) K.Yasu, 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. Using the molecular beam epitaxy (MBE) technique, Mizukami et al. where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. etal., Proc. InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. 0000065331 00000 n
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. 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. Expand 7.6 Renormalization S 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. j c The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. =QDhSCe/. J.D. Reppy, {\displaystyle \kappa \ln(R/a)} 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. C.Petrovic, 0000053919 00000 n
v+`>= o3n qB"`PV
vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI {\displaystyle \nabla \phi } The A.Johansson, 0000018171 00000 n
, as the number of free vortices will go as 1. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. , it has no physical consequences. {\displaystyle a} Phys. winds counter-clockwise once around a puncture, the contour integral y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. , the system will not have a vortex. Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. . M.Tinkham, and [Fenton, 1985]. A.Petrovic, The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. . 5(a)). z 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. B, A.Serafin, 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. A.J. Berlinsky, 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 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). = This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. 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. 0000065570 00000 n
In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. , which is the total potential energy of a two-dimensional Coulomb gas. A.D. Caviglia, The connection to the 2D Coulomb gas is presented in detail, as well as the To export a larger list you will need to increase the number of results per page. 0000070852 00000 n
The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. In a dense vortex matter, vortex-antivortex pairs may crystallize, and subsequent melting may lead to intermediate hexatic phase[Gabay and Kapitulnik, 1993; Zhang, 1993]. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. Europhys. 0000043510 00000 n
The superuid transition in 2D is the-oretically understood within the Berezinskii-Kosterlitz-Thouless (BKT) general framework [35]; the character-istic ngerprint of the BKT transition is the so-called universal jump of the superuid fraction s(T) as a function of temperature, from zero to a nite value as Tc 0000053338 00000 n
The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. exp 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. R Lett. Matter. On the other hand, when The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. In the following, we are going to check whether the experimental findings of Mizukami et al. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. , there are free vortices. i 0000071650 00000 n
C.Kallin, and Though implications have been found in numerous thin superconducting films [Minnhagen, 1987; Fiory etal., 1988; Davis etal., 1990; Matsuda etal., 1993; Crane etal., 2007], highly anisotropic cuprates [Wen etal., 1998; Corson etal., 1999; Li etal., 2005], oxide interfaces [Reyren etal., 2007; Caviglia etal., 2008; Schneider etal., 2009], the results have remained inconclusive (see e.g. /Length 4 0 R And, even though the basic details of this transition were worked out in 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 0000074018 00000 n
( Phys. 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. {\displaystyle F<0} Use of the American Physical Society websites and journals implies that We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. The specic heat only has a broad hump at temperatures somewhat above T KT, where Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. F Above the critical temperature, proliferation of unbound vortices is expected. 4). B, O.T. Valls, Phys. (4) in the main text), which is universal in the sense that, different from csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, this relation is identical for different systems. H.Ikeda, Note added: While this work was under review, we received a preprint by Fellows et al. This holds for classical models {\displaystyle 1/\Lambda } punctures located at 0000070606 00000 n
Itbeginswiththediscoveryofpossibleeldcongurationsthatone with Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT the bulk superconducting transition temperature, 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT the BCS coherence length, and \nuitalic_ a number of order unity. The complex argument function has a branch cut, but, because z We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed 0 E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 0000053029 00000 n
0 of the KosterlitzThouless transition. S.Komiyama, J.M. Wheatley, It has also been shown in Ref. From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. The unbounded vortices will give rise to finite resistance. c 0000027382 00000 n
Lett. i The combination of f-electron physics, low dimensionality and interface effects provides a rare opportunity to study new states in strongly correlated electron systems, e.g. Rev. 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, S.Doniach and H.Shishido, From Boltzmann's entropy formula, Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. At T=TBKT,r=formulae-sequencesubscriptBKTT=T_{\rm BKT},r=\inftyitalic_T = italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT , italic_r = , the scale-dependent dielectric constant becomes of the form (r=,TBKT)=02d/322b2(TBKT)kBTBKTcitalic-subscriptBKTsuperscriptsubscript0232superscript2subscriptsuperscript2bsubscriptBKTsubscriptsubscriptBKTsubscriptitalic-\epsilon(r=\infty,T_{\rm BKT})=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}_{\rm b}(T_{\rm BKT})k_{B}T_{\rm BKT}\equiv\epsilon_{c}italic_ ( italic_r = , 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 start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT ( italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. >> It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. is the system size, and and D.J. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature TBKT. This is generically observed for a BKT transition, and is attributed to the temperature difference between the formation of single vortices and the subsequent vortex condensation (see e.g. . WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. For such systems, one thus has Tc=TBKTsubscriptsubscriptBKTT_{c}=T_{\rm BKT}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. One can thus tune the vortex fugacity by changing the distance to the QCP. {\displaystyle S^{1}} The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau Rev. Near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, where both Hc2H_{c2\parallel}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT and Hc2subscriptperpendicular-to2absentH_{c2\perp}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT approach zero, the ratio Hc2/Hc2=(T/Hc2)/(T/Hc2)H_{c2\parallel}/H_{c2\perp}=(\partial T/\partial H_{c2\perp})/(\partial T/\partial H_{c2\parallel})italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT = ( italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT ) / ( italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT ) thus diverges, as seen in Fig. n Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. 0000075688 00000 n
We observe that the effective mass mismatch between the heavy fermion superconductor and the normal metal regions provides an effective barrier that enables quasi 2D superconductivity in such systems. Agreement. {\displaystyle T_{c}} We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. 0000002770 00000 n
L Soc. Kosterlitz jump for a BKT transition is demonstrated. | Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, 1 T.M. Klapwijk, When the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is large, d>(T)d>\xi(T)italic_d > italic_ ( italic_T ), the areas of defect-depressed order parameter do not overlap, and the gap is not affected by the defects. 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]. 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. Sondhi, Phys. = a D.P. Arovas, 0000018415 00000 n
arXiv:1205.1333v1 [cond-mat.str-el]. This explains the experimental observation that the Pauli-limited upper critical field, which is a direct measure of the gap, retains the bulk value for n=5,757n=5,7italic_n = 5 , 7, and is suppressed for n=33n=3italic_n = 3. {\displaystyle -2\pi \sum _{1\leq i
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