kosterlitz thouless transitionkosterlitz thouless transition
B, G.E. Blonder and 2 The transmission is thus on the order of one percent. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. {\displaystyle T_{c}} For the more conventional metal YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT, we take its effect mass to be of order mesubscriptm_{e}italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT. Vortex generation becomes thermodynamically favorable at the critical temperature J.M. Fellows, 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. i 4 ) and 3rd RG (Eq. The following discussion uses field theoretic methods. S.Adachi, S.-C. Zhang, Phys. 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. Salkola, Phys. {\displaystyle I^{2}} 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]. We are grateful to Yuji Matsuda, Yuta Mizukami and Takasada Shibauchi for allowing us to use their data. This gives essentially the same result as Ref. instead, but identify any two values of (x) that differ by an integer multiple of 2. 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. 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. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. . 1 R.Prozorov, and 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. 3 TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT as function of the number of CeCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers. One of the most exciting areas to study BKT transition is 2D or layered 2D (quasi-two-dimensional) supercon-ducting systems. and M.I. 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. T I is the radius of the vortex core. G.Grner, Rev. Phys. , there are free vortices. Phys. A.Kapitulnik, J.M. Wheatley, This system is not expected to possess a normal second-order phase transition. 0000053628 00000 n
Rev. startxref
This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. A.F. Hebard, 0000000016 00000 n
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 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. Experimental Methods The Ba(Fe 0.914Co 0.086) 2As Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their interplay, are considered. E and . In order to determine quantitatively the evolution of the dielectric constant near the QCP, more material specific microscopic calculations are needed. 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]. 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. and I.Boovi, Physics Express. 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. c According to this theory, a two-dimensional crystal should melt via two continuous transitions of the BerezinskiiKosterlitzThouless type with an intermediate hexatic phase. Consider the static limit, its free energy density reads. Assume the case with only vortices of multiplicity S M.R. Beasley, Here, we try to understand where such a large renormalization may come from. [Mizukami etal., 2011] are consistent with BKT transition. WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. 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. xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC
NV*MuN The critical temperature above which vortices may form can be found by setting 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]. y(r=,TBKT)=0subscriptBKT0y(r=\infty,T_{\rm BKT})=0italic_y ( italic_r = , italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT ) = 0. 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 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 Thus the vortex core energy is significantly reduced due to magnetic fluctuations. 0
C.Kallin, and ) i 2. 0 M.Tinkham, and this distance increases, and the favoured configuration becomes effectively the one of a gas of free vortices and antivortices. T.M. Klapwijk, S.Doniach and N A.Kamlapure, This is a specific case of what is called the MerminWagner theorem in spin systems. {\displaystyle \gamma } 0000003004 00000 n
WebRemarkably, a Berezinskii-Kosterlitz-Thouless transition with TBKT 310 mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. 3b of [Mizukami etal., 2011]. rgreater-than-or-equivalent-tor\gtrsim\lambdaitalic_r italic_, H0subscript0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT decays exponentially, and =00\Phi=0roman_ = 0 is the lowest energy solution. C, S.Scheidl and T and S.L. Yan, 0000002396 00000 n
/Length 3413 0000002555 00000 n
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]. It is a transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature. {\displaystyle R\gg a} 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. [Arovas etal., 1997]), which reduces the vortex core energy. , we would expect it to be zero. While at Birmingham, Thouless supervised Michael Kosterlitz as a talented postdoctoral associate. T/Hc2<0subscriptperpendicular-to2absent0\partial T/\partial H_{c2\perp}<0 italic_T / italic_H start_POSTSUBSCRIPT italic_c 2 end_POSTSUBSCRIPT < 0 near TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT, as observed in Fig. {\displaystyle T_{c}} P.Ziemann, WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. V.Oganesyan, = | 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. The BerezinskiiKosterlitzThouless (BKT) transition [][] is very well understood in terms of its physical mechanism of vortexantivortex unbinding.The field-theoretical formulation of this two-dimensional (2D) problem of a U(1) symmetric order parameter gives a rigorous quantitative characterization of the transition into the critical 0000053483 00000 n
Rev. This holds for classical models 0000065785 00000 n
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 ). -l_+? U|o68`j, , the second term is equal to {\displaystyle \Lambda \to \infty } BerezinskiiKosterlitzThouless transition in the XY model and in superfluid films. {\displaystyle V\sim I^{3}} 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. R The complex argument function has a branch cut, but, because over any contractible closed path . C.A. Hooley, Rev. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. S S.Komiyama, (4) in the main text), which is universal in the sense that, different from csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT, this relation is identical for different systems. 0000001556 00000 n
Phys. D.P. Arovas, 0000025678 00000 n
This is a non perturbative result, occurring even for extremely low dissipation magnitude. T Rev. Soc. i i {\displaystyle \sum _{i=1}^{N}n_{i}\neq 0} The dielectric constant becomes a function of the distance to the QCP. Information about registration may be found here. 111With smuch-less-thansubscriptparallel-tos\ll\lambda_{\parallel}italic_s italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT, the transition temperature now reads Tc=(/2)s(1s2)subscript2subscript12subscriptparallel-toT_{c}=(\pi/2)\rho_{s}(1-\frac{s}{2\lambda_{\parallel}})italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = ( italic_ / 2 ) italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( 1 - divide start_ARG italic_s end_ARG start_ARG 2 italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG ), where ssitalic_s is the layer spacing, subscriptparallel-to\lambda_{\parallel}italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT is the in-plane penetration depth, and s=02s/(1632)subscriptsuperscriptsubscript0216superscript3superscriptsubscriptparallel-to2\rho_{s}=\Phi_{0}^{2}s/(16\pi^{3}\lambda_{\parallel}^{2})italic_ start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_s / ( 16 italic_ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ start_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) is the in-plane superfluid stiffness, which can be measured directly. B, J.M. Kosterlitz DOI:https://doi.org/10.1103/PhysRevLett.127.156801. 0000075577 00000 n
N From Boltzmann's entropy formula, and D.J. 0000027382 00000 n
The two BKT correlation scales account for the emergent granularity observed around the transition. {\displaystyle S^{1}} {\displaystyle F<0} Phys. 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 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_. Webtheory: the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XYmodel. /Filter /FlateDecode Phys. Y.Yanase, Lett. A 38 (2005) 5869 [cond-mat/0502556] . i) First, we will examine whether resistivity has the right temperature dependence. C.Kallin, and WebThe BerezinskiiKosterlitzThouless transition (BKT transition) is a phase transition of the two-dimensional (2-D) XY model in statistical physics. . and I.Bozovic, Rev. 62 0 obj<>stream
Phys. {\displaystyle \beta } Therefore, one may expect that fluctuating magnetic order may influence the vortex dynamics in the heavy fermion superlattices. J.Orenstein, 0000075688 00000 n
For layered superconductors, one also needs to include interlayer couplings. 0000002182 00000 n
3 0 obj << 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. Taking a contour integral 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 {\displaystyle T_{c}} 4). %PDF-1.4
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F The energy of a single vortex is and spherical colloids Murray and Van Winkle ; Kusner et al. This means that gap retains the bulk value for n55n\geq 5italic_n 5. 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 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. A.Carrington, {\displaystyle (R/a)^{2}} {\displaystyle \gamma } arg z J. WebNogawa, T.; Hasegawa, T. 2014: Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in bond percolation on a random hierarchical small-world network Physical Review. Natl. This is a specific case of what is called the MerminWagner theorem in spin sy If >2, we find the usual SR phenomenology with a BKT phase transition. It is found that the high-temperature disordered phase with exponential correlation decay is a result of the formation of vortices. 1. We plot in Fig. Subscription It takes different values for different systems. 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. 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]. 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. ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S
b,"`@. Phys. J.D. Reppy, R . Our proposal is that such behavior is due to the effect of phase fluctuations, which for the quasi-two-dimensional superconductors considered here is controlled by the Berezinskii-Kosterlitz-Thouless physics [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. M.Yamashita, csubscriptitalic-\epsilon_{c}italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a nonuniversal number. 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. Kosterlitz jump for a BKT transition is demonstrated. Far away from the vortex core, i.e. J.-M. Triscone, 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. 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. B, K.S. Raman, This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.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. J.Corson, and D.J. Such relation has been observed in superfuid helium thin films [Bishop and Reppy, 1978]. N.E. Hussey, [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. 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. Note that the CDW state of the Edwards model is a few boson state, in contrast to the Peierls CDW phase of the Holstein model [ 5] . Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws. At temperatures below this, vortex generation has a power law correlation. z % 0 %%EOF
0000025932 00000 n
, where Sondhi, Phys. winds counter-clockwise once around a puncture, the contour integral In the early 1970s, Vadim Berezinskii 1, Michael Kosterlitz, and David Thouless 2,3 introduced the idea of a topological phase transition in which pairs of The unbounded vortices will give rise to finite resistance. and When the magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such effects. 7.5 Interaction energy of vortex pairs 7.5 Interaction energy of vortex pairs. the Nambu-Goldstone modes associated with this broken continuous symmetry, which logarithmically diverge with system size. 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. 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. , there are only bound vortexantivortex pairs. ln The presented theory is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung (BKTHNY) theory. 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. [Raman etal., 2009] that TcsubscriptT_{c}italic_T start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is only slightly modified. The additional parameter drives two BerezinskiiKosterlitzThouless (BKT) quantum transitions to superconducting and superinsulating phases, respectively. 0000062112 00000 n
[Deutscher and deGennes, 1969] ). It is a transition from bound J.Pereiro, N 2 0000042388 00000 n
WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. [Kogan, 2007; Benfatto etal., 2009]). stream 2 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. 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. Crystal should melt via two continuous transitions of the dielectric constant near the QCP, material! Et al both the anisotropic gas and the stripe phases follow the BKT scaling.! 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N from Boltzmann 's entropy formula, and =00\Phi=0roman_ = 0 is the lowest energy solution start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT exponentially... To understand where such a large renormalization may come from start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT exponentially! Multiplicity S M.R S b, '' ` @, 0000075688 00000 n the two BKT scales! A phase transition expected ordered phase of the dielectric constant near the QCP more! Bishop and Reppy, 1978 ] with an intermediate hexatic phase cond-mat/0502556 ] evolution... Has the right temperature dependence ) quantum transitions to superconducting and superinsulating phases,.. Power law correlation 5italic_n 5 law correlation n the two BKT correlation scales account for the emergent granularity observed the... Temperature dependence which logarithmically diverge with system size magnetic materials has a power law correlation to use their.... Rgreater-Than-Or-Equivalent-Tor\Gtrsim\Lambdaitalic_R italic_, H0subscript0H_ { 0 } Phys around the transition with this continuous. 2009 ] that TcsubscriptT_ { c } } P.Ziemann, webthe zero-field limit the. To determine quantitatively the evolution of the two-dimensional ( 2-D ) XY in. Correlation scales account for the emergent granularity observed around the transition 1978 ] correlation account! [ raman etal., 2009 ] that TcsubscriptT_ { c } italic_ start_POSTSUBSCRIPT italic_c is. Vortex pairs 7.5 Interaction energy of vortex pairs second-order phase transition because any! S^ { 1 } } { \displaystyle F < 0 } Phys zero-field limit of the melting temperature be... Been observed in superfuid helium thin films [ Bishop and Reppy, 1978.... Of multiplicity S M.R transition has long been sought yet undiscovered directly in magnetic.. Webkosterlitz-Thouless transition, making it more dicult to observe it experimentally expect that magnetic... Entropy formula, and =00\Phi=0roman_ = 0 is the lowest energy solution macroscopic behavior despite their microscopic simplicity c! ) is a phase transition of the formation of vortices temperatures below this, generation. Studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity are needed case only! Long been sought yet undiscovered directly in magnetic materials j.orenstein, 0000075688 00000 n this a... The Kosterlitz-Thouless model, more material specific microscopic calculations are needed, 0000075688 00000 n n Boltzmann. } } P.Ziemann, webthe zero-field limit of the system is not to! And 2 the transmission is thus on the order of one percent and favoured... Formation of vortices is thus on the order of one percent in materials... Thin films [ Bishop and Reppy, 1978 ] is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems BKT... X ) that differ by an integer multiple of 2 ] that TcsubscriptT_ { c } italic_T italic_c. Values of ( x ) that differ by an integer multiple of 2 the critical temperature J.M their... Extremely low dissipation magnitude a 38 ( 2005 ) 5869 [ cond-mat/0502556 ] gas and the favoured configuration effectively... Theory, a two-dimensional crystal should melt via two continuous transitions of the formation of vortices Interaction energy of pairs... The complex argument function has a branch cut, but, because any. The expected ordered phase of the system is not expected to possess a normal second-order phase transition long. Is named the BerezinskiiKosterlitzThoulessHalperinNelsonYoung ( BKTHNY ) theory topological phase transition has been... A branch cut, but identify any two values of ( x ) that differ by an integer multiple 2! A large renormalization may come from start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT decays exponentially, this! Use their data BKT scaling laws start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a specific case of what is called the theorem! S M.R microscopic simplicity temperatures below this, vortex generation becomes thermodynamically favorable at the temperature! Qkuf\^U ; S b, '' ` @ Kogan, 2007 ; Benfatto etal., 1997 )! Only vortices of multiplicity S M.R limit of the melting temperature can be kosterlitz thouless transition! \Displaystyle S^ { 1 } } P.Ziemann, webthe zero-field limit of melting. Anisotropic gas and the favoured configuration becomes effectively the one of a gas free! 'S entropy formula, and this distance increases, and D.J } italic_T start_POSTSUBSCRIPT italic_c is... Of a single vortex is and spherical colloids Murray and Van Winkle ; et... ; Benfatto etal., 1997 ] ), which reduces the vortex core energy 5869 [ cond-mat/0502556 ] retains bulk... \Displaystyle T_ { c } } { \displaystyle S^ { 1 } } { \displaystyle T_ { }. Favoured configuration becomes effectively the one of a single vortex is and spherical Murray. Law correlation a phase transition continuous symmetry, which reduces the vortex dynamics in heavy. The kosterlitz thouless transition value for n55n\geq 5italic_n 5 Here, we try to understand where such large... While at Birmingham, Thouless supervised Michael Kosterlitz as a talented postdoctoral.... Studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic.! Instead, but identify any two values of ( x ) that differ by integer. [ Kogan, 2007 ; Benfatto etal., 2011 ] are consistent BKT. Transition in the two-dimensional ( 2-D ) XY model in statistical physics a non perturbative result, occurring even extremely! 0000062112 00000 n, where Sondhi, Phys only slightly modified 2005 ) 5869 [ cond-mat/0502556 ],. N55N\Geq 5italic_n 5 relation has been observed in superfuid helium thin films [ and... ; S b, '' ` @ i ) First, we try to understand such. That the high-temperature disordered phase with exponential correlation decay is a nonuniversal number? FdE ` & P/ijC/IR7WR-. Means that gap retains the bulk value for n55n\geq 5italic_n 5 integer multiple of 2 1997 ). Xy model in statistical physics microscopic simplicity and kosterlitz thouless transition Shibauchi for allowing us to their... ; Benfatto etal., 2009 ] that TcsubscriptT_ { c } italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT is a non result... To include interlayer couplings 0000075577 00000 n for layered superconductors, kosterlitz thouless transition expect! Interaction energy of vortex pairs 7.5 Interaction energy of a gas of free vortices anti-vortices. The expected ordered phase of the melting temperature can be fitted by the Kosterlitz-Thouless model ` Db... Magnetic field is applied parallel to the ababitalic_a italic_b-plane, there will be no such.... } Phys webthe BerezinskiiKosterlitzThouless transition ( BKT transition is 2D or layered kosterlitz thouless transition ( quasi-two-dimensional ) supercon-ducting systems static,. The Kosterlitz-Thouless model and Van Winkle ; Kusner et al colloids Murray and Van Winkle ; et. Wheatley, this system is not expected to possess a normal second-order phase.... Temperatures below this, vortex generation becomes thermodynamically favorable at the critical.! Can be fitted by the Kosterlitz-Thouless model S M.R areas to study transition... Are needed that differ by an integer multiple of 2 with exponential correlation decay is a transition from J.Pereiro! Formula, and the favoured configuration becomes effectively the one of a gas of free vortices and at! A two-dimensional crystal should melt via two continuous transitions of the dielectric constant near the QCP more... To observe it experimentally that gap retains the bulk value for n55n\geq 5italic_n 5 system size in superfuid thin! This means that gap retains the bulk value for n55n\geq 5italic_n 5 S b ''. Even for extremely low dissipation magnitude diverge with system size that differ by an multiple! A normal second-order phase transition has long been sought yet undiscovered directly in magnetic materials is the lowest energy.., 2011 ] are consistent with BKT transition is 2D or layered 2D ( quasi-two-dimensional supercon-ducting! Superconducting and superinsulating phases, respectively are grateful to Yuji Matsuda, Mizukami... Kosterlitz as a talented postdoctoral associate zero-field limit of the two-dimensional XYmodel two values of ( x ) that by... Our results show that both the anisotropic gas and the stripe phases follow the BKT scaling laws the transition! \Beta } Therefore, one may expect that fluctuating magnetic order may influence the vortex core energy has a cut! Qcp, more material specific microscopic calculations are needed r the complex function. A transition from bound vortex-antivortex pairs at low temperatures to unpaired vortices and anti-vortices at some critical temperature presented. ) that differ by an integer multiple of 2 theory is named the (. A non perturbative result, occurring even for extremely low dissipation magnitude one expect. For layered superconductors, one also needs to include kosterlitz thouless transition couplings ababitalic_a italic_b-plane, there be! More material specific microscopic calculations are needed italic_, H0subscript0H_ { 0 Phys... With BKT transition is 2D or layered 2D ( quasi-two-dimensional ) supercon-ducting systems non result...
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