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Register a new userPhase Transitions Driven by Vortices in 2D Superfluids and Superconductors: From Kosterlitz-Thouless to 1st Order
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The Landau-Ginzburg-Wilson hamiltonian is studied for different values of the parameter $lambda$ which multiplies the quartic term (it turns out that this is equivalent to consider different values of the coherence length $xi$ in units of the lattice spacing $a$). It is observed that amplitude fluctuations can change dramatically the nature of the phase transition: for small values of $lambda$ ($xi/a > 0.7$), instead of the smooth Kosterlitz-Thouless transition there is a {em first order} transition with a discontinuous jump in the vortex density $v$ and a larger non-universal drop in the helicity modulus. In particular, for $lambda$ sufficiently small ($xi/a cong 1$), the density of bound pairs of vortex-antivortex below $T_c$ is so low that, $v$ drops to zero almost for all temperature $T<Tc$.
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The precondition for the BKT transition in thin superconducting films, the logarithmic intervortex interaction, is satisfied at distances short relative to $Lambda=2lambda^2/d$, $lambda$ is the London penetration depth of the bulk material and $d$ is the film thickness. For this reason, the search for the transition has been conducted in samples of the size $L<Lambda$. It is argued below that film edges turn the interaction into near exponential (short-range) thus making the BKT transition impossible. If however the substrate is superconducting and separated from the film by an insulated layer, the logarithmic intervortex interaction is recovered and the BKT transition should be observable.
We propose scaling theories for Kosterlitz-Thouless (KT) phase transitions on the basis of the hallmark exponential growth of their correlation length. Finite-size scaling, finite-entanglement scaling, short-time critical dynamics, and finite-time scaling, as well as some of their combinations are studied. Relaxation times of both a usual power-law and an unusual power-law with a logarithmic factor are considered. Finite-size and finite-entanglement scaling forms somehow similar to a frequently employed ansatz are presented. The Kibble-Zurek scaling of topological defect density for a linear driving across the KT transition point is investigated in detail. An implicit equation for a rate exponent in the theory is derived and the exponent varies with the distance from the critical point and the driving rate consistent with relevant experiments. To verify the theories, we utilize the KT phase transition of a one-dimensional Bose-Hubbard model. The infinite time-evolving-block-decimation algorithm is employed to solve numerically the model for finite bond dimensions. Both a correlation length and an entanglement entropy in imaginary time and only the entanglement entropy in real-time driving are computed. Both the short-time critical dynamics in imaginary time and the finite-time scaling in real-time driving, both including the finite bond dimension, for the measured quantities are found to describe the numerical results quite well via surface collapses. The critical point is also estimated and confirmed to be $0.302(1)$ at the infinite bond dimension on the basis of the scaling form.
We have recently reported the first direct calorimetric observation of a magnetic-field-induced first-order phase transition into a high-field FFLO superconducting state at the Clogston-Chandrasekar `Pauli paramagnetic limit $H_p$ in a 2D superconductor $kappa-{textrm{(BEDT-TTF)}}_2{textrm{Cu}}{textrm{(NCS)}}_2$. The high-field state is both higher entropy and strongly paramagnetic, as thermodynamically required for the FFLO state. Here we compare our results with theoretical predictions for the field dependence of the high-field FFLO state in the 2D limit, revealing tentative evidence for transitions between FFLO states of differing order parameter. We also present calorimetric evidence for a 1st order phase transition into the FFLO state for a second 2D organic superconductor: ${beta}^{primeprime}-{textrm{(BEDT-TTF)}}_2{textrm{SF}}_5{textrm{(CH)}}_2{textrm{(CF)}}_2{textrm{(SO)}}_3$.
We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a quantum avalanche. We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, we identify the scaling variables as the density of thermal regions and the lengthscale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law distributed in size. This points to the existence of a second transition within the MBL phase, at which these power-laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent $alpha_c=2$, and continuously varying exponents in the MBL phase consistent with the KT picture.
The conflicting observations in the highly anisotropic Bi2Sr2CaCu2O8+x, vidence for BKT behavior emerging from magnetization data and smeared 3D-xy behavior, stemming form the temperature dependence of the magnetic in-plane penetration depth are traced back to the rather small ratio, gsic+/gsic-=0.45, between the c-axis correlation length probed above (+) and below (-) Tc, and the comparatively large anisotropy. The latter leads to critical amplitudes gsic0+,-which are substantially smaller than the distance between two CuO2 double layers. In combination with gsic+/gsic-=0.45 and in contrast to the situation below Tc the c-axis correlation length gsic exceeds the distance between two CuO2 double layers very close to Tc only. Below this narrow temperature regime where 3D-xy fluctuations dominate, there is then an extended temperature regime where the units with two CuO2 double layers are nearly uncoupled so that 2D thermal fluctuations dominate and BKT features are observable.
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