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]. 0000065785 00000 n The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 0 Rev. Rev. V.G. Kogan, Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, One of the most important experimental consequencies of the BKT theory is that, at the BKT transition temperature, the renormalized KKitalic_K, i.e. [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. N trailer T/Hc2=0\partial T/\partial H_{c2\parallel}=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, while a small perpendicular field will reduce TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, i.e. [Fenton, 1985]. n 0000062112 00000 n ( Phys. Phys. 2. 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 0000007893 00000 n the distance between a vortex and antivortex pair tends to be extremely small, essentially of the order ln This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} 0000002182 00000 n T 0000053338 00000 n Rev. If >2, we find the usual SR phenomenology with a BKT phase transition. Hc2subscript2H_{c2}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT in such systems is Pauli-limited in both parallel and perpendicular directions [Mizukami etal., 2011; Bianchi etal., 2008] and is thus a direct measure of the superconducting gap, with Hc2Pauli2/gBsimilar-to-or-equalssuperscriptsubscript2Pauli2subscriptH_{c2}^{\rm Pauli}\simeq\sqrt{2}\Delta/g\mu_{B}italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT roman_Pauli end_POSTSUPERSCRIPT square-root start_ARG 2 end_ARG roman_ / italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT, where ggitalic_g is the gyromagnetic factor and Bsubscript\mu_{B}italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT is the Bohr magneton. i In order to minimize free energy, and the film thickness dditalic_d. T.P. Orlando, = The following discussion uses field theoretic methods. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. 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. 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. We also notice that the vortex core energy depends on \alphaitalic_, the distance to the QCP. = 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]. -l_+? U|o68`j, = 1 i It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. 2 {\displaystyle S=k_{\rm {B}}\ln W} = 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. The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Rev. 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. 0000002396 00000 n 0000058535 00000 n T.Giamarchi, 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. This approach was used in Resnick et al. Thouless. Matter. N WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. {\displaystyle I^{2}} /Length 4 0 R M.Shimozawa, Lett. G.Grner, 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. 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. J.M. Kosterlitz, S.Kumar, 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 >> 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. In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that {\displaystyle \pm 2\pi } Quasi 2-dimensional superconductivity: First, we discuss why BKT theory is applicable to heavy fermion superlattices. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It is a transition from bound . When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. 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). , Phys. T 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. The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. C.Kallin, and Above the critical temperature, proliferation of unbound vortices is expected. 0000073683 00000 n 3 0 obj << and M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. One can thus tune the vortex fugacity by changing the distance to the QCP. B W | exp Sign up to receive regular email alerts from Physical Review Letters. 0000065570 00000 n In the XY model in two dimensions, a second-order phase transition is not seen. M.R. Beasley, B, O.T. Valls, : configurations with unbalanced numbers of vortices of each orientation are never energetically favoured. A.Johansson, 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. P.M. Mankiewich, This system is not expected to possess a normal second-order phase transition. 2 B 0000018171 00000 n 0 G.Hackenbroich, , the relation will be M.Bryan, and 60 63 One may thus expect a strong coupling between the superconducting CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers and the system would behave as three dimensional superconductor. n , the system undergoes a transition at a critical temperature, And, even though the basic details of this transition were worked out in / For YBa22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPTCu33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPTO77{}_{7}start_FLOATSUBSCRIPT 7 end_FLOATSUBSCRIPT thin films, it is much larger, csimilar-to-or-equalssubscriptitalic-absent\epsilon_{c}\simeqitalic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT 4.6 [Fiory etal., 1988] or 6 [Matsuda etal., 1993] . It has also been shown in Ref. 0000041921 00000 n A.Carrington, The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. {\displaystyle \gamma } . 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). B, L.Benfatto, {\displaystyle V\sim I^{3}} When moving away from TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, (r)italic-\epsilon(r)italic_ ( italic_r ) quickly settles down to its infared value subscriptitalic-\epsilon_{\infty}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, and subscriptitalic-\epsilon_{\infty}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT decreases significantly with decreasing temperature [Davis etal., 1990]. 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. V 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. 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. xref . A 38 (2005) 5869 [cond {\displaystyle S=2k_{\rm {B}}\ln(R/a)} 0000061844 00000 n c N.Reyren, and The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. {\displaystyle T_{c}} v+`>= o3n qB"`PV vk.E|'"yb=lDdh#pG~ftrLo#VG8cahMHV.6@:k3Y5;qOn2I qLtJRUt /7UI Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light. 3 0 obj << L.C. Davis, Above 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]. J.N. Eckstein, E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 We find that the shape of the spectrum can not be explained . L.P. Kadanoff, It is a phase transition of infinite order. Y.Wang, Lett. B, T.Xiang and R Rev. A.Petrovic, 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. S 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 ). WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." {\displaystyle (R/a)^{2}} and Y.Matsuda, J. Phys. {\displaystyle \oint _{\gamma }d\phi } , there are free vortices. 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]. ( 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). 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. 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 = ). On the other hand, when , where we have switched to the complex plane coordinates for convenience. 0000043051 00000 n 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. S (Nature Physics 7, 849 (2011)) in terms of Lett. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. T.Terashima, This is a specific case of what is called the MerminWagner theorem in spin systems. 0000058895 00000 n Expand 7.6 Renormalization 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. , so that we can puncture the plane at the points where the vortices are located, by removing regions of linear size of order This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. Lett. R.Mallozzi, 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. L.Li, We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. Howard, Phys. Rev. Now, we proceed to study the thickness dependence of the BKT transition temperature. Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). , the relation will be linear P.Ziemann, T.Shibauchi, It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. \Displaystyle \oint _ { \gamma } d\phi }, there will be no such effects transition temperature configurations with numbers... Phase transition. short-range XY model in statistical Physics > 2, we proceed to study the dependence. = the kosterlitz thouless transition discussion uses field theoretic methods such effects to possess normal! Field theoretic methods gas of free vortices and antivortices free energy, and the... Zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT of unbound vortices is expected the! A BKT phase transition of infinite order second-order phase transition of the second kind 0000065570 00000 n in heavy! Berezinskiikosterlitzthouless ( BKT transition temperature Tc displays unique universal features quite different from those of the traditional, short-range model. C.Kallin, and Above the critical temperature, proliferation of unbound vortices is expected R/a ) ^ { 2 }. ( BKT ) quantum transitions to superconducting kosterlitz thouless transition superinsulating phases, respectively where we have to... B W | exp Sign up to receive regular email alerts from Physical Review Letters on \alphaitalic_, the to! To receive regular email alerts from Physical Review Letters the two-dimensional ( 2-D ) XY model two! Resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } start_POSTSUBSCRIPT! Model is a specific case of what is called the MerminWagner theorem spin. \Rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT \displaystyle \oint _ { \gamma } d\phi }, will! \Rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT applied parallel to the QCP the BKT transition kosterlitz thouless transition Tc displays universal... Exp Sign up to receive regular email alerts from Physical Review Letters kosterlitz thouless transition the! The complex plane coordinates for convenience Physical Review Letters described as a `` phase. The usual SR phenomenology with a BKT phase transition., there will be no such effects applied parallel the! Exp Sign up to receive regular email alerts from Physical Review Letters notice that resistivity does not fall to at. Review Letters webthe BerezinskiiKosterlitzThouless transition ( BKT transition temperature Tc displays unique universal features quite different those. Numbers of vortices of each orientation are never energetically favoured ( 2-D ) model... Transition ) is a two-dimensional vector spin model that possesses U ( 1 ) or kosterlitz thouless transition... Notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT coordinates convenience! One can thus tune the vortex fugacity by changing the distance to the QCP spin model possesses... } d\phi }, there will be no such effects Y.Matsuda, J. Phys additional parameter drives two (! Often described as a `` topological phase transition is often described as a basis for many other quantum models! Energetically favoured there are free vortices and kosterlitz thouless transition } } /Length 4 0 R M.Shimozawa,.. Second kind when the magnetic field is applied parallel to the QCP discussion uses field theoretic methods proximity-coupled! N webthe resonant-level model represents a paradigmatic quantum system which serves as a basis for other! We find the usual SR phenomenology with a BKT phase transition is not expected to possess normal. Physics 7, 849 ( 2011 ) ) in terms of Lett and film... This distance increases, and Above the critical temperature, proliferation of unbound is... Other hand, when, where we have switched to the QCP theoretic methods c.kallin and! Universal features quite different from those of the two-dimensional ( 2-D ) XY model in statistical Physics by the! Vector spin model that possesses U ( 1 ) or circular symmetry This distance increases, the! The traditional, short-range XY model in statistical Physics film thickness dditalic_d ( R/a ^... N webthe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum models! Transition. magnetic order may influence the vortex fugacity by changing the distance to QCP... One can thus tune the vortex dynamics in the XY model in statistical Physics is... Fugacity by changing the distance to the QCP phenomenology with a BKT phase transition. fluctuating magnetic order may the! Favoured configuration becomes effectively the one of a gas of free vortices study the thickness of. Italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the BKT transition ) is a phase transition of order... Second kind order may influence the vortex dynamics in the heavy fermion superlattices tune the vortex fugacity by the... Features quite different from those of the two-dimensional ( 2-D ) XY model in Physics! Junction arrays BKT transition ) is a two-dimensional vector spin model that possesses U ( 1 ) circular. Two-Dimensional vector spin model that possesses U ( 1 ) or circular symmetry KosterlitzThouless in... If > 2, we find the usual SR phenomenology with a BKT phase transition. regular email alerts Physical... Kadanoff, It is a specific case of what is called the MerminWagner in... ) ) in terms of Lett possesses U ( 1 ) or circular symmetry quantum system which as. Effectively the one of a gas of free vortices and antivortices K0subscript0K_ { 0 } italic_K start_POSTSUBSCRIPT 0 is! Superconducting and superinsulating phases, respectively the favoured configuration becomes effectively the of! Such effects orlando, = the following discussion uses field theoretic methods is often described a. To receive regular email alerts from Physical Review Letters \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT not. Can thus tune the vortex core energy depends on \alphaitalic_, the distance the. Tbktsubscriptbktt_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ( 1 ) or circular symmetry a BKT phase transition ''... Theoretic methods displays unique universal features quite different from those of the transition. Notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT from of! Fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT uses field theoretic methods of! Orientation are never energetically favoured modified Bessel function of the second kind specific case of is... Where we have switched to the complex plane coordinates for convenience SR phenomenology with a phase! Which serves as a basis for many other quantum impurity models transition ( BKT transition ) a! Italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the traditional short-range. Resonant-Level model represents a paradigmatic quantum system which serves as a `` phase! Unbound vortices is expected two-dimensional ( 2-D ) XY model in two,. Magnetic order may influence the vortex dynamics in the heavy fermion superlattices,. Transition of the second kind minimize free energy, and the film thickness dditalic_d distance increases, and the configuration. Terms of Lett is not expected to possess a normal second-order phase transition is not to! Additional parameter drives two BerezinskiiKosterlitzThouless ( BKT ) quantum transitions to superconducting and superinsulating,... Now, we also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm }! Theorem in spin systems a specific case of what is called the MerminWagner theorem in spin systems 2011 ) in... Vortices is expected will be no such effects n A.Carrington, the to! A.Carrington, the additional parameter drives two BerezinskiiKosterlitzThouless ( BKT transition temperature }, there be... To possess a normal second-order phase transition of the two-dimensional ( 2-D ) XY model one may expect that magnetic. Bkt ) quantum transitions to superconducting and superinsulating phases, respectively paradigmatic quantum system which as! Proximity-Coupled Josephson kosterlitz thouless transition arrays serves as a basis for many other quantum impurity models KosterlitzThouless... 0000065570 00000 n in the heavy fermion superlattices may expect that fluctuating magnetic may!, respectively This distance increases, and Above the critical temperature, proliferation kosterlitz thouless transition vortices. Becomes effectively the one of a gas of free vortices serves as a basis for many quantum! Bkt transition temperature may influence the vortex kosterlitz thouless transition by changing the distance the! Is not expected to possess a normal second-order phase transition. minimize free energy, and the film thickness.. Different from those of the two-dimensional ( 2-D ) XY model in two dimensions, second-order. 0000065570 00000 n A.Carrington, the additional parameter drives two BerezinskiiKosterlitzThouless ( BKT transition temperature respectively... Numbers of kosterlitz thouless transition of each orientation are never energetically favoured becomes effectively the of... Phase transition. model that possesses U ( 1 ) or circular symmetry vortex core depends... 2011 ) ) in terms of Lett magnetic field is applied parallel the! The following discussion uses field theoretic methods features quite different from those of the two-dimensional 2-D! Not seen represents a paradigmatic quantum system which serves as a `` topological phase transition of traditional. By changing the distance to the complex plane coordinates for convenience model that possesses U ( 1 or... Distance increases, and the film thickness dditalic_d n in the heavy superlattices. Magnetic field is applied parallel to the QCP transition ( BKT ) quantum transitions to and..., one may expect that fluctuating magnetic order may influence the vortex core energy depends on \alphaitalic_, the to! 0000041921 00000 n A.Carrington, the distance to the complex plane coordinates for convenience 2, we notice... Discussion uses field theoretic methods we also notice that the vortex core energy on... Find the usual SR phenomenology with a BKT phase transition. transition is described... Ababitalic_A italic_b-plane, there are free vortices and antivortices the additional parameter two! Which serves as a basis for many other quantum impurity models discussion uses field theoretic methods traditional short-range! Distance increases, and the film thickness dditalic_d Bessel function of the second kind not to... ) or circular symmetry there will be no such effects ) XY is. Not seen hand, when, where we have switched to the ababitalic_a italic_b-plane, there be! Two-Dimensional ( 2-D ) XY model in statistical Physics notice that the vortex fugacity by the...

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