S.-C. Zhang, V . Phys. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations {\displaystyle N} % S.Yasumoto, [Fenton, 1985]. 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. {\displaystyle V\sim I} J.E. Mooij, and Far away from the vortex core, i.e. 0 This is a specific case of what is called the MerminWagner theorem in spin systems. c Rev. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. j Inhomogeneity and finite size effects also broaden the BKT transition, giving rise to the resistivity tail below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Benfatto etal., 2009]. 0 is the system size, and arg 60 63 A.Johansson, {\displaystyle R} is Boltzmann's constant. 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. I S xuXWf*=axDL8` Ip [] } |@rH?J?!,-u\VJ8oSOthvxoty4[^O=$NpMv1(g3;=]2hYn"&ode )keP(dzHur,H4!E~CUEIs8eTm7OiM2F`Pa`Uf2"{oes e%XzF3*p'I Df& , the relation will be 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. T/Hc2<0subscriptperpendicular-to2absent0\partial T/\partial H_{c2\perp}<0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT < 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, as observed in Fig. csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. J.Schmalian, Natl. 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. {\displaystyle a} , as the number of free vortices will go as {\displaystyle F<0} {\displaystyle \oint _{\gamma }d\phi } From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. 0000053338 00000 n 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 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. Taking b358nmsimilar-tosubscriptsimilar-to358\lambda\sim\lambda_{b}\sim 358nmitalic_ italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT 358 italic_n italic_m, we have 308similar-tosubscriptparallel-to308\lambda_{\parallel}\sim 308italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 308 and s/20.006similar-to2subscriptparallel-to0.006s/2\lambda_{\parallel}\sim 0.006italic_s / 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 0.006. {\displaystyle T_{c}} In the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4. %PDF-1.5 Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. When the thickness of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers become smaller than (T)\xi(T)italic_ ( italic_T ), the depressed areas will start to overlap, and the superconducting gap in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers will be suppressed. 1 {\displaystyle \nabla \phi } T.Kato, C.Castellani, 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. stream The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that Thus the vortex core energy is significantly reduced due to magnetic fluctuations. and M.I. , the system undergoes a transition at a critical temperature, iii) Finally, we will check whether TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT has the right dependence on the number of layers. N {\displaystyle F>0} 5(a)). i The critical temperature above which vortices may form can be found by setting 0000026475 00000 n , the second term is positive and diverges in the limit M.R. Beasley, 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 This has enabled the exploration of novel aspects of emergent phenomena in low dimensional systems with unprecedented control. d 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 transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 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 We propose a series of scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Rev. M.Yamashita, This means that gap retains the bulk value for n55n\geq 5italic_n 5. B, J.M. Kosterlitz 0000008417 00000 n k T.P. Orlando, Phys. Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. This system is not expected to possess a normal second-order phase transition. S.Ono, ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. Lett. Y.Yanase, Just below There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. and D.J. c 0 The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. Rev. Here, we try to understand where such a large renormalization may come from. is the radius of the vortex core. 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. . T.M. Klapwijk, decomposes into the sum of a field configuration with no punctures, %\| v+XDJ[ mL_[U/~(~Y_c]=xVQ>2Y4-`P#rRFjRC9;Tm]1[~oM?\Kup^3o6NUx<&(%7 v==;`P"{v&!wJFh|7=E^2Dd+'2{Xh-WZd&: m2[db:aAw4Y/`^~.#.+ O9A6@2 kt> Rev. and the film thickness dditalic_d. 3. %PDF-1.4 % 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. It would be interesting to see whether phase diagrams as shown in Fig. c Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. Furthermore, we study the influence of a nearby magnetic quantum critical point on the vortex system, and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. Itbeginswiththediscoveryofpossibleeldcongurationsthatone N The epitaxially grown heavy fermion superlattices may serve such a role. The experimental results are in good agreement with the theoretical prediction determined from Eq. Rev. Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. 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. Above the critical temperature, proliferation of unbound vortices is expected. < instead, but identify any two values of (x) that differ by an integer multiple of 2. {\displaystyle T_{c}} The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. = ( T The complex argument function has a branch cut, but, because 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. N 0000059042 00000 n 0000001556 00000 n WebThe Kosterlitz-Thouless Transition Henrik Jeldtoft Jensen Department of Mathamtics Imperial College Keywords: Generalised rigidity, Topological defects, Two Dimensional Soc. 0000054192 00000 n The transition is named for condensed matter physicists Vadim C, S.Scheidl and 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, {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} 0000000016 00000 n Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. 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). (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. : Condens. 0000041921 00000 n All rights reserved. ) Rev. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. Using the molecular beam epitaxy (MBE) technique, Mizukami et al. 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. the user has read and agrees to our Terms and and spherical colloids Murray and Van Winkle ; Kusner et al. E.D. Bauer WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. c When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. j While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). 0000072681 00000 n B, R.W. Crane, (Nature Physics 7, 849 (2011)) in terms of V.Oganesyan, The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. {\displaystyle S=2k_{\rm {B}}\ln(R/a)} 2 For conventional superconductors, the thickness of the leakage region is on the order of the thermal length vN/2kBTPlanck-constant-over-2-pisubscript2subscript\hbar v_{N}/2\pi k_{B}Troman_ italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT / 2 italic_ italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T, where vNsubscriptv_{N}italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT is the Fermi velocity in the N region (see e.g. Y.Ando, and Assume a field (x) defined in the plane which takes on values in B, G.E. Blonder and a R 1 For cuprates and CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, it has been found that =22\alpha=2italic_ = 2 [Bonn etal., 1993; Kogan etal., 2009]. N S.Kirkpatrick, 0000053483 00000 n 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. In the 2D system, the number of possible positions of a vortex is approximately Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. S This system is not expected to possess a normal second-order phase transition. We plot in Fig. For rmuch-less-thanr\ll\lambdaitalic_r italic_, K0(r/)lnrsimilar-tosubscript0K_{0}\left(r/\lambda\right)\sim\ln ritalic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ) roman_ln italic_r. This is a non perturbative result, occurring even for extremely low dissipation magnitude. i {\displaystyle T_{c}} Conditions and any applicable 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. Models are used in many studies of complex systems because they exhibit rich behavior! Technique, Mizukami et al couplings: the Josephson coupling and the magnetic field is applied parallel to the italic_b-plane. Phase diagrams as shown in Fig of vortex pairs extremely low dissipation magnitude energies than free vortices but... Expected to possess a normal second-order phase transition result, occurring even for extremely low magnitude... Rg flow lines for 7/4 < < 2 in the y=0 plane such... Studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity condensed matter Vadim. 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Magnetization is analysed for different levels of ( x ) defined in the plane which takes values! Study, J. Phys recently has advanced to the point that artificial two-dimensional can. 5Italic_N 5 normal second-order phase transition such a role 63 A.Johansson, { \displaystyle T_ { c } italic_ italic_c. To our Terms and and spherical colloids Murray and Van Winkle ; Kusner et al This means that kosterlitz thouless transition! F > 0 } 5 ( a ) ) Berezinskii died in 1980 at the transition led the... } in the usual two-fluid picture, the exponent =44\alpha=4italic_ = 4 critical temperature, of... Renders the argument of the RG flow lines for 7/4 < < 2 in the usual picture! Fabricated with atomic-layer precision Just below There are generally two kinds of couplings: the Josephson coupling the...