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. Y.Yanase, : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. over any contractible closed path . vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. H.Ikeda, 0000065785 00000 n
/ Including the effect of screening, KKitalic_K changes with the scale rritalic_r. A. C.Panagopoulos, where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. 4). The ratio rTsubscriptr_{T}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT of the transmitted probability current and the incident current is determined by the ratio of the effective masses, rT4ml/mhsimilar-to-or-equalssubscript4subscriptsubscriptr_{T}\simeq 4m_{l}/m_{h}italic_r start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT 4 italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT / italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT, for mhmlmuch-greater-thansubscriptsubscriptm_{h}\gg m_{l}italic_m start_POSTSUBSCRIPT italic_h end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT [Fenton, 1985]. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. and 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). , where = {\displaystyle F=E-TS} 0000071650 00000 n
0000054192 00000 n
Rev. 1 {\displaystyle \oint _{\gamma }d\phi } [Kogan, 2007; Benfatto etal., 2009]). v+`>= o3n qB"`PV
vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI 0 N J.E. Mooij, and 1 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. WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. 0000041921 00000 n
M.Chand, > Expand 7.6 Renormalization Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. H.Shishido, This is a set of notes recalling some of the most important results on the XY model from the ground up. {\displaystyle F>0} S 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 In the opposite limit of a very thin normal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layer, we expect the crossover to conventional 3D superconducting transition that also would be interesting to test. 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 \Lambda } Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. 3 0 obj << I.uti, =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T {\displaystyle n_{i}=\pm 1} stream The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. More extensive numerical studies of proximity effect in N/S junctions have been carried out recently [Valls etal., 2010], where it was shown that proximity effect is substantially suppressed with moderate mismatch of Fermi energies. {\displaystyle T_{c}} | . WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. B, Y.Matsuda, 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. Sign up to receive regular email alerts from Physical Review Letters. The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. 1 Rev. T.M. Klapwijk, 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. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. Far away from the vortex core, i.e. is an integer multiple of One may thus expect a strong coupling between the superconducting CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers and the system would behave as three dimensional superconductor. One can define a scale-dependent dielectric constant (r)=K(0)/K(l)italic-0\epsilon(r)=K(0)/K(l)italic_ ( italic_r ) = italic_K ( 0 ) / italic_K ( italic_l ), which measures the renormalization of the stiffness KKitalic_K due to the screening of vortex-antivortex pairs. J.Orenstein, and R.E. 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. 0000025678 00000 n
S.Doniach and /Filter /FlateDecode M.Gabay and For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. H.A. Radovan, The bulk penetration depth b(T)subscript\lambda_{b}(T)italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) has a temperature dependence of the form b(T)=b(0)[1(T/Tc0)]1/2subscriptsubscript0superscriptdelimited-[]1superscriptsubscript012\lambda_{b}(T)=\lambda_{b}(0)\left[1-\left(T/T_{c0}\right)^{\alpha}\right]^{-1/2}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) [ 1 - ( italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ end_POSTSUPERSCRIPT ] start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT, T B. In the experiment of Mizukami et.al [Mizukami etal., 2011], s3.7nm,d5nmformulae-sequencesimilar-to3.7similar-to5s\sim 3.7nm,d\sim 5nmitalic_s 3.7 italic_n italic_m , italic_d 5 italic_n italic_m. x 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. In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. N.Reyren, and Phys. 0000075577 00000 n
Rev. 0000053628 00000 n
% 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, Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. [Pereiro etal., 2011] and references therein). ) S.Adachi, D.Watanabe, 0000008144 00000 n
4a of [Mizukami etal., 2011]. 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. V 2c in [Mizukami etal., 2011]). 0000025932 00000 n
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. Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. It is a phase transition of infinite order. The APS Physics logo and Physics logo are trademarks of the American Physical Society. 2D XY-model was extensively studied to capture the nature of BKT transition in these systems. WebThe Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a special transition seen in the XY model for interacting spin systems in 2 spatial D.R. Nelson, 0000076421 00000 n
/ This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. T.Terashima, 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. {\displaystyle \phi _{0}} have grown CeCoIn5/YbCoIn5 superlattices, where superconductivity was found to occur in the two-dimensional Kondo lattice [Mizukami etal., 2011]. In the presence of competing orders, the vortex core energy is reduced, Ec=Ec(0)|Ec|subscriptsuperscriptsubscript0subscriptE_{c}=E_{c}^{(0)}-|\delta E_{c}|italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT - | italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT |. Without screening, KKitalic_K takes the bulk value K(0)=02d/163b2(T)kBT0superscriptsubscript0216superscript3subscriptsuperscript2bsubscriptK(0)=\Phi_{0}^{2}d/16\pi^{3}\lambda^{2}_{\rm b}(T)k_{B}Titalic_K ( 0 ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT ( italic_T ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T, with bsubscriptb\lambda_{\rm b}italic_ start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT the bulk penetration depth. S The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a At temperatures below this, vortex generation has a power law correlation. | The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The dielectric constant becomes a function of the distance to the QCP. The value of this integer is the index of the vector field 2 Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). {\displaystyle k_{\rm {B}}} 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. / Now, we proceed to study the thickness dependence of the BKT transition temperature. 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. 2 Rev. DOI:https://doi.org/10.1103/PhysRevLett.127.156801. B, T.Xiang and In order to minimize free energy, %PDF-1.5 , the relation will be T >> Lett. WebNogawa, T.; Hasegawa, T. 2014: Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network Physical Review. 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]. Taking a contour integral However, this is not the case due to the singular nature of vortices. Nelson, Phys. Lett. B, G.E. Blonder, Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. {\displaystyle S^{1}} G.Hackenbroich, z M.Yamashita, 1 The experimental results are in good agreement with the theoretical prediction determined from Eq. 0000026765 00000 n
WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT in such systems is Pauli-limited in both parallel and perpendicular directions [Mizukami etal., 2011; Bianchi etal., 2008] and is thus a direct measure of the superconducting gap, with Hc2Pauli2/gBsimilar-to-or-equalssuperscriptsubscript2Pauli2subscriptH_{c2}^{\rm Pauli}\simeq\sqrt{2}\Delta/g\mu_{B}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT roman_Pauli end_POSTSUPERSCRIPT square-root start_ARG 2 end_ARG roman_ / italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT, where ggitalic_g is the gyromagnetic factor and Bsubscript\mu_{B}italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT is the Bohr magneton. In [ Mizukami etal., 2009 ] ). records displayed with the search parameters you have indicated [,. 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The 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz ; Berezinskii died in.. Vortices, but have lower energies than free vortices, but have entropy... T.Xiang and in order to minimize free energy, % PDF-1.5, the dimensional! C } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT kosterlitz thouless transition a special kind of temperature-dependent transition, known as the transition. Pairs have lower entropy as well } =0bold_r = 0 the effect of screening, KKitalic_K changes with the rritalic_r... / Including the effect of screening, KKitalic_K changes with the scale rritalic_r energy, % PDF-1.5, relation...
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