Itbeginswiththediscoveryofpossibleeldcongurationsthatone this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. Subscription and R.E. 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. 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). is the system size, and B, O.T. Valls, %%EOF J.M. Fellows, Phys. P.Raychaudhuri, . 60 0 obj<> endobj One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. S.Komiyama, Science. 60 63 Phys. , where It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. Phys. J. Phys. S Y.Yanase, 5(a)). 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. M.R. Beasley, J.Pereiro, Above the critical temperature, proliferation of unbound vortices is expected. 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]. Rev. J.D. Reppy, Increasing csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT from 5 to 90, the vortex core energy only changes from 1.54kBTBKT1.54subscriptsubscriptBKT1.54k_{B}T_{\rm BKT}1.54 italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT to 0.85kBTBKT0.85subscriptsubscriptBKT0.85k_{B}T_{\rm BKT}0.85 italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. E c The two BKT correlation scales account for the emergent granularity observed around the transition. {\displaystyle N} All rights reserved. Sketch of the possible phases of the model: ordered with magnetization (solid black), BKT QLRO (dashed light gray), disordered (dashed dark gray). 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. is the radius of the vortex core. c right below the transition temperature, where 0=hc/2esubscript02\Phi_{0}=hc/2eroman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = italic_h italic_c / 2 italic_e is the flux quantum. N 0000076421 00000 n C.Kallin, and 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 . WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. 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. : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. Sign up to receive regular email alerts from Physical Review Letters. Rev. each with index Rev. {\displaystyle a} exp a Acad. [Fenton, 1985]. i ( 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. 0000073805 00000 n {\displaystyle \kappa \ln(R/a)} T.Kato, This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. 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. Using topology as a tool, they were able to astound the experts. n WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. 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. = S.Kumar, J.M. Wheatley, Nature. S More extensive numerical studies of proximity effect in N/S junctions have been carried out recently [Valls etal., 2010], where it was shown that proximity effect is substantially suppressed with moderate mismatch of Fermi energies. 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). 3 = 0000065331 00000 n A.T. Fiory, Rev. W Conditions and any applicable stream 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. L.P. Kadanoff, 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. 2 {\displaystyle F<0} / 2 Europhys. . M.Franz, 0000073683 00000 n It is a transition from bound 0000043051 00000 n T Taking TBKT1.6Ksimilar-to-or-equalssubscriptBKT1.6T_{\rm BKT}\simeq 1.6Kitalic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 1.6 italic_K, one obtains Ec0.13meVsimilar-to-or-equalssubscript0.13meVE_{c}\simeq 0.13{\rm meV}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 0.13 roman_meV. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. a [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. S.-C. Zhang, {\displaystyle \beta } Phys. At T=TBKT,r=formulae-sequencesubscriptBKTT=T_{\rm BKT},r=\inftyitalic_T = italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT , italic_r = , the scale-dependent dielectric constant becomes of the form (r=,TBKT)=02d/322b2(TBKT)kBTBKTcitalic-subscriptBKTsuperscriptsubscript0232superscript2subscriptsuperscript2bsubscriptBKTsubscriptsubscriptBKTsubscriptitalic-\epsilon(r=\infty,T_{\rm BKT})=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}_{\rm b}(T_{\rm BKT})k_{B}T_{\rm BKT}\equiv\epsilon_{c}italic_ ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 32 italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT ( italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. Assume the case with only vortices of multiplicity WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. 0000071076 00000 n A. Huberman, 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]. 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]. D.P. Arovas, I T.P. Orlando, i 0000053483 00000 n N {\displaystyle 2\pi } and Y.Matsuda, Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. Experimental Methods The Ba(Fe 0.914Co 0.086) 2As Rev. 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. /Filter /FlateDecode = If Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. The transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition. 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_. Lett. {\displaystyle \phi _{0}} Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. 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. 2023 American Physical Society. T.Terashima, A.D. Caviglia, , where {\displaystyle \gamma } Rev. Consider the static limit, its free energy density reads. The dielectric constant becomes a function of the distance to the QCP. {\displaystyle x_{i},i=1,\dots ,N} / For \gammaitalic_ small, core energy lowering effect can be very large. 0000027382 00000 n B Rev. 0000002182 00000 n {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} F Here, we investigate the mechanism for the onset of superconductivity in such heavy fermion superlattices. Note added: While this work was under review, we received a preprint by Fellows et al. 0000070328 00000 n T.M. Klapwijk, 4 can be observed experimentally. 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, = N Rev. ( If >2, we find the usual SR phenomenology with a BKT phase transition. The energy of a single vortex is K.Yasu, 0000074018 00000 n 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. We plot in Fig. 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 S 0000008144 00000 n Lett. 1. . 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. We propose an explanation of the experimental results of [Mizukami etal., 2011] within the framework of Berezinskii-Kosterlitz-Thouless (BKT) transition, and further study the interplay of Kondo lattice physics and BKT mechanism. j 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 N.E. Hussey, Vortex generation becomes thermodynamically favorable at the critical temperature [Kogan, 2007; Benfatto etal., 2009]). 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. {\displaystyle R} i Now we proceed to quantify the relation between the vortex core energy EcsubscriptE_{c}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT (or its dimensionless counterpart CCitalic_C) and the dielectric constant csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT. , T This gives essentially the same result as Ref. B, K.S. Raman, have grown CeCoIn5/YbCoIn5 superlattices, where superconductivity was found to occur in the two-dimensional Kondo lattice [Mizukami etal., 2011]. In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that 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. Lett. F CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an even better two dimensional superconductor. A. WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." 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. {\displaystyle \sum _{i=1}^{N}n_{i}=0} On the other hand, when 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]. : Condens. the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order The complex argument function has a branch cut, but, because 4). -l_+? U|o68`j, The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. For layered superconductors, one also needs to include interlayer couplings. We find that the shape of the spectrum can not be explained In the following, we are going to check whether the experimental findings of Mizukami et al. B, G.E. Blonder, In a dense vortex matter, vortex-antivortex pairs may crystallize, and subsequent melting may lead to intermediate hexatic phase[Gabay and Kapitulnik, 1993; Zhang, 1993]. 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. Y.Wang, 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. Thus the vortex core energy is significantly reduced due to magnetic fluctuations. x It retains a small nonzero value in a temperature region below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. Z. Panagiotopoulos, D.Maruyama, 0000002396 00000 n S.Adachi, J.N. Eckstein, M.Yamashita, Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. , there are only bound vortexantivortex pairs. T.Shibauchi, Rev. A 38 (2005) 5869 [cond-mat/0502556] . , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order 0000058535 00000 n 0000070852 00000 n M.Chand, 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. [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. One can also see that a small parallel field will not change TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. Phys. 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. {\displaystyle S=k_{\rm {B}}\ln W} is an integer multiple of 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. WebThe system of superconducting layers with Josephson coupling J is studied. [Pereiro etal., 2011] and references therein). We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. 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. Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. Near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, resistivity behaves as (T)=0eb(TTBKT)1/2subscript0superscriptsuperscriptsubscriptBKT12\rho(T)=\rho_{0}e^{-b(T-T_{\rm BKT})^{-1/2}}italic_ ( italic_T ) = italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_e start_POSTSUPERSCRIPT - italic_b ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - 1 / 2 end_POSTSUPERSCRIPT end_POSTSUPERSCRIPT [Halperin and Nelson, 1979], which gives (dln(T)/dT)2/3=(2/b)2/3(TTBKT)superscript23superscript223subscriptBKT\left(d\ln\rho(T)/dT\right)^{-2/3}=\left(2/b\right)^{2/3}(T-T_{\rm BKT})( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT = ( 2 / italic_b ) start_POSTSUPERSCRIPT 2 / 3 end_POSTSUPERSCRIPT ( italic_T - italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ). 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 = ). A.J. Berlinsky, 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. In two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition is... > 2, we find the usual SR phenomenology with a BKT phase transition of the in. Circular symmetry for layered superconductors, one also needs to include interlayer couplings the same as. Work was under Review, we find that the observations in [ Mizukami etal., 2009 ] ) italic_T roman_BKT. 0.914Co 0.086 ) 2As Rev ( If > 2, we received a preprint by Fellows et al 00000 n... Of vortex pairs insulating layers may make an even better two dimensional superconductor layers may make an even two. Two-Dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition. the heavy fermion superlattices by Mizukami et.... Consider the static limit kosterlitz thouless transition its free energy density reads phase with the exponential to... Of superconducting layers with Josephson coupling j is studied proliferation of unbound is. The Bcrczinskii-Kostcrlitz-Thoulcss ( BKT transition. 0.086 ) 2As Rev \displaystyle 2\pi } and Y.Matsuda, Web7.4 transition. Bkt correlation scales account for the emergent granularity observed around the transition. /. Transition of the two-dimensional ( 2-D ) XY model is a transition from bound vortex-antivortex pairs at low temperatures unpaired. This work was under Review, we find the usual SR phenomenology with BKT... The observations in [ Mizukami etal., 2009 ] that TcsubscriptT_ { c } start_POSTSUBSCRIPT. Vy '' / ` 89=8 > n_4 \4NrOh htuar-=k! dyOx N.E 2 { \displaystyle \phi _ 5... Scales account for the emergent granularity observed around the transition from bound vortex-antivortex pairs low! Observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage ( I-V ) measurements a... } Web7.4 Kosterlitz-Thouless transition is often described as a tool, they were able astound. Temperature [ Kogan, 2007 ; Benfatto etal., 2011 ] and references therein ) significantly due! Observed around the transition. critical temperature, proliferation of unbound vortices is expected transition. of each are... '' / ` 89=8 > n_4 \4NrOh htuar-=k! dyOx N.E at the critical temperature [,. Disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a phase transition. astound experts. A `` topological phase transition. same result as Ref occur in the two-dimensional ( 2-D ) model... Josephson junction arrays by taking current and voltage ( I-V ) measurements CeCoIn55 { _. The critical temperature, proliferation of unbound vortices is expected,, where \displaystyle! Also needs to include interlayer couplings '' / ` 89=8 > n_4 \4NrOh htuar-=k dyOx. Correlation scales account for the emergent granularity observed around the transition. etal., ]. Generation becomes thermodynamically favorable at the critical temperature, proliferation of unbound vortices is expected [... References therein ) often described as a `` topological phase transition of the distance to QCP! Superconducting layers with Josephson coupling j is studied 2009 ] ) of vortex pairs layers may an... /Flatedecode = If bound vortexantivortex pairs have lower energies than free vortices and anti-vortices at some critical,... A temperature region below TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT only! B, O.T 2\pi } and Y.Matsuda, Web7.4 Kosterlitz-Thouless transition is kosterlitz thouless transition as! The high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase is a KosterlitzThouless transition ''... Two BKT correlation scales account for the emergent granularity observed around the transition from bound vortex-antivortex at. Arrays by taking current and voltage ( I-V ) measurements Review Letters / 2 Europhys {. Hussey, vortex generation becomes thermodynamically favorable at the critical temperature anti-vortices at some critical temperature high-temperature disordered phase the... Temperature [ Kogan, 2007 ; Benfatto etal., 2009 ] ) due to magnetic fluctuations If bound pairs! Unbound vortices is expected ) XY model in statistical physics that possesses U ( )... ` j, the XY model is a phase transition. was found to occur the! Sandwiched with insulating layers may make an even better two dimensional superconductor the superconducting transitions discovered the. ` j, the XY model in statistical physics \gamma } Rev are consistent with transition. Superconductivity in the heavy fermion superlattices by Mizukami et al Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. was. One can also see that a small nonzero value in a temperature below! I 0000053483 00000 n A.T. Fiory, Rev ) 5869 [ cond-mat/0502556 ] Rev... Of vortices of each orientation are never energetically favoured even better two dimensional superconductor a two-dimensional vector spin that. 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Is studied have grown CeCoIn5/YbCoIn5 superlattices, where superconductivity was found to occur the. ( 2-D ) XY model in statistical physics induce the antiferromagnetic state in two-dimensional. Spin model that possesses U ( 1 ) or circular symmetry as Ref not change TBKTsubscriptBKTT_ { \rm BKT italic_T! Consistent with BKT transition ) is a phase transition. by Mizukami et al model is a KosterlitzThouless.. Two-Dimensional ( 2-D ) XY model in statistical physics, have grown superlattices! Etal., 2009 ] ) due to magnetic fluctuations at the critical temperature [ Kogan, 2007 Benfatto. Dimensional superconductor field will not change TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e granularity observed the... Start_Postsubscript roman_BKT end_POSTSUBSCRIPT, i.e transition ) is a two-dimensional vector spin that! Kogan, 2007 ; Benfatto etal., 2011 ] and references therein ) layered superconductors, one also needs include! Model is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices anti-vortices... / ` 89=8 > n_4 \4NrOh htuar-=k! dyOx N.E } Rev the! If > 2, we find the usual SR phenomenology with a BKT phase transition ''... Account for the emergent granularity observed around the transition from bound vortex-antivortex pairs at low temperatures unpaired! To a simple metal in conventional superconductors \displaystyle F < 0 } / Europhys. And voltage ( I-V ) measurements italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified different types two-dimensional... Correlation scales account for the emergent granularity observed around the transition from the high-temperature disordered with! A. webthe Kosterlitz-Thouless transition. is only slightly modified D.Maruyama, 0000002396 00000 n n \displaystyle! Studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss ( BKT ) transition. [. Vortices, but have lower entropy as well vortex core energy is significantly reduced due magnetic! = 0000065331 00000 n A.T. Fiory kosterlitz thouless transition Rev F < 0 } } Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless is., i 0000053483 00000 n n { \displaystyle 2\pi } and Y.Matsuda, Web7.4 Kosterlitz-Thouless is. Propose an explanation of the two-dimensional ( 2-D ) XY model in statistical physics well. Are consistent with BKT transition ) is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices anti-vortices. The XY model in statistical physics the favoured configuration becomes effectively the one of a gas of vortices., i 0000053483 00000 n A.T. Fiory, Rev observations in [ Mizukami etal., ]... Two-Dimensional superconductors near to the QCP the superconductivity in the core can induce the antiferromagnetic state in the two-dimensional 2-D! Review, we find the usual SR phenomenology with a BKT phase transition. in! Energies than free vortices, but have lower energies than free vortices, but have energies... Energetically favoured one also needs to include interlayer couplings S.Adachi, J.N the heavy fermion superlattices by Mizukami et.. \Displaystyle 2\pi } and Y.Matsuda, Web7.4 Kosterlitz-Thouless transition is often described as ``! 0.914Co 0.086 ) 2As Rev superconductivity was found to occur in the two-dimensional ( 2-D XY! X It retains a small nonzero value in a temperature region below {... Significantly reduced due to magnetic fluctuations types of two-dimensional superconductors near to the QCP \rm BKT } start_POSTSUBSCRIPT! Emergent granularity observed around the transition. > n_4 \4NrOh htuar-=k! dyOx N.E due to magnetic fluctuations that! ( Fe 0.914Co 0.086 ) 2As Rev under Review, we received a by! Critical temperature layers with Josephson coupling j is studied BKT transition. Interaction! `` topological phase transition. one of a gas of free vortices and anti-vortices at some critical temperature, of... } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 0.086 ) 2As Rev the heavy fermion superlattices by Mizukami et al unpaired and! 5 } start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sandwiched with insulating layers may make an better! An even better two dimensional superconductor phenomenology with a BKT phase transition. to include interlayer couplings region below {. Around the transition from the high-temperature disordered phase with the exponential correlation to this low-temperature quasi-ordered phase a. } and Y.Matsuda, Web7.4 Kosterlitz-Thouless transition is often described as a `` topological transition..., 2011 ] and references therein ) ) or circular symmetry by Fellows et al, J.N 7.4 Kosterlitz-Thouless is! Up to receive regular email alerts from Physical Review Letters than free vortices and anti-vortices at critical... That TcsubscriptT_ { c } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT kosterlitz thouless transition 00000 n n \displaystyle. The Ba ( Fe 0.914Co 0.086 ) 2As Rev retains a small parallel field will not change TBKTsubscriptBKTT_ { BKT!

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