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Register a new userSelf-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films
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Our general interest is in self-consistent-field (scf) theories of disordered fermions. They generate physically relevant sub-ensembles (scf-ensembles) within a given Altland-Zirnbauer class. We are motivated to investigate such ensembles (i) by the possibility to discover new fixed points due to (long-range) interactions; (ii) by analytical scf-theories that rely on partial self-consistency approximations awaiting a numerical validation; (iii) by the overall importance of scf-theories for the understanding of complex interaction-mediated phenomena in terms of effective single-particle pictures. In this paper we present an efficient, parallelized implementation solving scf-problems with spatially local fields by applying a kernel-polynomial approach. Our first application is the Boguliubov-deGennes (BdG) theory of the attractive-$U$ Hubbard model in the presence of on-site disorder; the scf-fields are the particle density $n(mathbf{r})$ and the gap function $Delta(mathbf{r})$. For this case, we reach system sizes unprecedented in earlier work. They allow us to study phenomena emerging at scales substantially larger than the lattice constant, such as the interplay of multifractality and interactions, or the formation of superconducting islands. For example, we observe that the coherence length exhibits a non-monotonic behavior with increasing disorder strength already at moderate $U$. With respect to methodology our results are important because we establish that partial self-consistency (energy-only) schemes as typically employed in analytical approaches tend to miss qualitative physics such as island formation.
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Disordered thin films close to the superconducting-insulating phase transition (SIT) hold the key to understanding quantum phase transition in strongly correlated materials. The SIT is governed by superconducting quantum fluctuations, which can be revealed for example by tunneling measurements. These experiments detect a spectral gap, accompanied by suppressed coherence peaks that do not fit the BCS prediction. To explain these observations, we consider the effect of finite-range superconducting fluctuations on the density of states, focusing on the insulating side of the SIT. We perform a controlled diagrammatic resummation and derive analytic expressions for the tunneling differential conductance. We find that short-range superconducting fluctuations suppress the coherence peaks, even in the presence of long-range correlations. Our approach offers a quantitative description of existing measurements on disordered thin films and accounts for tunneling spectra with suppressed coherence peaks observed, for example, in the pseudo gap regime of high-temperature superconductors.
High-quality KFe2As2 (K122) single crystals synthesized by different techniques have been studied by magnetization and specific heat (SH) measurements. There are 2 types of samples both affected by disordered magnetic phases: (i) cluster-glass (CG) like or (ii) Griffiths phase (G) like. For (i) at low applied magnetic fields the T-dependence of the zero field cooled (ZFC) linear susceptibility (chi_l) exhibits an anomaly with an irreversible behavior in ZFC and field cooled (FC) data. This anomaly is related to the freezing temperature T_f. The extrapolated T_f to B=0 varies between 50 K and 90 K. Below T_f we observed a magnetic hysteresis in the field dependence of the isothermal magnetization (M(B)). The frequency shift of the freezing temperature delta T_f=Delta T_f/[T_fDelta(ln u)]sim 0.05$ has an intermediate value, which provides evidence for the formation of a CG-like state in the K122 samples of type (i). The frequency dependence of their T_f follows a conventional power-law divergence of critical slowing down: tau=tau_0 [T_f(nu)/T_f(0)-1]^{-z u^{}} with the critical exponent z u^{}=10(2) and a relatively long characteristic time constant tau_0 =6.9 x10^{-11}$s also supporting a CG behavior. The large value of the Sommerfeld coefficient was related to magnetic contribution from a CG. Samples from (ii) did not show a hysteresis behavior for chi_l(T) and M(B). Below a crossover temperature T^* sim 40 K a power-law dependence in the chi_l propto T^[lambda_G-1}], with a non-universal lambda_G was observed, suggesting a quantum G-like behavior. In this case chi_l and M(B) can be scaled using the scaling function M_s(T,B)= B^{1-lambda_{tiny G}}Y(mu B/k_BT) with the scaling moment mu of the order of 3.5mu_b. The same non-universal exponent was found also in SH measurements, where the magnetic contribution C/T propto T^(lambda_G-1).
Mesoscopic fluctuations of the local density of states encode multifractal correlations in disorderedelectron systems. We study fluctuations of the local density of states in a superconducting state of weakly disordered films. We perform numerical computations in the framework of the disordered attractive Hubbard model on two-dimensional square lattices. Our numerical results are explained by an analytical theory. The numerical data and the theory together form a coherent picture of multifractal correlations of local density of states in weakly disordered superconducting films.
We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.
We introduce a first principles approach to determine the strength of the electronic correlations based on the fully self consistent GW approximation. The approach provides a seamless interface with dynamical mean field theory, and gives good results for well studied correlated materials such as NiO. Applied to the recently discovered iron arsenide materials, it accounts for the noticeable correlation features observed in optics and photoemission while explaining the absence of visible satellites in X-ray absorption experiments and other high energy spectroscopies.
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