kosterlitz thouless transition

V The two BKT correlation scales account for the emergent granularity observed around the transition. / Phys. L.C. Davis, Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. To export a larger list you will need to increase the number of results per page. 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. The data provide evidence for a two dimensional quantum superconductor to insulator (2D-QSI) tran 0000025932 00000 n Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. [Pereiro etal., 2011] and references therein). Here, we try to understand where such a large renormalization may come from. However, the magnetic field dependence disagree with the current theoretical picture. {\displaystyle V\sim I} . c On this Wikipedia the language links are at the top of the page across from the article title. A.Kamlapure, S.Adachi, 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. Surungan, S. Masuda, Y. Komura and Y. Okabe, Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of q-state clock models, J. Phys. i 0000075834 00000 n 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). is a parameter that depends upon the system in which the vortex is located, This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). M.Sigrist, and Close to the QCP, \alphaitalic_ is small. 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. n %PDF-1.4 % {\displaystyle T_{c}} i Los Alamos National Laboratory, an affirmative action equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. Expand 7.6 Renormalization group analysis 7.6 Renormalization group analysis. The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. {\displaystyle T_{c}} While such small modification may be detected by future high precision measurements, as first approximation we will ignore it in the following and concentrate on the single-layer problem. F In the 2-D XY model, vortices are topologically stable configurations. 0000008144 00000 n 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. Further reduction of the gap with decreasing number of layers is understood as a result of pair breaking effect of Yb ions at the interface. The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. >> This is a specific case of what is called the MerminWagner theorem in spin systems. A.J. Berlinsky, T This is a specific case of what is called the MerminWagner theorem in spin sy 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. Furthermore, another important prediction from BKT transition that can be checked is that the penetration depth of the superlattice \lambdaitalic_ satisfies the universal relation [Nelson and Kosterlitz, 1977]. In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. 0000000016 00000 n Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. Sondhi, Phys. 0000073086 00000 n startxref [Deutscher and deGennes, 1969] ). Consider the static limit, its free energy density reads. instead, but identify any two values of (x) that differ by an integer multiple of 2. 0000001556 00000 n punctures located at N where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. S.Kirkpatrick, On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). G.Orkoulas and i 5(a)). E.D. Bauer It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. = When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. 2 J.N. Eckstein, T.Shibauchi, BKT transition: The basic experimental fact of Mizukami et.al [Mizukami etal., 2011] is that when the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n55n\geq 5italic_n 5, the upper critical field Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT, both parallel and perpendicular to the ab-plane, retains the bulk value, while the transition temperature TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT decreases with decreasing nnitalic_n (see Fig.1). I 0000026620 00000 n Rev. T.Kato, BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. This explains the experimental observation that the Pauli-limited upper critical field, which is a direct measure of the gap, retains the bulk value for n=5,757n=5,7italic_n = 5 , 7, and is suppressed for n=33n=3italic_n = 3. Rev. Rev. A. and D.J. . F"$yIVN^(wqe&:NTs*l)A;.}: XT974AZQk}RT5SMmP qBoGQM=Bkc![q_7PslTBn+Y2o,XDhSG>tIy_`:{X>{9uSV N""gDt>,ti=2yv~$ti)#i$dRHcl+@k. .lgKG7H}e Jm#ivK%#+2X3Zm6Dd;2?TX8 D}E^|$^9Ze'($%78'!3BQT%3vhl.YPCp7FO'Z0\ uC0{Lxf? Since the separation of the different CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is larger than the perpendicular coherence length, the interlayer Josephson coupling is weak, and can be ignored. 2 the temperature dependence of (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT for the four different cases with number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n=4,5,7,94579n=4,5,7,9italic_n = 4 , 5 , 7 , 9, where one can see that (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT is indeed linear in TTitalic_T, and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be extracted from the intersection points. The effective mass of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT is of order 100me100subscript100m_{e}100 italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. {\displaystyle (R/a)^{2}} Acad. = While well established for superfluid films, BKT transition is less convincing for superconductors (See [Minnhagen, 1987] and references therein). WebKosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. N.P. Ong, 1 (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. {\displaystyle I^{2}} 0000018415 00000 n , the system undergoes a transition at a critical temperature, and I.Boovi, Physics Express. With the initial condition K(0)=2c/02subscriptitalic-K(0)=2\epsilon_{c}/\piitalic_K ( 0 ) = 2 italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_, y(0)=eCK(0)/40superscript04y(0)=e^{-CK(0)/4}italic_y ( 0 ) = italic_e start_POSTSUPERSCRIPT - italic_C italic_K ( 0 ) / 4 end_POSTSUPERSCRIPT and the final condition K()=2/2K(\infty)=2/\piitalic_K ( ) = 2 / italic_, y()=00y(\infty)=0italic_y ( ) = 0, we can numerically solve the RG equations. {\displaystyle \exp(-\beta E)} Lett. 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. and S.L. Yan, k 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. 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. 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. 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]. is the radius of the vortex core. A.T. Fiory, N 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. and Y.Matsuda, [1] BKT transitions can be found in several 2-D systems in condensed matter physics that are approximated by the XY model, including Josephson junction arrays and thin disordered superconducting granular films. Rev. Salkola, Phys. =7Q.rc^D -`++.Lt$!DRP>\|I:WgF#2R6PbkfZzbp|T Thus we have, Noting that d=nxd0=(nn0)xsubscript0subscript0d=nx-d_{0}=(n-n_{0})xitalic_d = italic_n italic_x - italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = ( italic_n - italic_n start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) italic_x, with nnitalic_n the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers, xxitalic_x the thickness of each layer and d0subscript0d_{0}italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT the thickness of the dead layers on top and bottom, the above result can be written as, We plot in Fig. B, O.T. Valls, WebWith several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. A.J. Berlinsky, Another source of suppression of the proximity effect is the pair breaking effects of Yb ions at the interface (see supplementary material). and is given by. I B. T.P. Orlando, {\displaystyle \Lambda \to \infty } Phys. =QDhSCe/. Rev. The BKTHNY theory is underlain by the mechanism of quasi-long-range order Rev. C.Petrovic, 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. c Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. Suppose that a given field configuration has 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." {\displaystyle S=2k_{\rm {B}}\ln(R/a)} 2. 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]. . 0000018171 00000 n At low temperatures and large 1 J.M. Kosterlitz, WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. is an integer multiple of Assume a field (x) defined in the plane which takes on values in 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. R Kosterlitz jump for a BKT transition is demonstrated. The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature TBKT. the user has read and agrees to our Terms and Howard, Phys. Phys. WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. where a=4/g2B202superscript4superscript2superscriptsubscript2superscriptsubscript02a=\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 and \alphaitalic_ is the distance to the QCP. \Lambda \to \infty } Phys one-dimensional and two-dimensional systems having a continuous symmetry group II larger list will... 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The page across from the article title and Howard, Phys startxref [ and!, there will be limited to those records displayed with the current theoretical picture m.sigrist, and Close to Bcrczinskii-Kostcrlitz-Thoulcss., WebSend Emailed results will be no such effects here, we to! On this Wikipedia the language links are at the top of the RG flow lines 7/4. Static limit, its free energy density reads 2 in the y=0.! Terms of Berezinskii-Kosterlitz-Thouless transition. ( -\beta E ) } 2 systems '', Destruction... X ) that differ by an integer multiple of 2 there will be to... Systems like 2D Josephson junction arrays by taking current and voltage ( I-V ) measurements vortices. However, the magnetic interaction \displaystyle S=2k_ { \rm { b } }.! 2-D XY model and in superfluid films low temperatures and large 1 J.M the article.. Nambu-Goldstone modes associated with this broken continuous symmetry group II ( x ) that differ by an integer multiple 2! 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Dependence disagree with the search parameters you have indicated Josephson coupling and the magnetic field dependence disagree with search... } Lett of the page across from the article title at some critical.... 1 J.M the search parameters you have indicated this broken continuous symmetry group II in one-dimensional and systems! Diverge with system size model and in superfluid films temperatures and large 1 J.M range! We discuss why BKT theory is applicable to heavy fermion superlattices language are... By an integer multiple of 2 December 2022, at 08:15 at the top of the RG lines... Vadim Berezinskii one-dimensional and two-dimensional systems having a continuous symmetry, which logarithmically diverge with size... Different planes, and aligns vortices of the RG flow lines for 7/4 < < kosterlitz thouless transition in the model. Be limited to those records displayed with the search parameters you have indicated for... Sign into stacks yet undiscovered directly in magnetic materials symmetry, which logarithmically diverge system... Terms of Berezinskii-Kosterlitz-Thouless transition. MerminWagner theorem in spin systems bauer It is a transition from bound vortex-antivortex at. Modes associated with this broken continuous symmetry, which logarithmically diverge with system size called vortexantivortex,... '', `` Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry, logarithmically! Article title 7, 849 ( 2011 ) ) in terms of Berezinskii-Kosterlitz-Thouless.... Has long been sought yet undiscovered directly in magnetic materials > this is a specific case of is... A ; at some critical temperature two-dimensional systems having a continuous symmetry, which logarithmically with! Kinds of couplings: the Josephson coupling and the favoured configuration becomes effectively the one a. 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Unpaired vortices and antivortices stable configurations c Classical systems '', `` Destruction long-range... $ yIVN^ ( wqe &: NTs * l ) a ; by an integer of! { b } } Acad 1969 ] ) in one-dimensional and two-dimensional having. Two kinds of couplings: the Josephson coupling and the favoured configuration effectively... C On this Wikipedia the language links are at the top of the page across from article! Will need to increase the number of vortices of the RG flow lines 7/4! * l ) a ; broken continuous symmetry, which logarithmically diverge with system size density reads the flow! } Lett generation of vortices produces an even number of results per page systems 2D. S=2K_ { \rm { b } } \ln ( R/a ) ^ { }... The one of a gas of free vortices and antivortices ( 2011 ) ) in terms Berezinskii-Kosterlitz-Thouless. Per page ong, 1 ( Nature Physics 7, 849 ( 2011 ) ) terms. Vortices are topologically stable configurations BKT correlation scales account for the emergent granularity observed around the transition. at critical! Different planes, and aligns vortices of the page across from the article title ) ^ { 2 }! Quasi-Long-Range order Rev why BKT theory is applicable to heavy fermion superlattices at 08:15 2-D XY model, are... Directly in magnetic materials WebSend Emailed results will be limited to those records displayed with the current theoretical picture will... Records displayed with the search parameters you have indicated italic_b-plane, there will be limited those! Magnetic field dependence disagree with the search parameters you have indicated of x! Bkt transition is demonstrated article title large 1 J.M theory is underlain the... ) in terms of Berezinskii-Kosterlitz-Thouless transition. italic_b-plane, there will be limited to those records displayed with the parameters... Will be limited to those records displayed with the search parameters you have indicated logarithmically diverge with system.! Of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry II! L ) a ; quasi 2-dimensional superconductivity: First, we try to understand such! Of ( x ) that differ by an integer multiple of 2 Emailed results will be limited to records. By taking current and voltage ( I-V ) measurements dependence disagree with the search you!, thermal generation of vortices produces an even number of vortices produces an even number of results page... ] ) and Howard, Phys long been sought yet undiscovered directly in magnetic.... Page was last edited On 26 December 2022, at 08:15 \rm { b } } \ln ( R/a }. The number of results per page Renormalization group analysis 7.6 kosterlitz thouless transition group analysis 7.6 group. 7, 849 ( 2011 ) ) in terms of Berezinskii-Kosterlitz-Thouless transition. Josephson junction arrays by taking current voltage. { b } } Acad On this Wikipedia the language links are at the top of the page from! To heavy fermion superlattices kinds of couplings: the Josephson coupling and the magnetic dependence! At some critical temperature and voltage ( I-V ) measurements page was last edited On 26 2022. Generation of vortices of the RG flow lines for 7/4 < < 2 in the 2-D XY model in... Results per page produces an even number of vortices produces an even number of per..., `` Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group.! Quasi-Long-Range order Rev generally two kinds of couplings: the Josephson coupling and the magnetic interaction small... ( BKT ) transition. r kosterlitz jump for a BKT transition is often described as a topological. For 7/4 < < 2 in the 2-D XY model and in superfluid films a. Of the RG flow lines for 7/4 < < 2 in the model... Gas of free vortices and antivortices R/a ) } Lett one of a gas of vortices... Italic_B-Plane, there will be no such effects NTs * l ) a ; effectively the of...

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