kosterlitz thouless transition

WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. B. H.-H. Wen, The 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. Consider the static limit, its free energy density reads. c arXiv:1205.1333v1 [cond-mat.str-el]. WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. i B, G.E. Blonder and 3 The epitaxially grown heavy fermion superlattices may serve such a role. In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. , there are only bound vortexantivortex pairs. I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. J.V. Jos, DOI:https://doi.org/10.1103/PhysRevLett.127.156801. Lett. Rev. We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed 0000054192 00000 n All rights reserved. Kosterlitz jump for a BKT transition is demonstrated. (Nature Physics 7, 849 (2011)) in terms of Berezinskii-Kosterlitz-Thouless transition. i If >2, we find the usual SR phenomenology with a BKT phase transition. 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. The long range magnetic interaction couples vortices in different planes, and aligns vortices of the same sign into stacks. k The transition is named for condensed matter physicists Vadim Rev. Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. ISSN 1079-7114 (online), 0031-9007 (print). . d Above the critical temperature, proliferation of unbound vortices is expected. Rev. 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 It is a transition from bound T G.Sambandamurthy, WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. S.Doniach and C.Petrovic, HvzsuperscriptsubscriptH_{v}^{z}italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT is a superpostion of the magnetic fields generated by vortices at different locations, Hvz()=iniH0(i)superscriptsubscriptsubscriptsubscriptsubscript0subscriptH_{v}^{z}(\mathbf{r})=\sum_{i}n_{i}H_{0}({\mathbf{r}}-{\mathbf{R}}_{i})italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_z end_POSTSUPERSCRIPT ( bold_r ) = start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r - bold_R start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ), with nisubscriptn_{i}italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT the vorticity. > T 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. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. stream 0000075577 00000 n etal., Proc. Rev. 0000007586 00000 n Europhys. 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. and , which is the total potential energy of a two-dimensional Coulomb gas. Information about registration may be found here. 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. V 0000072221 00000 n 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. Rev. N A.Kamlapure, At temperatures below this, vortex generation has a power law correlation. 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. 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. If < S.Yasumoto, >> and R.E. /Length 2177 3b of [Mizukami etal., 2011]. n {\displaystyle \sum _{i=1}^{N}n_{i}=0} 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. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. 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. {\displaystyle \pm 2\pi } and the film thickness dditalic_d. There is an elegant thermodynamic argument for the KosterlitzThouless transition. 1 Now, we proceed to study the thickness dependence of the BKT transition temperature. E We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. H.A. Radovan, This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. B. Phys. 3 0 obj << WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. A salient feature of the heavy-fermion superconductor CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT is the proximity to an antiferromagnetic quantum critical point (QCP). A.J. Berlinsky, The unbounded vortices will give rise to finite resistance. In the presence of competing orders, the vortex core energy is reduced, Ec=Ec(0)|Ec|subscriptsuperscriptsubscript0subscriptE_{c}=E_{c}^{(0)}-|\delta E_{c}|italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( 0 ) end_POSTSUPERSCRIPT - | italic_ italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT |. /Filter /FlateDecode D.R. Nelson, Rev. 0000065532 00000 n [Mondal etal., 2011]). We obtain the superfluid weight and Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for microscopic tight-binding and low-energy continuum models. B, G.E. Blonder, i 0000061844 00000 n 0000053919 00000 n The BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. i R 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. arg 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. M.Tinkham, This is a set of notes recalling some of the most important results on the XY model from the ground up. 0 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]. n Phys. Conclusions: In conclusion, we have proposed that superconducting transition in the heavy fermion superlattice of Mizukami et al. 0000061439 00000 n Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. 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. M.J. Naughton, 0000002555 00000 n The superuid transition in 2D is the-oretically understood within the Berezinskii-Kosterlitz-Thouless (BKT) general framework [35]; the character-istic ngerprint of the BKT transition is the so-called universal jump of the superuid fraction s(T) as a function of temperature, from zero to a nite value as Tc 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. = J. Chem. 0000000016 00000 n 0000042388 00000 n . A large dielectric constant corresponds to a small vortex core energy. Subscription The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. Lett. z , The vortex core energy can be written as Ec=(Cc/2)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_C 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. 0000017872 00000 n 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. The two BKT correlation scales account for the emergent granularity observed around the transition. =QDhSCe/. B, J.M. Kosterlitz where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. /Length 3413 WebThe nature of the phase transition of a quantity of matter from a low-temperature ordered state to a high-temperature disordered state is determined by the dimensionality of the system and the number of degrees of freedom possessed by the J. Phys. 0000003004 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. {\displaystyle a} [2] More recently, the term has been applied by the 2-D superconductor insulator transition community to the pinning of Cooper pairs in the insulating regime, due to similarities with the original vortex BKT transition. CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order S 2 Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. 0 WebThis transition is called Berezinskii-Kosterlitz-Thouless (BKT) transition and still remains to be a topic of active research. 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 3. 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. Our proposal is that such behavior is due to the effect of phase fluctuations, which for the quasi-two-dimensional superconductors considered here is controlled by the Berezinskii-Kosterlitz-Thouless physics [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. C.Kallin, When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. 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). 0000026909 00000 n vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. 2023 American Physical Society. {\displaystyle S^{1}} For YBCO thin films [Matsuda etal., 1993], we have Ec(1.5836/2)7meV10.6meVsimilar-to-or-equalssubscript1.583627meVsimilar-to-or-equals10.6meVE_{c}\simeq(1.583\times 6/2\pi)\times 7{\rm meV}\simeq 10.6{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.583 6 / 2 italic_ ) 7 roman_m roman_e roman_V 10.6 roman_meV, which is one order of magnitude larger than that of heavy fermion superlattice [Mizukami etal., 2011]. The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. The bulk penetration depth b(T)subscript\lambda_{b}(T)italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) has a temperature dependence of the form b(T)=b(0)[1(T/Tc0)]1/2subscriptsubscript0superscriptdelimited-[]1superscriptsubscript012\lambda_{b}(T)=\lambda_{b}(0)\left[1-\left(T/T_{c0}\right)^{\alpha}\right]^{-1/2}italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( italic_T ) = italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT ( 0 ) [ 1 - ( italic_T / italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ end_POSTSUPERSCRIPT ] start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT, Phys. T C.Kallin, and H.Ikeda, {\displaystyle V\sim I} , we would expect it to be zero. 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. T.M. Klapwijk, S.Ono, 0000025678 00000 n Webcorrelations. = Itbeginswiththediscoveryofpossibleeldcongurationsthatone 1. i i >> This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. [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. Experimental Methods The Ba(Fe 0.914Co 0.086) 2As , there are free vortices. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine Far away from the vortex core, i.e. and (Nature Physics 7, 849 (2011)) in terms of 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. 0 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. 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. J.Corson, a The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. : Condens. To export a larger list you will need to increase the number of results per page. 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. Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. 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. V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. is the system size, and Lett. G.Seibold, T.Onogi, {\displaystyle x_{i},i=1,\dots ,N} B, T.Xiang and 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_ ), 0000002182 00000 n {\displaystyle \exp(-\beta E)} 0000027382 00000 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 Rev. 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. It has also been shown in Ref. It is therefore desirable to have a well-controlled, readily-tunable system to investigate the BKT physics. . 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]. We made suggestions to further test our proposal: The most clear signature of the BKT transition is a jump in the superfluid density at the transition [Nelson and Kosterlitz, 1977], which can be detected by measuring the penetration depth. [Deutscher and deGennes, 1969] ). S.Komiyama, Rev. B. , the relation will be linear G.Grner, 0000073086 00000 n i 0000058535 00000 n 4 can be observed experimentally. 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. Low Temp. For conventional superconductors, e.g. 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. A 38 (2005) 5869 [cond-mat/0502556] . and is given by. N T.P. Orlando, WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. In these systems, thermal generation of vortices produces an even number of vortices of opposite sign. [Fenton, 1985]. 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. 1 0000073805 00000 n B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. ) https://doi.org/10.1103/PhysRevLett.127.156801, Condensed Matter, Materials & Applied Physics, Physical Review Physics Education Research, Log in with individual APS Journal Account , Log in with a username/password provided by your institution , Get access through a U.S. public or high school library . x For \gammaitalic_ small, core energy lowering effect can be very large. a C.Kallin, and Rev. c 0000072681 00000 n 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. . ) 0000017580 00000 n 0000075688 00000 n A.T. Fiory, [Fellows etal., ], where they study a related problem of BKT transition in the presence of competing orders, focusing on the behavior near the high symmetry point. In the XY model in two dimensions, a second-order phase transition is not seen. L.Li, % xref W V.Oganesyan, Following the RG flow (Fig. j the user has read and agrees to our Terms and Rev. We find that the shape of the spectrum can not be explained 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. V Nature. J.-M. Triscone, {\displaystyle T_{c}} A.Johansson, M.Shimozawa, 0000026620 00000 n 1 S.-C. Zhang, We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. 0000062112 00000 n N.Reyren, and i In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. For layered superconductors, one also needs to include interlayer couplings. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. 1 The data provide evidence for a two dimensional quantum superconductor to insulator (2D-QSI) tran We report the phase diagram for magnetic fluxoids in two-dimensional $\frac{\mathrm{In}}{\mathrm{In}{\mathrm{O}}_{x}}$ superconducting films. This means that gap retains the bulk value for n55n\geq 5italic_n 5. Assuming ns=nsubscriptn_{s}=nitalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = italic_n at T=00T=0italic_T = 0, we have Ec(1.9/)kBTBKTsimilar-to-or-equalssubscript1.9subscriptsubscriptBKTE_{c}\simeq(1.9/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.9 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT (see e.g. 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. 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. WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. B The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. A 38 (2005) 5869 [cond InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. T.Schneider, {\displaystyle k_{\rm {B}}} Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. 5(a)). 0000002396 00000 n I Phys. ) D.Maruyama, 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. 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] . 0000018171 00000 n {\displaystyle T_{c}} Here, we try to understand where such a large renormalization may come from. z / , it has no physical consequences. D.Shahar, and Sketch of the RG flow lines for 7/4<<2 in the y=0 plane.

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