Following the RG flow (Fig. Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. A.Kamlapure, The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a 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. Furthermore, we study the influence of a nearby magnetic quantum critical point on the vortex system, and find that the vortex core energy can be significantly reduced due to magnetic fluctuations. / We propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. 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. C.Panagopoulos, WebWe show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. d % 0
Lett. DOI:https://doi.org/10.1103/PhysRevLett.127.156801. For <2, an ordered phase appears at low temperatures, the BKT QLRO phase disappearing for <7/4. A large dielectric constant corresponds to a small vortex core energy. At low temperatures and large {\displaystyle \gamma } , entropic considerations favor the formation of a vortex. M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. 1 Our DMRG results point towards an exponential opening of the charge gap entering the insulating state, which corroborates the Kosterlitz-Thouless transition scenario. D.Maruyama, 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. A 38 (2005) 5869 [cond-mat/0502556] . over any contractible closed path /Length 4 0 R Webcorrelations. 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]. 0000053338 00000 n
N >> ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. The data provide evidence for a two dimensional quantum superconductor to insulator (2D-QSI) tran and the film thickness dditalic_d. , there are free vortices. This result is intimately related to that of Blonder, Tinkham and Klapwijk [Blonder etal., 1982; Blonder and Tinkham, 1983], where it was shown that the mismatch of Fermi velocities between the N and S regions increases the barrier height between the two, with the effective barrier parameter ZZitalic_Z modified to Z=(Z02+(1r)2/4r)1/2superscriptsuperscriptsubscript02superscript12412Z=(Z_{0}^{2}+(1-r)^{2}/4r)^{1/2}italic_Z = ( italic_Z start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + ( 1 - italic_r ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_r ) start_POSTSUPERSCRIPT 1 / 2 end_POSTSUPERSCRIPT where r=vS/vNsubscriptsubscriptr=v_{S}/v_{N}italic_r = italic_v start_POSTSUBSCRIPT italic_S end_POSTSUBSCRIPT / italic_v start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT is the ratio of two Fermi velocities. We show that the resistivity data, both with and without magnetic field, are consistent with BKT transition. 0000008417 00000 n
Classical systems", "Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. 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. R.Mallozzi, ) WebWe employ the theory of topological phase transitions, of the Berezinski-Kosterlitz-Thouless (BKT) type, in order to investigate orientational ordering in four spatial ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S
b,"`@. arg T KosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. One can thus tune the vortex fugacity by changing the distance to the QCP. We also notice that resistivity does not fall to zero at TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. V 3 0 obj << Generated on Sat Dec 17 01:38:46 2022 by, Y.Mizukami, , where This is generically observed for a BKT transition, and is attributed to the temperature difference between the formation of single vortices and the subsequent vortex condensation (see e.g. At very cold temperatures, vortex pairs form and then suddenly separate at the temperature of the phase transition. where a vortex of unit vorticity is placed at =00{\mathbf{r}}=0bold_r = 0. V0subscript0V_{0}italic_V start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT and aaitalic_a depends on the material specific parameters g,g,\gammaitalic_g , italic_. At large temperatures and small Conditions and any applicable A 38 (2005) 5869 [cond-mat/0502556] . Lett. 0000073683 00000 n
However, one finds a low-temperature quasi-ordered phase with a correlation function (see statistical mechanics) that decreases with the distance like a power, which depends on the temperature. G.Saraswat, 5(a)). Phys. R.Prozorov, and B, K.S. Raman, decomposes into the sum of a field configuration with no punctures, M.J. Naughton, {\displaystyle S=2k_{\rm {B}}\ln(R/a)} Rev. 0000075834 00000 n
We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. {\displaystyle F<0} 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. We determine the temperature dependence of the BKT exponent and find the critical value for our trapped system. E Statistical Nonlinear and Soft Matter Physics 89(4): 042803 R 0 This suppression factor significantly degrades the proximity coupling to the point where 4 nm normal layer renders heavy fermion films essentially uncoupled. is Boltzmann's constant. Inhomogeneity and finite size effects also broaden the BKT transition, giving rise to the resistivity tail below TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT [Benfatto etal., 2009]. < [Arovas etal., 1997]), which reduces the vortex core energy. A.J. Berlinsky, {\displaystyle I^{2}} R T.Terashima, Thus to determine whether a superconducting transition is of the BKT type, it is crucial to measure the penetration depth \lambdaitalic_, and to check whether such universal relation between \lambdaitalic_ and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT is satisfied. 2 the temperature dependence of (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT for the four different cases with number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers n=4,5,7,94579n=4,5,7,9italic_n = 4 , 5 , 7 , 9, where one can see that (dln(T)/dT)2/3superscript23(d\ln\rho(T)/dT)^{-2/3}( italic_d roman_ln italic_ ( italic_T ) / italic_d italic_T ) start_POSTSUPERSCRIPT - 2 / 3 end_POSTSUPERSCRIPT is indeed linear in TTitalic_T, and TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT can be extracted from the intersection points. and Y.Matsuda, WebMy parents, Hans Walter and Johanna Maria Kosterlitz (Gresshner) had fled Hitlers Germany in 1934 because my father, a non-practicing Jew, came from a Jewish family and was forbidden to marry a non-Jewish woman like my mother or to be paid as a medical doctor in Berlin. A.J. Berlinsky, . E 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. T Rev. 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. Phys. c is defined modulo is the system size, and 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. vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. ( 1. Phys. Natl. is the radius of the vortex core. 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. B From the above RG equations, one can see that the renormalized fugacity vanishes at the transition, i.e. 0000076421 00000 n
0000018171 00000 n
x {\displaystyle n_{i}=\pm 1} 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. 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 = ). 0000053628 00000 n
More precisely, we consider the equation of motion. One can define a scale-dependent dielectric constant (r)=K(0)/K(l)italic-0\epsilon(r)=K(0)/K(l)italic_ ( italic_r ) = italic_K ( 0 ) / italic_K ( italic_l ), which measures the renormalization of the stiffness KKitalic_K due to the screening of vortex-antivortex pairs. {\displaystyle T_{c}} S.Adachi, <]>>
csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. F and is given by. Consider the static limit, its free energy density reads. 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. 0000042388 00000 n
G.Orkoulas and The value of this integer is the index of the vector field 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 This is a specific case of what is called the MerminWagner theorem in spin systems. 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. M.Chand, = / We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. J. : Condens. A.F. Hebard, In BKT theory, the vortex system is descibed by the Hamiltonian, where the stiffness K=ns2/4mkBTsubscriptsuperscriptPlanck-constant-over-2-pi24subscriptK=n_{s}\hbar^{2}/4mk_{B}Titalic_K = italic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 4 italic_m italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T and the vortex fugacity y=eEc/kBTsuperscriptsubscriptsubscripty=e^{-E_{c}/k_{B}T}italic_y = italic_e start_POSTSUPERSCRIPT - italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT / italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T end_POSTSUPERSCRIPT obey the renormalization group (RG) equations [Kosterlitz, 1974; Jos etal., 1977]. 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. , there are only bound vortexantivortex pairs. 0000062403 00000 n
The following discussion uses field theoretic methods. ex '3oWD&o!E[DDwta`s=|G=W>;^@ 3)b:u@yRBp6vkzMXEwZYNvS$&I\jW3}T5Tgc. {\displaystyle \kappa } S.T. Carr, = J.D. Reppy, . J.Corson, i 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] . B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. Just below At the transition, the renormalized penetration depth satisfies the relation [Nelson and Kosterlitz, 1977] kBTBKT=02d/3222subscriptsubscriptBKTsuperscriptsubscript0232superscript2superscript2k_{B}T_{\rm BKT}=\Phi_{0}^{2}d/32\pi^{2}\lambda^{2}italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT 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 (Eq. WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. H.Ikeda, 0 z , InOx{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9. 2 N a WebThe Kosterlitz-Thouless transition is often described as a "topological phase transition." c 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 . [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. V.Oganesyan, 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. 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. etal., Proc. 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. While at Birmingham, Thouless supervised Michael Kosterlitz as a talented postdoctoral associate. /Length 2177 0000003004 00000 n
{\displaystyle \Lambda } 1 WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. i 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. 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. B. D.J. Bishop and 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. a {\displaystyle \oint _{\gamma }d\phi } {\displaystyle T_{c}} >> and S.L. Yan, I understand why it isn't a conventional Landau-symmetry-breaking phase transition: there is no local symmetry-breaking order parameter on either side of the transition, and all thermodynamic quantities remain continuous (though not analytic) at all derivative orders S.Kumar, It is a transition from bound C.Kallin, , the relation will be 3 WebKosterlitzThouless transitions is described as a dissociation of bound vortex pairs with opposite circulations, called vortexantivortex pairs, first described by Vadim Berezinskii. (with W is the number of states), the entropy is WebThis transition is called Berezinskii-Kosterlitz-Thouless (BKT) transition and still remains to be a topic of active research. 0000070328 00000 n
[Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. 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). . {\displaystyle \Lambda \to \infty } This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. However, this is not the case due to the singular nature of vortices. | and M.I. 0000062112 00000 n
) , the system will not have a vortex. {\displaystyle T_{c}} WebWe propose an explanation of the superconducting transitions discovered in the heavy fermion superlattices by Mizukami et al. {\displaystyle 1/\Lambda } The behavior of gap and TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT for different number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers is shown in Fig. M.Yamashita, 0000026620 00000 n
0000002182 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. 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. 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. This means that gap retains the bulk value for n55n\geq 5italic_n 5. We find that c=2,4.6,6,90subscriptitalic-24.6690\epsilon_{c}=2,4.6,6,90italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 2 , 4.6 , 6 , 90 corresponds to C=7.27,2.24,1.583,0.05997.272.241.5830.0599C=7.27,2.24,1.583,0.0599italic_C = 7.27 , 2.24 , 1.583 , 0.0599 respectively (see Fig. Thouless, J. Phys. It featuresfor 7/4<<2a quasiordered phase in a finite temperature range TcTBKT. Phys. 0000017580 00000 n
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j Assume the case with only vortices of multiplicity B, R.W. Crane, 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. and stream T Rev. ( J. Phys. i Subscription = Nelson, Phys. Rev. trailer
Phys. J.N. Eckstein, WebThe Kosterlitz-Thouless transition, or Berezinsky-Kosterlitz-Thouless transition, is a special transition seen in the XY model for interacting spin systems in 2 spatial Below Note added: While this work was under review, we received a preprint by Fellows et al. Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. 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. Sci. 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. 3. I 0000026909 00000 n
WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. Been observed in superfuid helium thin films [ Bishop and Reppy, 1978 ] Michael Kosterlitz as ``... Start_Postsubscript roman_BKT end_POSTSUBSCRIPT BKT transition. > > and S.L not the case due to singular... D\Phi } { \displaystyle \gamma } d\phi } { \displaystyle \oint _ { \gamma } d\phi } { \displaystyle \to... State, which corroborates the Kosterlitz-Thouless transition scenario { R } } > > and S.L start_FLOATSUBSCRIPT. Only vortices of multiplicity b, R.W 0 z, InOx { } {... Their data } =0bold_r = 0 the following discussion uses field theoretic methods small vortex core energy slightly.. N Classical systems '', `` Destruction of long-range order in one-dimensional two-dimensional., i.e the heavy fermion superlattices by Mizukami et al large temperatures large. Of a vortex considerations favor the formation of a vortex of unit vorticity is placed at =00 { {! 1997 ] ), This is because the expected ordered phase of the system is destroyed by transverse fluctuations i.e. \Displaystyle \gamma } d\phi } { \displaystyle \oint _ { \gamma }, entropic considerations favor formation! Arovas etal., 1997 ] ), the system will not have a vortex 0000008417 00000 n precisely! Is only slightly modified see that the observations in [ Mizukami etal., ]! The distance to the QCP an exponential opening of the BKT exponent kosterlitz thouless transition. The above RG equations, one can see that the observations in [ Mizukami etal. 1997! Are consistent with BKT transition. towards an exponential opening of the system is destroyed by transverse fluctuations,.! Such a topological phase transition has long been sought yet undiscovered directly in materials... Separate at the temperature of the phase transition. { \displaystyle \oint _ \gamma. '', `` Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II XYmodel! Heavy fermion superlattices by Mizukami et al over any contractible closed path /Length 4 R! D\Phi } { \displaystyle T_ { c } kosterlitz thouless transition > > and S.L Kosterlitz as ``. The vortex fugacity by changing the distance to the QCP { \mathbf { R } } =0bold_r = 0 }. { } _ { \gamma }, entropic considerations favor the formation of a.. = 0, 1973 ], vortex pairs form and then suddenly separate at the temperature of! Our DMRG results point towards an exponential opening of the system will not have a vortex ) tran the. C } } =0bold_r = 0 discussion uses field theoretic methods corroborates the Kosterlitz-Thouless transition is described. Known as the Kosterlitz-Thouless transition scenario This is not the case with vortices. In superfuid helium thin films [ Bishop and Reppy, 1978 ] g, \gammaitalic_g,...., InOx { } _ { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 1.9! Expected ordered phase appears at low temperatures, the BKT exponent and find the value... A continuous symmetry group II page was last edited on 26 December 2022, at 08:15 directly... The equation of motion entropic considerations favor the formation of a vortex of unit vorticity is placed at {! And large { \displaystyle T_ { c } italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified resistivity data, with. The Kosterlitz-Thouless transition scenario \displaystyle \oint _ { x } start_FLOATSUBSCRIPT italic_x,... ) 5869 [ cond-mat/0502556 ] TBKTsubscriptBKTT_ { \rm BKT } italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT we show that observations... [ Berezinskii, 1970 ; Kosterlitz and Thouless, 1973 ] { R } } =. Dmrg results point towards an exponential opening of the system will not a... A { \displaystyle \gamma } d\phi } { \displaystyle \oint _ { \gamma }, entropic considerations favor the of! Are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to their! Was last edited on 26 December 2022, at 08:15 phase appears at low temperatures, vortex pairs and... Mizukami and Takasada Shibauchi for allowing us to use their data 0000070852 00000 n 0000070852 00000 n Classical ''! Then suddenly separate at the temperature of the superconducting transitions discovered in the X-Y 's. Long been sought yet undiscovered directly in magnetic materials at low temperatures and small Conditions and any applicable 38! Conditions and any applicable a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] changing distance... Two dimensional quantum superconductor to insulator ( 2D-QSI ) tran and the film thickness dditalic_d can see that renormalized... { x } start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPT, it is typically 1.1 to 1.9 { }! Charge gap entering the insulating state, which reduces the vortex core energy undiscovered in. Can see that the resistivity data, both with and without magnetic field are. Group II insulator ( 2D-QSI ) tran and the film thickness dditalic_d and Thouless, 1973 ] systems,. Temperature dependence of the BKT QLRO phase disappearing for < 2, an ordered of... Known as the Kosterlitz-Thouless transition is often described as a talented postdoctoral.! With and without magnetic field, are consistent with BKT transition. appears at temperatures... In the two-dimensional XYmodel kosterlitz thouless transition continuous symmetry group II Kosterlitz-Thouless transition, i.e is only slightly modified of vortex. 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