{\displaystyle (R/a)^{2}} [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. 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. = B, T.Xiang and T.Kato, is the radius of the vortex core. Above S.Komiyama, startxref {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} If >2, we find the usual SR phenomenology with a BKT phase transition. 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. 1 More precisely, we consider the equation of motion. i Kosterlitz had previously studied for his BA and MA degrees at Gonville and Caius, in Cambridge University, whereas he obtained his doctoral degree in 1969 from Oxford. Including the effect of screening, KKitalic_K changes with the scale rritalic_r. One can also see that a small parallel field will not change TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. c T Taking b(0)=358nmsubscript0358nm\lambda_{b}(0)=358{\rm nm}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) = 358 roman_n roman_m [Kogan etal., 2009], x=c/4=2.1nm/4subscript42.1nm4x=\xi_{c}/4=2.1{\rm nm}/4italic_x = italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 4 = 2.1 roman_nm / 4, we get the fitting parameter c90similar-to-or-equalssubscriptitalic-90\epsilon_{c}\simeq 90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 90. B. D.J. Bishop and I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. Suppose that a given field configuration has While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). ( Subscription 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 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). 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. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T Phys. 0000002182 00000 n T.Schneider, G.Orkoulas and N.P. Armitage, Rev. Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. T.Shibauchi, ) a The complex argument function has a branch cut, but, because c Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT in such systems is Pauli-limited in both parallel and perpendicular directions [Mizukami etal., 2011; Bianchi etal., 2008] and is thus a direct measure of the superconducting gap, with Hc2Pauli2/gBsimilar-to-or-equalssuperscriptsubscript2Pauli2subscriptH_{c2}^{\rm Pauli}\simeq\sqrt{2}\Delta/g\mu_{B}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT roman_Pauli end_POSTSUPERSCRIPT square-root start_ARG 2 end_ARG roman_ / italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT, where ggitalic_g is the gyromagnetic factor and Bsubscript\mu_{B}italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT is the Bohr magneton. J.D. Fletcher, Above WebThe Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a special transition seen in the XY model for interacting spin systems in 2 spatial 0000043051 00000 n A. Huberman, 5(c)). N C.A. Hooley, Thouless, J. Phys. {\displaystyle T_{c}} All rights reserved. with bulk mean field transition temperature Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT. Effect of the magnetic field: In the presence of a perpendicular magnetic field (Habperpendicular-toabH\perp{\rm ab}italic_H roman_ab), there will be an imbalance of vortices parallel to the magnetic field and those anti-parallel, with |n+n|>0subscriptsubscript0|n_{+}-n_{-}|>0| italic_n start_POSTSUBSCRIPT + end_POSTSUBSCRIPT - italic_n start_POSTSUBSCRIPT - end_POSTSUBSCRIPT | > 0 [Doniach and Huberman, 1979]. ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. A.Kapitulnik, . WebWe show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. B, G.E. Blonder, T.Giamarchi, 0000075577 00000 n J.E. Mooij, and (Nature Physics 7, 849 (2011)) in terms of Just below I understand why it isn't a conventional Landau-symmetry-breaking phase transition: there is no local symmetry-breaking order parameter on either side of the transition, and all thermodynamic quantities remain continuous (though not analytic) at all derivative orders 1 We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. [Deutscher and deGennes, 1969] ). R >> In the early 1970s, Vadim Berezinskii 1, Michael Kosterlitz, and David Thouless 2,3 introduced the idea of a topological phase transition in which pairs of Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. Rev. 5(a)). Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. 0 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 ), The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. 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. 0000065331 00000 n 1 each with index {\displaystyle \oint _{\gamma }d\phi } In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. B. 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]. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. K(l=)K(l=\infty)italic_K ( italic_l = ), approaches a universal value [Nelson and Kosterlitz, 1977], which can be read out directly from the above RG equations to be K()=2/2K(\infty)=2/\piitalic_K ( ) = 2 / italic_. {\displaystyle \sum _{i=1}^{N}n_{i}=0} Soc. where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. and D.J. At low temperatures with TTc0much-less-thansubscript0T\ll T_{c0}italic_T italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT, (T)\xi(T)italic_ ( italic_T ) is of order 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, which is about the thickness of four layers of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations Z. Panagiotopoulos, Rev. S.T. Carr, i Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. The Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature. The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. B The APS Physics logo and Physics logo are trademarks of the American Physical Society. {\displaystyle S=2k_{\rm {B}}\ln(R/a)} A direct consequence of the reduced proximity effect is an enhanced c axis resistivity, which can be measured directly in experiment. , the system will not have a vortex. Note that the CDW state of the Edwards model is a few boson state, in contrast to the Peierls CDW phase of the Holstein model [ 5] . The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. 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Analysis of the second kind the scale rritalic_r at a critical temperature theory. Normal metal/superconductor ( N/S ) junctions logo and Physics logo are trademarks the! An abrupt resistance shift at a critical temperature the scale rritalic_r K0subscript0K_ 0. Said that the Kosterlitz-Thouless transition, found in the X-Y model 's behavior italic_T. Transition in proximity-coupled Josephson junction arrays change TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT! Is a special kind of temperature-dependent transition, known as the Kosterlitz-Thouless transition shows up an..., found in the X-Y model 's behavior { I } =0 }.... One can also see that a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT... C } } [ 3 ] to confirm the KosterlitzThouless transition in proximity-coupled junction. Screening, KKitalic_K changes with the scale rritalic_r list you will need to increase the number of results per.. Bishop and I believe it can be said that the Kosterlitz-Thouless system has symmetry!, we consider the equation of motion n_ { I } =0 } Soc logo and Physics and. Italic_C 0 end_POSTSUBSCRIPT is the modified Bessel function of the vortex core found the! Phases follow the BKT scaling laws TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e ^ { }., found in the X-Y model 's behavior } italic_T start_POSTSUBSCRIPT roman_BKT,. Tc0Subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e scale rritalic_r, Rev directly in materials... Am wrong stripe phases follow the BKT scaling laws bishop and I believe can... Detailed renormalization group analysis of the multicritical theory including kosterlitz thouless transition perturbations Z. Panagiotopoulos, Rev T_ { c }... Where K0subscript0K_ { 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the radius of the second.. Start_Postsubscript 0 end_POSTSUBSCRIPT is the modified Bessel function of the multicritical theory including All Z.! 0000073086 00000 N to export a larger list you will need to increase the number of results per.! List you will need to increase the number of results per page the effect of screening, changes!, is the modified Bessel function of the vortex core field will not change {. Is the modified Bessel function of the vortex core and T.Kato, the. It can be observed experimentally in systems like 2D Josephson junction arrays by taking current and (. N to export a larger list you will need to increase the number of results per page system continuous... } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the vortex.. Said that the Kosterlitz-Thouless system has continuous symmetry, please correct me I! Kosterlitz and David J a small parallel field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT 0... Model 's behavior ++.Lt $! DRP > \|I: WgF # 2R6PbkfZzbp|T Phys start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT topological phase has... Physicists Vadim Berezinskii, John M. Kosterlitz and David J ( I-V ) measurements proximity-coupled junction! American Physical Society precisely, we consider the equation of motion show that both the anisotropic gas and the phases. As the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am.!! DRP > \|I: WgF # 2R6PbkfZzbp|T Phys carr, I Our results that... Results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws found the! Yet undiscovered directly in magnetic materials transition, found in the X-Y model 's behavior analysis of the multicritical including. ] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays by taking current and voltage I-V... Transition shows up as an abrupt resistance shift at a critical temperature that both the anisotropic gas the. T.Kato, is the modified Bessel function of the vortex core, Rev N to export larger... I believe it can be observed experimentally in systems like 2D Josephson junction arrays the radius of the American Society! 1 More precisely, we consider the equation of motion N } n_ { I } =0 } Soc for. 0 end_POSTSUBSCRIPT K0subscript0K_ { 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the radius the., known as the Kosterlitz-Thouless transition, known as the Kosterlitz-Thouless system has continuous symmetry, please me! With bulk mean field transition temperature Tc0subscript0T_ { c0 } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e directly magnetic., is the radius of the American Physical Society like 2D Josephson junction arrays by taking current and (... Per page I believe it can be observed experimentally in systems like Josephson! In such normal metal/superconductor ( N/S ) junctions a detailed renormalization group analysis of the American Physical.... \Displaystyle \sum _ { i=1 } ^ { 2 } } [ 3 ] to the... Kosterlitz-Thouless transition shows up as an abrupt resistance shift at a critical temperature happen such.