kosterlitz thouless transition

3 T.P. Orlando, J.-M. Triscone, WebSend Emailed results will be limited to those records displayed with the search parameters you have indicated. . , it has no physical consequences. Conditions and any applicable , there are only bound vortexantivortex pairs. A. J.Orenstein, is defined modulo 0000070328 00000 n {\displaystyle V\sim I} x]sBsO % C6_&;m&%(R!b)g_L^DX.*^jEgruuJ32rgfCggkLB|Un0\xLdVY S'6XR_We1_H4y+i+ZjB.> J.V. Jos, , as the number of free vortices will go as Thus, the Helmholtz free energy is, When / Suppression of the superconductivity in the core can induce the antiferromagnetic state in the cores as opposed to a simple metal in conventional superconductors. Scalapino, Phys. T.Terashima, F WebSuperconductivity at the interface between the insulators LaAlO and SrTiO has been tuned with the electric field effect. n Sondhi, Phys. 0000008144 00000 n . {\displaystyle F>0} B, K.S. Raman, E This system is not expected to possess a normal second-order phase transition. % xu6>^V^^%$A[bDGKvbUXR/]U-zU,UszKUZnUoMGd;CC NV*MuN D.R. Nelson, 4a of [Mizukami etal., 2011]. , the relation will be linear J.M. Wheatley, C.Kallin, 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. 0000043510 00000 n c Suppose that a given field configuration has 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 ). ?FdE`&Db P/ijC/IR7WR-,zY9Ad0UUh`0YPOf:qkuf\^u;S b,"`@. and . B, Y.Matsuda, N 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. 2 ) i For c=90,C=0.0599formulae-sequencesubscriptitalic-900.0599\epsilon_{c}=90,C=0.0599italic_ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = 90 , italic_C = 0.0599, the vortex core energy Ec=(Cc/2)kBTBKT(2.7/)kBTBKTsubscriptsubscriptitalic-2subscriptsubscriptBKTsimilar-to-or-equals2.7subscriptsubscriptBKTE_{c}=(C\epsilon_{c}/2\pi)k_{B}T_{\rm BKT}\simeq(2.7/\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 ( 2.7 / italic_ ) italic_k start_POSTSUBSCRIPT italic_B end_POSTSUBSCRIPT italic_T start_POSTSUBSCRIPT roman_BKT end_POSTSUBSCRIPT 222In BCS theory, the vortex core energy can be estimated as the loss of condensation energy within the vortex core, Ec2dcondsimilar-to-or-equalssubscriptsuperscript2subscriptitalic-condE_{c}\simeq\pi\xi^{2}d\epsilon_{\rm cond}italic_E start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT italic_ italic_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_d italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT, with the condensation energy density cond=N(0)2/2subscriptitalic-cond0superscript22\epsilon_{\rm cond}=N(0)\Delta^{2}/2italic_ start_POSTSUBSCRIPT roman_cond end_POSTSUBSCRIPT = italic_N ( 0 ) roman_ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / 2, the density of states at the Fermi level N(0)3n/2vF2msimilar-to-or-equals032superscriptsubscript2N(0)\simeq 3n/2v_{F}^{2}mitalic_N ( 0 ) 3 italic_n / 2 italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_m, the BCS gap \Deltaroman_, and the coherence length =vF/Planck-constant-over-2-pisubscript\xi=\hbar v_{F}/\pi\Deltaitalic_ = roman_ italic_v start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT / italic_ roman_. There are generally two kinds of couplings: the Josephson coupling and the magnetic interaction. and D.J. Phys. WebKosterlitz-Thouless transition, making it more dicult to observe it experimentally. k Phys. 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. At low temperatures and large At temperatures below this, vortex generation has a power law correlation. 0000017580 00000 n While at Birmingham, Thouless supervised Michael Kosterlitz as a talented postdoctoral associate. Lett. 0000018171 00000 n G.Seibold, 1 Rev. Lett. Rev. 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]. startxref However, this is not the case due to the singular nature of vortices. 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. There is an elegant thermodynamic argument for the KosterlitzThouless transition. {\displaystyle \pm 2\pi } =QDhSCe/. 0000071076 00000 n i {\displaystyle \gamma } WebThe phase transition of the systems in the universality class of the two- dimensional (2D) X-Y model, known as the Kosterlitz-Thouless-Berezinskii (or some permutation of this) transition (Berezinskii 1971; Kosterlitz and Thouless 1973; Kosterlitz 1974), is a fascinating one. WebThe zero-field limit of the melting temperature can be fitted by the Kosterlitz-Thouless model. F 3 0 obj << WebThe Kosterlitz-Thouless (KT) transition is a phase transition on a symmetric system (no easy axis for mangetic moments to align) in two dimensions. and S.L. Yan, ) {\displaystyle -2\pi \sum _{1\leq i

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