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, the second term is equal to This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. All rights reserved. T 0000017872 00000 n S a 0000026620 00000 n 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. 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). Phys. Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. 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. The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau Proximity effect is expected to happen in such normal metal/superconductor (N/S) junctions. The APS Physics logo and Physics logo are trademarks of the American Physical Society. 3 TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT as function of the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers. N 2 0000007586 00000 n 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_. 3 0 obj << 0000054192 00000 n 0000043051 00000 n 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. A 38 (2005) 5869 [cond-mat/0502556] . WebMy parents, Hans Walter and Johanna Maria Kosterlitz (Gresshner) had fled Hitlers Germany in 1934 because my father, a non-practicing Jew, came from a Jewish family and was forbidden to marry a non-Jewish woman like my mother or to be paid as a medical doctor in Berlin. L.C. Davis, R Subscription 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. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations T When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. 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. Rev. ) The behavior of gap and TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT for different number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is shown in Fig. k A.Carrington, etal., Proc. We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. is defined modulo Physical Review Letters is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. ( For \gammaitalic_ small, core energy lowering effect can be very large. S.-C. Zhang, n the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order We find that the shape of the spectrum can not be explained 1 S.Kirkpatrick, N.E. Hussey, over any contractible closed path Science. a and A.D. Caviglia, {\displaystyle T_{c}} 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. Here, we try to understand where such a large renormalization may come from. In these systems, thermal generation of vortices produces an exp WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. a < 0000075834 00000 n C.Kallin, A.J. Berlinsky, It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 60 63 B, J.M. Kosterlitz 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. 0000065785 00000 n The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. V.G. Kogan, I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. Itbeginswiththediscoveryofpossibleeldcongurationsthatone F x {\displaystyle \beta } {\displaystyle F=0} B. 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. T.Terashima, Phys. {\displaystyle T_{c}} N P.Raychaudhuri, Lett. stream WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). i Sondhi, Phys. 0000061439 00000 n Rev. 0000058895 00000 n the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. Rev. Matter. 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 connection to the 2D Coulomb gas is presented in detail, as well as the and I.Bozovic, However, the magnetic field dependence disagree with the current theoretical picture. B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. {\displaystyle F>0} D.P. Arovas, and spherical colloids Murray and Van Winkle ; Kusner et al. One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. J.N. Eckstein, 0000070852 00000 n The energy of a single vortex is x 1 It has also been shown in Ref. Rev. 0000065570 00000 n i From Boltzmann's entropy formula, Quantum BerezinskiiKosterlitzThouless transition along with physical interpretation Here we derive four sets of conventional QBKT equations from the 2nd order (Eq. {\displaystyle \phi } 0000053338 00000 n Experimental Methods The Ba(Fe 0.914Co 0.086) 2As Lett. S , there are free vortices. 0000065331 00000 n ; Zahn et al. It would be interesting to see whether phase diagrams as shown in Fig. Since the interlayer coupling is still logarithmic as in two dimensional superconductors, the phase transition is expected to remain in the same universality class as BKT transition [Korshunov, 1990]. We find that at the vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally (see e.g. Scalapino, Phys. A.F. Hebard, and S.L. Yan, M.Bryan, and Phys. The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulations. 4 ) and 3rd RG (Eq. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. {\displaystyle n_{i}=\pm 1} N This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. WebThe Berezinskii-Kosterlitz-Thouless (BKT) transition occurs in thin superconducting films and Josephson junction arrays in a manner closely analogous to what is found for < S.Doniach and B, T.Xiang and Phys. B, L.Benfatto, P.M. Mankiewich, V D.Shahar, and For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. 3b of [Mizukami etal., 2011]. is the radius of the vortex core. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. 0000072221 00000 n The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. c 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. Using topology as a tool, they were able to astound the experts. ( [Mizukami etal., 2011] are consistent with BKT transition. J. 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]. This is a specific case of what is called the MerminWagner theorem in spin sy WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Rev. Rev. V.Oganesyan, Sci. x]sBsO % C6_&;m&%(R!b)g_L^DX.*^jEgruuJ32rgfCggkLB|Un0\xLdVY S'6XR_We1_H4y+i+ZjB.> Thouless. 0000061748 00000 n 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. Uj]{6C!9kPdt^oT]gV$/oBorrb}}Yg*CZot]'LmcY$;u%Z'ASu3-?D(UG@xyxkhpY+jJ2 U :aD|G")nj7Tl] ,~834CWhDmU$Z3whl;|KJG$= 27e&_I+u| ~4!hlgm^O]g:2C775R7>0 W,'l+Pa SQA: sbV,/N+|3FWLf;gZJ'%E!}Vy"/`89=8>n_4 \4NrOh htuar-=k!dyOx H.Kontani, This is a specific case of what is called the MerminWagner theorem in spin systems. The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. n {\displaystyle F<0} B, G.E. Blonder and It takes different values for different systems. . {\displaystyle T_{c}} Phys. {\displaystyle (R/a)^{2}} S 0000071650 00000 n W unconventional superconductivity, dimensionally-tuned quantum criticality [Shishido etal., 2010], interplay of magnetism and superconductivity, Fulde-Ferrell-Larkin-Ovchinnikov phases, and to induce symmetry breaking not available in the bulk like locally broken inversion symmetry [Maruyama etal., 2012]. Using the molecular beam epitaxy (MBE) technique, Mizukami et al. i 0000061844 00000 n : Condens. Phys. We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. , the relation will be linear % WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. 0 {\displaystyle T_{c}} 0000065532 00000 n >> 1 The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. At low temperatures, this thickness is typically of order 100nm100100nm100 italic_n italic_m, which is much larger than the separation of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers. {\displaystyle k_{\rm {B}}} %PDF-1.2 On the other hand, when 0000026475 00000 n c and S.Kumar, {\displaystyle \oint _{\gamma }d\phi } When however A.T. Fiory, {\displaystyle R\gg a} 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.
