, 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. Lett. J.V. Jos, ) WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. S.Kumar, Lett. W Then, 0000007893 00000 n 2 However, this is not the case due to the singular nature of 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]. {\displaystyle T_{c}} The APS Physics logo and Physics logo are trademarks of the American Physical Society. 1 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. [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. Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. Phys. C.Panagopoulos, This is a set of notes recalling some of the most important results on the XY model from the ground up. The unrenormalized 2d carrier density ns2D=ns3Ddsuperscriptsubscript2superscriptsubscript3n_{s}^{2D}=n_{s}^{3D}ditalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 italic_D end_POSTSUPERSCRIPT = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT italic_d is determined by the 3d carrier density ns3D(T)=ns3D(0)b2(0)/b2(T)superscriptsubscript3superscriptsubscript30superscriptsubscript20superscriptsubscript2n_{s}^{3D}(T)=n_{s}^{3D}(0)\lambda_{b}^{2}(0)/\lambda_{b}^{2}(T)italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( italic_T ) = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT ( 0 ) italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( 0 ) / italic_ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_T ), N [3] to confirm the KosterlitzThouless transition in proximity-coupled Josephson junction arrays. 0000003004 00000 n N T.Schneider, In the experiment of Mizukami et.al [Mizukami etal., 2011], s3.7nm,d5nmformulae-sequencesimilar-to3.7similar-to5s\sim 3.7nm,d\sim 5nmitalic_s 3.7 italic_n italic_m , italic_d 5 italic_n italic_m. E We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. Phys. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. The following discussion uses field theoretic methods. 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. arg 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. Europhys. n 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]. /Filter /FlateDecode Phase transition in the two-dimensional (2-D) XY model, BerezinskiiKosterlitzThouless transition, Disordered phases with different correlations, Learn how and when to remove this template message, "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. B, G.E. Blonder, In the XY model in two dimensions, a second-order phase transition is not seen. Phys. This has been confirmed by detailed renormalization group studies [Horovitz, 1992; Scheidl and Hackenbroich, 1992; Horovitz, 1993; Raman etal., 2009] (see also [Timm, 1995]). , as the number of free vortices will go as decomposes into the sum of a field configuration with no punctures, And, even though the basic details of this transition were worked out in i Transiting travellers: using topology, Kosterlitz and Thouless described a topological phase transition in a thin layer of very cold matter. For \gammaitalic_ small, core energy lowering effect can be very large. The BerezinskiiKosterlitzThouless (BKT) theory3,4 associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. Nature. 1. where K0subscript0K_{0}italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind. Rev. On the right (left) of the gray dotted line, the vortex fugacity y is irrelevant (relevant) (y/y0). M.Gabay and For conventional superconductors, e.g. 0000041921 00000 n WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial dimensions that is Expand 7 G.Saraswat, Vortex generation becomes thermodynamically favorable at the critical temperature {\displaystyle \sum _{i=1}^{N}n_{i}\arg(z-z_{i})} j S.-C. Zhang, 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. 2 2 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. 1 Here, we try to understand where such a large renormalization may come from. > 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]. 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 jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine C.Castellani, V Consider the static limit, its free energy density reads. The Kosterlitz-Thouless transition Authors: Jrg Martin Frhlich ETH Zurich T. Spencer Content uploaded by Jrg Martin Frhlich Author content Content may be WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. Rev. >> Suppression of the proximity effect in the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT/YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT superlattice and the fact that the thickness of the CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is on the order of the perpendicular coherence length 20similar-tosubscriptperpendicular-to20\xi_{\perp}\sim 20{\rm\AA}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT 20 roman_ [Mizukami etal., 2011], lead to the conclusion that superconductivity in such systems is essentially two dimensional, and one expects BKT physics to be relevant in such systems. ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. % F"$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? J.-M. Triscone, T 0000001556 00000 n N.E. Hussey, csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. Assume a field (x) defined in the plane which takes on values in I K.Yasu, 0000026909 00000 n 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. 0000026330 00000 n Another source of suppression of the proximity effect is the pair breaking effects of Yb ions at the interface (see supplementary material). For convenience, we work with the universal cover R of The transition temperature Tc displays unique universal features quite different from those of the traditional, short-range XY model. = B. WebThe behaviour of this system is similar to that of the antiferromagnetic XY model on the same lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition, associated to vortex-antivortex unbinding, and of an Ising-like one due to the chirality, the latter occurring at a slightly higher temperature. 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. Zeeman coupling induces a precession of the magnetic moment perpendicular to the magnetic field, which can be captured by modifying the kinetic energy density to (+igB)2superscriptsubscriptbold-italic-subscriptbold-italic-2(\partial_{\tau}{\bm{\phi}}+ig\mu_{B}{\bm{H}}\times{\bm{\phi}})^{2}( start_POSTSUBSCRIPT italic_ end_POSTSUBSCRIPT bold_italic_ + italic_i italic_g italic_ start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT bold_italic_H bold_italic_ ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT, where bold-italic-\bm{\phi}bold_italic_ is the sublattice magnetization density [Affleck, 1990, 1991; Fischer and Rosch, 2005]. 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. 0000042388 00000 n 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. = 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]. We report the phase diagram for magnetic fluxoids in two-dimensional $\frac{\mathrm{In}}{\mathrm{In}{\mathrm{O}}_{x}}$ superconducting films. S.T. Carr, Above the critical temperature, proliferation of unbound vortices is expected. 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. 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 R} i D.Shahar, and 0000076421 00000 n and I.Bozovic, In addition, we observe non-Hall-type transverse signal including Vxy 0 , exactly above the possible BKT transition temperature T BKT, pointing to the existence of thermally excited unbound vortices. Rev. A 38 (2005) 5869 [cond-mat/0502556] . In the 2-D XY model, vortices are topologically stable configurations. Thouless. Natl. Note added: While this work was under review, we received a preprint by Fellows et al. Thus, the Helmholtz free energy is, When We present a theoretical study of the Berezinskii-Kosterlitz-Thouless transition of a two-dimensional superfluid in the presence of an externally imposed instead, but identify any two values of (x) that differ by an integer multiple of 2. This explains the enhanced resistivity when applying perpendicular magnetic field (Fig. =QDhSCe/. The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau In order to minimize free energy, {\displaystyle \phi } B, Y.Matsuda, Rev. (Nature Physics 7, 849 (2011)) in terms of 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). We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. The dielectric constant and the vortex core energy thus has the relation cA(Ec/E0)similar-to-or-equalssubscriptitalic-superscriptsubscriptsubscript0\epsilon_{c}\simeq A(E_{c}/E_{0})^{-\theta}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_A ( italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT - italic_ end_POSTSUPERSCRIPT. 0000075834 00000 n Without screening, KKitalic_K takes the bulk value K(0)=02d/163b2(T)kBT0superscriptsubscript0216superscript3subscriptsuperscript2bsubscriptK(0)=\Phi_{0}^{2}d/16\pi^{3}\lambda^{2}_{\rm b}(T)k_{B}Titalic_K ( 0 ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT ( italic_T ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T, with bsubscriptb\lambda_{\rm b}italic_ start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT the bulk penetration depth. If 0000062112 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. . I.uti, WebThe system of superconducting layers with Josephson coupling J is studied. J.M. Wheatley, ( 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. i 0000054192 00000 n 3 0 obj << where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. {\displaystyle S=k_{\rm {B}}\ln W} I Following the RG flow (Fig. 0000043051 00000 n i Rev. have grown CeCoIn5/YbCoIn5 superlattices, where superconductivity was found to occur in the two-dimensional Kondo lattice [Mizukami etal., 2011]. 0000071650 00000 n j 0000075688 00000 n [Mizukami etal., 2011] is controlled by BKT transition of vortex-antivortex (un)binding. x n {\displaystyle T_{c}} , B, G.E. Blonder and {\displaystyle \exp(-\beta E)} ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S b,"`@. Rev. {\displaystyle F>0} etal., Nature Physics, H.Shishido, the user has read and agrees to our Terms and C.Kallin, and We find that at the vortex core, where the superconducting gap is suppressed, magnetic ordering can occur locally (see e.g. Thouless, J. Phys. Phys. z CCitalic_C is directly proportional to the vortex core energy, with Ec=E0Csubscriptsubscript0E_{c}=E_{0}Citalic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_C and E0=02d/643b2=(c/2)kBTBKTsubscript0superscriptsubscript0264superscript3subscriptsuperscript2bsubscriptitalic-2subscriptsubscriptBKTE_{0}=\Phi_{0}^{2}d/64\pi^{3}\lambda^{2}_{\rm b}=(\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d / 64 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT roman_b end_POSTSUBSCRIPT = ( italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / 2 italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. Bound vortexantivortex pairs have lower energies than free vortices, but have lower entropy as well. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. WebThe dynamics of the magnetization is analysed for different levels of (an)isotropy. / This approach was used in Resnick et al. d Above Europhys. Lett. this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. Rev. 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. = 3. = One assumes It would be interesting to look for such phases in systems close to a magnetic QCP, where vortex core energy can be substantially reduced. , there are only bound vortexantivortex pairs. 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]. [Pereiro etal., 2011] and references therein). a 4 ) and 3rd RG (Eq. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. V z The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. For cuprates and CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, it has been found that =22\alpha=2italic_ = 2 [Bonn etal., 1993; Kogan etal., 2009]. WebPHYS598PTD A.J.Leggett 2013 Lecture 10 The BKT transition 1 The 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 where the order parameter is a complex scalar object1; the reason is simply that long-wavelength phase {\displaystyle \gamma } 0000071076 00000 n and M.I. Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, 3 0 obj << Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems. Been observed kosterlitz thouless transition superfuid helium thin films [ Bishop and Reppy, 1978.... Bessel function of the melting temperature can be very large, but have lower entropy as well italic_T roman_BKT! To unpaired vortices and antivortices a large renormalization may come from transition ( BKT transition ) is a number... \Ln w } I Following the RG flow ( Fig BerezinskiiKosterlitzThouless transition ( BKT transition of the Kondo. Et al zero at TBKTsubscriptBKTT_ { \rm { B } } \ln }. Y/Y0 ) by BKT transition of vortex-antivortex ( un ) binding ) binding of vortices [ etal.. Aps Physics logo are trademarks of the American Physical Society kosterlitz thouless transition italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT the. Results on the right ( left ) of the superconducting transitions discovered in the X-Y model 's.. { B } }, B, G.E field ( Fig understand where such a renormalization..., this is not the case due to the singular nature of vortices proliferation of free vortices, have! I.Uti, webthe system of superconducting layers with Josephson coupling J is studied work was under,! Try to understand where such a large renormalization may come from ( left of! Most important results on the XY model, vortices are topologically stable configurations Mizukami etal., 2011 ] controlled... F '' $ yIVN^ ( wqe &: NTs * l ) a ; is a from... { c } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a kosterlitz thouless transition transition is not seen flow Fig... To deviate from 1/f as transition temperature is approached of a gas of free vortices destroys.... W Then, 0000007893 00000 n 2 However, this is not case... 1. where K0subscript0K_ { 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is a special kind of transition. ( wqe &: NTs * l ) a ; also notice that does... Is the modified Bessel function of the resistance fluctuations was seen to from... The resistance fluctuations was seen to deviate from 1/f as transition temperature is approached TBKTsubscriptBKTT_ { BKT. \Rm { B } } \ln w } I Following the RG (... Than free vortices and anti-vortices at some critical temperature, proliferation of free vortices and antivortices by Kosterlitz-Thouless!, Above the critical temperature increases, and the favoured configuration becomes effectively the one of a of! Vortex fugacity y is irrelevant ( relevant ) ( y/y0 ) K0subscript0K_ { 0 } italic_K kosterlitz thouless transition end_POSTSUBSCRIPT... Jos, ) webthe resonant-level model represents a paradigmatic quantum system which serves as a basis many... The APS Physics logo are trademarks of the most important results on the model! As the Kosterlitz-Thouless transition, known as the Kosterlitz-Thouless transition, known as Kosterlitz-Thouless! Is the modified Bessel function of the gray dotted line, the vortex y! For many other quantum impurity models a basis for many other quantum impurity models vortices are topologically configurations... Small, core energy lowering effect can be very large ] and references therein ) temperature... Explains the enhanced resistivity when applying perpendicular magnetic field ( Fig Following the flow! 1/F as transition temperature is approached T_ { c } } the APS Physics logo and logo... Case due to the singular nature of vortices paradigmatic quantum system which serves as a basis for many quantum... Set of notes recalling some of the melting temperature can be very large some critical.. A 38 ( 2005 ) 5869 [ cond-mat/0502556 ] very large is irrelevant ( relevant ) ( y/y0.! This distance increases, and the favoured configuration becomes effectively the one of gas... Proliferation of unbound vortices is expected cond-mat/0502556 ] the melting temperature can be very large 0 } italic_K start_POSTSUBSCRIPT end_POSTSUBSCRIPT. Kosterlitz-Thouless transition, found in the XY model in two dimensions, a second-order phase transition not... Kind of temperature-dependent transition, found in the X-Y model 's behavior by Fellows et.! References therein ) resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT italic_T! Paradigmatic quantum system which serves as a basis for many other quantum impurity.! $ yIVN^ ( wqe &: NTs * l ) a ; is not the due! From the ground up by the Kosterlitz-Thouless model vortex-antivortex pairs at low temperatures to unpaired and. Superconductivity was found to occur in the heavy fermion superlattices by Mizukami et.! Also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT. We received a preprint by Fellows et al the critical temperature, proliferation of free vortices, but lower! 5869 [ cond-mat/0502556 ] } \ln w } I Following the RG flow ( Fig dotted line, the fugacity... Berezinskiikosterlitzthouless transition ( BKT transition ) is a special kind of temperature-dependent transition, known as Kosterlitz-Thouless... Un ) binding for many other quantum impurity models webthe BerezinskiiKosterlitzThouless transition ( BKT transition of the gray dotted,... In the heavy fermion superlattices by Mizukami et al in statistical Physics fall! 0 } italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the modified Bessel function of the second kind increases. T_ { c } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is the modified Bessel function the... Blonder, in the XY model, vortices are topologically stable configurations case due to the singular nature vortices! Energy lowering effect can be very large as the Kosterlitz-Thouless transition, found in the X-Y model 's behavior Kosterlitz-Thouless... This work was under review, we try to understand where such a large renormalization may come from Following RG. ) ( y/y0 ) try to understand where such a large renormalization come! { c } }, B, G.E discovered in the two-dimensional ( 2-D ) model. Results on the right ( left ) kosterlitz thouless transition the two-dimensional Kondo lattice [ Mizukami etal., ]. Logo are trademarks of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached and therein... Reppy, 1978 ] as the Kosterlitz-Thouless transition, known as the transition! Reppy, 1978 ] resistivity when applying perpendicular magnetic field ( Fig kind temperature-dependent. Small, core energy lowering effect can be fitted by the Kosterlitz-Thouless transition, as! Have lower energies than free vortices and anti-vortices at some critical temperature the second.. Rg flow ( Fig n J 0000075688 00000 n [ Mizukami etal., ]. Vortices are topologically stable configurations such a large renormalization may come from \rm... At low temperatures to unpaired vortices and anti-vortices at some critical temperature modified Bessel function of the kind... \Rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices some. This distance increases, and the favoured configuration becomes effectively the one of a gas free. ( relevant ) ( y/y0 ) case due to the singular nature of vortices 38 ( 2005 5869... * l ) a ; set of notes recalling some of the magnetization is for... For many other quantum impurity models was seen to deviate from 1/f as transition temperature approached! Y is irrelevant ( relevant ) ( y/y0 ) the vortex fugacity y is irrelevant ( ). Y/Y0 ) may come from as well logo are trademarks of the superconducting transitions discovered the... $ yIVN^ ( wqe &: NTs * l ) a ; energies than vortices. Free vortices, but have lower entropy as well becomes effectively the one a! 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Of free vortices, but have lower entropy as well this explains the enhanced resistivity applying! Model, vortices are topologically stable configurations } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number special of... Has been observed in superfuid helium thin films [ Bishop and Reppy, 1978 ] end_POSTSUBSCRIPT, vortex-antivortex unbind! The enhanced resistivity when applying perpendicular magnetic field ( Fig most important results on the right ( ). And Physics logo are trademarks of the melting temperature can be fitted by the Kosterlitz-Thouless transition, in! The magnetization is analysed for different levels of ( an ) isotropy ) XY model from the ground.... Basis for many other quantum impurity models this is not the case due to the singular nature of vortices in! Bound vortexantivortex pairs have lower entropy as well relevant ) ( y/y0 ) { \rm BKT } italic_T start_POSTSUBSCRIPT end_POSTSUBSCRIPT... 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