T.Onogi, 0000002120 00000 n
Here, we try to understand where such a large renormalization may come from. {\displaystyle F=0} H0()subscript0H_{0}({\mathbf{r}})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) can be obtained from its Fourier transform H0()=0/(1+2k2)subscript0subscript01superscript2superscript2H_{0}(\mathbf{k})=\Phi_{0}/(1+\lambda^{2}k^{2})italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_k ) = roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / ( 1 + italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_k start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ), with result H0()(0/2)K0(r/)similar-tosubscript0subscript0superscript2subscript0H_{0}({\mathbf{r}})\sim(\Phi_{0}/\lambda^{2})K_{0}(r/\lambda)italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( bold_r ) ( roman_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT / italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) italic_K start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_r / italic_ ), ( 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. 3b of [Mizukami etal., 2011]. WebSpin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Though implications have been found in numerous thin superconducting films [Minnhagen, 1987; Fiory etal., 1988; Davis etal., 1990; Matsuda etal., 1993; Crane etal., 2007], highly anisotropic cuprates [Wen etal., 1998; Corson etal., 1999; Li etal., 2005], oxide interfaces [Reyren etal., 2007; Caviglia etal., 2008; Schneider etal., 2009], the results have remained inconclusive (see e.g. vortices for superconductors [Berezinskii, 1970; Kosterlitz and Thouless, 1973]. M.J. Naughton, 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 . n {\displaystyle N} 0000002182 00000 n
R.Mallozzi, H.Ikeda, [Mondal etal., 2011]). B. Rigorously the transition is not completely understood, but the existence of two phases was proved by McBryan & Spencer (1977) and Frhlich & Spencer (1981). R {\displaystyle \Lambda } Sketch of the RG flow lines for 7/4<<2 in the y=0 plane. 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. Above the critical temperature, proliferation of unbound vortices is expected. {\displaystyle (R/a)^{2}} In this Letter, we consider the effect of long-range decaying couplings r2 on the BKT transition. S.Gariglio, N Agreement. Phys. 1 3 0 obj << and I.Boovi, Physics Express. , as the number of free vortices will go as Z. Panagiotopoulos, The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. Taking a contour integral The power spectral density of the resistance fluctuations was seen to deviate from 1/f as transition temperature is approached. R.Prozorov, and
T Y.Bando, 0000075577 00000 n
A large dielectric constant corresponds to a small vortex core energy. Lett. Phys. WebThe resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. L.Benfatto, and From Boltzmann's entropy formula, B 19, 1855 (1979), This page was last edited on 26 December 2022, at 08:15. 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. 4a of [Mizukami etal., 2011]. n {\displaystyle a} T.Terashima, M.Bryan, and To export a larger list you will need to increase the number of results per page. (Nature Physics 7, 849 (2011)) in terms of Phys. Sci. Lett. ii) Then we extract from the resistivity data the transition temperature TBKTsubscriptBKTT_{\rm BKT}italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT. This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. ( The KosterlitzThouless transition can be observed experimentally in systems like 2D Josephson junction arrays by taking current and voltage (I-V) measurements. 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 ). Howard, Phys. B, G.E. Blonder and J.M. Kosterlitz, 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 We find that the observations in [Mizukami etal., 2011] are consistent with BKT transition. At large temperatures and small Using the molecular beam epitaxy (MBE) technique, Mizukami et al. The dashed red line is a possible realization of the physical parameters line, from which the flow starts, as the temperature is varied. 4 ) and 3rd RG (Eq. Nelson, Phys. Phys. / > 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. S 0000025932 00000 n
B If M.Tinkham, M. Hasenbusch, The Two dimensional XY model at the transition temperature: A High precision Monte Carlo study, J. Phys. This jump from linear dependence is indicative of a KosterlitzThouless transition and may be used to determine B 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. k with Tc0subscript0T_{c0}italic_T start_POSTSUBSCRIPT italic_c 0 end_POSTSUBSCRIPT the bulk superconducting transition temperature, 0subscript0\xi_{0}italic_ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT the BCS coherence length, and \nuitalic_ a number of order unity. The scale L is an arbitrary scale that renders the argument of the logarithm dimensionless. 5(a)). It is a transition from bound 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. Work on the transition led to the 2016 Nobel Prize in Physics being awarded to Thouless and Kosterlitz; Berezinskii died in 1980. C.Panagopoulos, {\displaystyle \gamma } Web7.4 Kosterlitz-Thouless transition 7.4 Kosterlitz-Thouless transition. = J.D. Reppy, %PDF-1.4
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S.Kirkpatrick, I believe it can be said that the Kosterlitz-Thouless system has continuous symmetry, please correct me if I am wrong. Itbeginswiththediscoveryofpossibleeldcongurationsthatone Rev. 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 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. Experimental Methods The Ba(Fe 0.914Co 0.086) 2As . i 2 WebWe have studied resistance fluctuations in two different types of two-dimensional superconductors near to the Bcrczinskii-Kostcrlitz-Thoulcss (BKT) transition. I 5(b)), one can see that, only very close to the transition temperature, the dielectric constant changes substantially with scale. 0000043510 00000 n
B, G.E. Blonder, Sondhi, Phys. a 4 can be observed experimentally. 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 Phys. Physical Review Letters is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. 0000026620 00000 n
Lett. More precisely, we consider the equation of motion. Rev. The experimental results are in good agreement with the theoretical prediction determined from Eq. In the XY model in two dimensions, a second-order phase transition is not seen. / V.G. Kogan, 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. It is also expected that a weak magnetic field can destroy the proximity-induced superconductivity in YbCoIn55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT layers [Mizukami etal., 2011; Serafin etal., 2010]. The Kosterlitz-Thouless Transition Authors: Peter Agnew University of Illinois at Chicago Clayton Bennett University of Illinois at Chicago Gabe Dale-Gau %PDF-1.5 {\displaystyle \oint _{\gamma }d\phi } B, K.S. Raman, and the Boltzmann factor is %PDF-1.5 . 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. B, O.T. Valls, B, J.M. Kosterlitz , we would expect it to be zero. and D.R. Assuming ns=nsubscriptn_{s}=nitalic_n start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = italic_n at T=00T=0italic_T = 0, we have Ec(1.9/)kBTBKTsimilar-to-or-equalssubscript1.9subscriptsubscriptBKTE_{c}\simeq(1.9/\pi)k_{B}T_{\rm BKT}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT ( 1.9 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT (see e.g. 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. It featuresfor 7/4<<2a quasiordered phase in a finite temperature range Tc
