Recent experiments on 2D superconductors allow the characterization of the critical temperature and of the phase diagram across the BCS-BEC crossover as a function of density. We obtain from these experiments the microscopic parameters of the superconducting state at low temperatures by the BCS mean-field approach. For
LixZrNCl, the extracted parameters are used to evaluate the superconducting phase stiffness and the Berezinskii-Kosterlitz-Thouless (BKT) critical temperature throughout the BCS-BEC crossover by implementing the corresponding renormalization group (RG) approach. In this way, we make a quantitative test of the predictive power of the BKT theory for evaluating the critical temperature. The RG flow equations turn out to give a sizable renormalization of the phase stiffness and of the critical temperature, which is crucial to obtain a satisfactory agreement between the BKT theory and the experiments, in particular, in the BCS-BEC crossover regime. We predict the temperature range where phase stiffness renormalization can be measured in
LixZrNCl across the BCS-BEC crossover. Contrary to other microscopic theories of superconductivity, we find that the BKT theory can be exploited to evaluate quantitatively the critical temperature of 2D superconductors in different pairing regimes.
The inhomogeneous nature of critical phenomena in semi-infinite systems is studied by calculating the full crossover for both the two-point correlation function and the surface susceptibility ${\ensuremath{\chi}}_{11}$(z) as a function of the distance z from the surface at z=0 for a semi-infinite system near the special transition. We introduce z-dependent counterterms to derive the renormalization-group (RG) equation describing this full crossover. The solution to the RG equation in the one-loop approximation is obtained explicitly and in the long-distance regime is shown to approach bulk behavior exponentially fast. In contrast to the usual approach, our RG equation also contains all information about the short-distance (near-surface) behavior of the theory and its crossover to the bulk. Applications of our method to the descriptions of crossovers for other problems of critical phenomena with several competing lengths are also discussed.
Abstract We derive a theory of crossover scaling based on a scaling variable gξg, where g is the anisotropy parameter inducing the crossover and ξg is the correlation length in the presence of g. Our considerations are field theoretic and based on a renormalization group with a g dependent differential generator that interpolates between qualitatively different degrees of freedom. ξg is a nonlinear scaling field for this renormalization group and interpolates between (T – Tc(g))–v0 and (T – Tc(g))–v∞ (v0 and v∞ being the isotropic and anisotropic exponents respectively). By expanding about a ‘floating’ fixed point we can make corrections to scaling small throughout the crossover. In this formulation effective scaling exponents obey standard scaling laws, e. g. γeff = veff(2 – ɳeff). We discuss its advantages giving for various crossovers explicit supporting perturbative calculations of the susceptibility, which is found to conform to the general form derived from the g dependent renormalization group.