kosterlitz thouless transitionkosterlitz thouless transition
Rev. A.Petrovic, C.Castellani, WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. 0000027382 00000 n
The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a >> L.P. Kadanoff, H.Shishido, This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. Assume the case with only vortices of multiplicity {\displaystyle T_{c}} Lett. At temperatures below this, vortex generation has a power law correlation. ; Zahn et al. Rev. z Here we elaborate on the understanding of the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. After working with Thouless in Birmingham, he spent 2 years at Cornell. 0000041921 00000 n
the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order H.Ikeda, H0()subscript0H_{0}({\mathbf{r}})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) can be obtained from its Fourier transform H0()=0/(1+2k2)subscript0subscript01superscript2superscript2H_{0}(\mathbf{k})=\Phi_{0}/(1+\lambda^{2}k^{2})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_k ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / ( 1 + italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_k start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ), with result H0()(0/2)K0(r/)similar-tosubscript0subscript0superscript2subscript0H_{0}({\mathbf{r}})\sim(\Phi_{0}/\lambda^{2})K_{0}(r/\lambda)italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) ( roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ), (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. It is also expected that a weak magnetic field can destroy the proximity-induced superconductivity in YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers [Mizukami etal., 2011; Serafin etal., 2010]. A.J. Berlinsky, The transition is named for condensed matter physicists Vadim Berezinskii, John M. Kosterlitz and David J. {\displaystyle \oint _{\gamma }d\phi } Rev. 60 0 obj<>
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Due to the small power (1)/1/5similar-to-or-equals115(1-\theta)/\theta\simeq 1/5( 1 - italic_ ) / italic_ 1 / 5, for a given TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, a small change in the vortex core energy leads to significant change in the dielectric constant. / However, as we will argue below, the large mismatch of Fermi velocities across the interface changes the story completely and enables quasi 2D superconductivity in CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT thin layers. This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. T D.Maruyama, S.Doniach and 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. 0000058535 00000 n
When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. and I.Bozovic, Above CCitalic_C is directly proportional to the vortex core energy, with Ec=E0Csubscriptsubscript0E_{c}=E_{0}Citalic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_C and E0=02d/643b2=(c/2)kBTBKTsubscript0superscriptsubscript0264superscript3subscriptsuperscript2bsubscriptitalic-2subscriptsubscriptBKTE_{0}=\Phi_{0}^{2}d/64\pi^{3}\lambda^{2}_{\rm b}=(\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 64 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT = ( italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. Phys. T.P. Orlando, To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations > {\displaystyle F<0} J.Schmalian, B, A.Serafin, 0000059042 00000 n
B.I. Halperin and >> I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. {\displaystyle \phi } ln i 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. ( Suppose that a given field configuration has So we expect that for n4much-greater-than4n\gg 4italic_n 4, gap has the same value as the bulk material; while for n4less-than-or-similar-to4n\lesssim 4italic_n 4, gap gets suppressed. and 0000073683 00000 n
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. 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 5(c)). However, this is not the case due to the singular nature of vortices. 0000072221 00000 n
and the Boltzmann factor is x ISSN 1079-7114 (online), 0031-9007 (print). {\displaystyle \Lambda } Rev. {\displaystyle I^{2}} 2 While at Birmingham, Thouless supervised Michael Kosterlitz as a talented postdoctoral associate. i S WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. /Filter /FlateDecode 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. This approach was used in Resnick et al. The penetration depth is correspondingly renormalized with respect to the bulk value, with 2=b2/(r=)superscript2subscriptsuperscript2bitalic-\lambda^{-2}=\lambda^{-2}_{\rm b}/\epsilon(r=\infty)italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT = italic_ start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT / italic_ ( italic_r = ). 1. , where ) It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. {\displaystyle \pm 2\pi } {\displaystyle S^{1}} 5(a)). We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. The transmission is thus on the order of one percent. 3b of [Mizukami etal., 2011]. N B, K.S. Raman, The two BKT correlation scales account for the emergent granularity observed around the transition. , as the number of free vortices will go as M.Gabay and i) First, we will examine whether resistivity has the right temperature dependence. Rev. Science. It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. . B, G.E. Blonder, At the interface, the Yb ions disorder (due to cross diffusion and displacements) and act as nonmagnetic impurities to locally suppress superconductivity in CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers [Bauer etal., 2011]. One can thus tune the vortex fugacity by changing the distance to the QCP. trailer
D.Watanabe, It is a transition from bound B, Y.Matsuda, Lett. All rights reserved. A.Johansson, C.Kallin, Soc. Taking a contour integral This is a specific case of what is called the MerminWagner theorem in spin systems. stream L.Benfatto, and 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]. 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 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. J.Orenstein, 0000008417 00000 n
This holds for classical models Rev. and spherical colloids Murray and Van Winkle ; Kusner et al. 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. A. Huberman, Phys. 0 Above {\displaystyle \kappa } WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial We find that c=2,4.6,6,90subscriptitalic-24.6690\epsilon_{c}=2,4.6,6,90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 2 , 4.6 , 6 , 90 corresponds to C=7.27,2.24,1.583,0.05997.272.241.5830.0599C=7.27,2.24,1.583,0.0599italic_C = 7.27 , 2.24 , 1.583 , 0.0599 respectively (see Fig. / The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be ( J.Pereiro, 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. From Boltzmann's entropy formula, WebThe Berezinskii-Kosterlitz-Thouless transition In the last lecture we saw that true long-range order is impossible in 2D and a fortiori in 1D at any nite temperature for a system 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 0000070328 00000 n
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. WebThe system of superconducting layers with Josephson coupling J is studied. 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 ( Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. {\displaystyle T_{c}} v+`>= o3n qB"`PV
vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI 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 Expand 7 I F One assumes DOI:https://doi.org/10.1103/PhysRevLett.127.156801. (Nature Physics 7, 849 (2011)) in terms of 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]. | I , Using the molecular beam epitaxy (MBE) technique, Mizukami et al. c S.Ono, 0000054192 00000 n
In normal metal/heavy fermion superconductor proximity effect studies, it was realized that the large mismatch of effective mass at the interface leads to huge suppression of transmission of electron probability currents [Fenton, 1985]. Phys. A.J. Berlinsky, {\displaystyle N} The BerezinskiiKosterlitzThouless (BKT) transition [][] is very well understood in terms of its physical mechanism of vortexantivortex unbinding.The field-theoretical formulation of this two-dimensional (2D) problem of a U(1) symmetric order parameter gives a rigorous quantitative characterization of the transition into the critical . WebRemarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. 0000003004 00000 n
, 0000070606 00000 n
Above TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs unbind, and the proliferation of free vortices destroys superconductivity. is a parameter that depends upon the system in which the vortex is located, 0000008144 00000 n
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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. 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]. J.Corson, 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. We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. 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. 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. 0000002396 00000 n
E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 {\displaystyle \sum _{i=1}^{N}n_{i}=0} , the second term is positive and diverges in the limit Rev. H.A. Radovan, Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. In the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice, one has a layered structure of alternating heavy fermion superconductor (CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT) and conventional metal (YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT), typically 3.5 nm thick. V.G. Kogan, i 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_. 1 D.R. Nelson, 0000061439 00000 n
0000053029 00000 n
= J.M. Kosterlitz, N We can parameterize the vortex fugacity in term of a dimensionless quantity CCitalic_C, with y(0)=exp[CK(0)/4]004y(0)=\exp[-CK(0)/4]italic_y ( 0 ) = roman_exp [ - italic_C italic_K ( 0 ) / 4 ] [Davis etal., 1990]. {\displaystyle F=E-TS} . 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. 0000017872 00000 n
After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. . D.Shahar, and A 38 (2005) 5869 [cond-mat/0502556] . / Phys. ( = It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. j A 38 (2005) 5869 [cond 0000061748 00000 n
B Subscription C.Petrovic, {\displaystyle T_{c}} [Mizukami etal., 2011] are consistent with BKT transition. In the following, we are going to check whether the experimental findings of Mizukami et al. A large dielectric constant corresponds to a small vortex core energy. 1 ) {\displaystyle \Lambda \to \infty } R . Phys. 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. 0000025932 00000 n
The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. T.Terashima, M.Tinkham, 111With smuch-less-thansubscriptparallel-tos\ll\lambda_{\parallel}italic_s italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, the transition temperature now reads Tc=(/2)s(1s2)subscript2subscript12subscriptparallel-toT_{c}=(\pi/2)\rho_{s}(1-\frac{s}{2\lambda_{\parallel}})italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_ / 2 ) italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( 1 - divide start_ARG italic_s end_ARG start_ARG 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG ), where ssitalic_s is the layer spacing, subscriptparallel-to\lambda_{\parallel}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT is the in-plane penetration depth, and s=02s/(1632)subscriptsuperscriptsubscript0216superscript3superscriptsubscriptparallel-to2\rho_{s}=\Phi_{0}^{2}s/(16\pi^{3}\lambda_{\parallel}^{2})italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_s / ( 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) is the in-plane superfluid stiffness, which can be measured directly. M.J. Naughton, E G.Orkoulas and {\displaystyle \phi } 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. n 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. S.Kirkpatrick, 1 4a of [Mizukami etal., 2011]. Sign up to receive regular email alerts from Physical Review Letters. {\displaystyle \phi _{0}} 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. 0 and , there are free vortices. 0000025678 00000 n
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. T.Shibauchi, 0000054567 00000 n
It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. =QDhSCe/. For large csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, we have Ec/kBTBKT(A1//2)c(1)/similar-to-or-equalssubscriptsubscriptsubscriptBKTsuperscript12superscriptsubscriptitalic-1E_{c}/k_{B}T_{\rm BKT}\simeq(A^{1/\theta}/2\pi)\epsilon_{c}^{-(1-\theta)/\theta}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ( italic_A start_POSTSUPERSCRIPT 1 / italic_ end_POSTSUPERSCRIPT / 2 italic_ ) italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - ( 1 - italic_ ) / italic_ end_POSTSUPERSCRIPT (see Fig. J. Chem. = 3 0000018415 00000 n
On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). Thin film growth technology recently has advanced to the point that artificial two-dimensional structures can be fabricated with atomic-layer precision. Now, we proceed to study the thickness dependence of the BKT transition temperature. Below the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortices and antivortices are bound into pairs, and the resistance vanishes. One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. startxref
In these systems, thermal generation of vortices produces an With the dimensionless quantity a4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a\equiv\alpha\lambda^{4}/g^{2}\mu_{B}^{2}\Phi_{0}^{2}italic_a italic_ italic_ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT / italic_g start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, the change of vortex core energy is EcV00r*/xx(ln2xa)2similar-tosubscriptsubscript0superscriptsubscript0superscriptdifferential-dsuperscriptsuperscript22\delta E_{c}\sim-V_{0}\int_{0}^{r^{*}/\lambda}xdx(\ln^{2}x-a)^{2}italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT - italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT / italic_ end_POSTSUPERSCRIPT italic_x italic_d italic_x ( roman_ln start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_x - italic_a ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where r*=easuperscriptsuperscriptr^{*}=\lambda e^{-\sqrt{a}}italic_r start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = italic_ italic_e start_POSTSUPERSCRIPT - square-root start_ARG italic_a end_ARG end_POSTSUPERSCRIPT is the radius where magnetic condensate vanishes. S We report the phase diagram for magnetic fluxoids in two-dimensional $\frac{\mathrm{In}}{\mathrm{In}{\mathrm{O}}_{x}}$ superconducting films. This work was supported, in part, by UCOP-TR01, by the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility and in part by LDRD. 0000053483 00000 n
{\displaystyle n_{i}=\pm 1} 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]. and S.L. Yan, Conditions and any applicable K.Yasu, y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. ln WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. Agreement. For conventional superconductors, e.g. . J. . / %\| 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&:
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kt> {\displaystyle \exp(-\beta E)} B, M.Franz, 0000053772 00000 n
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]. T.Terashima, In the 2-D XY model, vortices are topologically stable configurations. N {\displaystyle T_{c}} Rev. Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. 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S WebThe BerezinskiiKosterlitzThouless transition ( BKT transition ) is a phase transition of the BKT transition is...
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