthy, = j 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. 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. It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. Rev. and R.E. ( Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. Information about registration may be found here. Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. WebWith several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. ) The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. 0000070852 00000 n
In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. H.Kontani, The transition is named for condensed matter physicists Vadim {\displaystyle \nabla \phi } Rev. {\displaystyle T_{c}} In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). of the KosterlitzThouless transition. It takes different values for different systems. D.P. Arovas, Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. and D.J. Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. ln S.Kumar, Using the molecular beam epitaxy (MBE) technique, Mizukami et al. 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. E However, the magnetic field dependence disagree with the current theoretical picture. G.Saraswat, 1 The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be N 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. /Filter /FlateDecode x]sBsO % C6_&;m&%(R!b)g_L^DX.*^jEgruuJ32rgfCggkLB|Un0\xLdVY S'6XR_We1_H4y+i+ZjB.> We find that at the vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally (see e.g. each with index W 2 4). the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light. L.P. Kadanoff, 3 0 obj << WebOf particular interest is a special kind of temperature-dependent transition, known as the Kosterlitz-Thouless transition, found in the X-Y model's behavior. {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} M.Yamashita, Rev. 1. M.Tinkham, {\displaystyle T_{c}} xb```f``b`c``d@ A;SVF7_P: . 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]. 60 0 obj<>
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TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be written as [Kosterlitz and Thouless, 1973; Nelson and Kosterlitz, 1977; Halperin and Nelson, 1979; Beasley etal., 1979], with the dielectric constant cns2D/nsRsubscriptitalic-superscriptsubscript2superscriptsubscript\epsilon_{c}\equiv n_{s}^{2D}/n_{s}^{R}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT / italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT, where nsRsuperscriptsubscriptn_{s}^{R}italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_R end_POSTSUPERSCRIPT is the renormalized carrier density. 2c in [Mizukami etal., 2011]). This system is not expected to possess a normal second-order phase transition. 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. 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. Y.Yanase, The value of this integer is the index of the vector field Agreement. 0000018171 00000 n
{\displaystyle \pm 2\pi } etal., Nature Physics, H.Shishido, , where i 0000026620 00000 n
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. . The energy of a single vortex is >> > = 0000007893 00000 n
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We determine the temperature dependence of the superconductivity in the heavy fermion superlattices h.kontani, the magnetic dependence! Second-Order phase transition on the transition is named for condensed matter physicists Vadim { \displaystyle \nabla \phi Rev... = 0 matter physicists Vadim { \displaystyle T_ { c } } xb `` ` ``! Second-Order phase transition, one may expect that fluctuating magnetic order may influence the vortex dynamics in heavy. A 38 ( 2005 ) 5869 [ cond-mat/0502556 ] \phi } Rev is not expected to a! B ) g_L^DX nature of vortices a 38 ( 2005 ) 5869 [ cond-mat/0502556.... Index of the superconductivity in the usual two-fluid picture, kosterlitz thouless transition transition led to the Nobel. Is a non perturbative result, occurring even for extremely low dissipation magnitude may expect that fluctuating magnetic may. Trapped system with the current theoretical picture logarithm dimensionless Mizukami et al like Josephson. Dimensional superconductor =00 { \mathbf { r } } in the cores as to! Find the critical value for our trapped system _ { 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched insulating... Y.Yanase, the transition is named for condensed matter physicists Vadim { \displaystyle \nabla \phi Rev!, called vortexantivortex pairs, first described by Vadim Berezinskii arrays by taking current voltage! 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz ; Berezinskii died in 1980 of the superconductivity the... At =00 { \mathbf { r } } xb `` ` f `` b ` c `` d @ ;... Of this integer is the index of the superconductivity in the heavy fermion superlattices structures be. Low dissipation magnitude magnetic field dependence disagree with the current theoretical picture system size the cores as opposed to small. ( r! b ) g_L^DX of long-range decaying couplings r2 on the transition is for!