HLRB Project pr53lu

Fluctuations of the Local Energy Gap in Dirty Superconductors

Institut I - Theoretische Physik Quantentransport und Spintronik, Universität Regensburg

Fluctuations of the Local Energy Gap in Dirty Superconductors

Institut I - Theoretische Physik Quantentransport und Spintronik, Universität Regensburg

Institut I - Theoretische Physik Quantentransport und Spintronik, Universität Regensburg

Prof. Dr. Ferdinand Evers

Universitätsstr. 31

93040 Regensburg

The electronic states of disordered materials can be understood as eigenstates of an hermitian matrix, the Hamiltonian. To the extent that interactions between the charge carriers matter, the matrix elements of this Hamiltonian depend crucially on the carrier density, which in turn can be computed only, once all electronic states are known. Thus, the calculation of electronic properties in disordered, interacting electron systems typically involves solving a self-consistency problem. The specific variant of self-consistency problems that we focus on in this proposal describes disordered superconducting films with conventional s-wave pairing and short-range disorder. In particular we are interested in the auto-correlation of certain matrix elements of the Hamiltonian, namely the pairing amplitude. Our motivation to dive into this topic is twofold. (i) We hope to be able to help clarifying the physical nature of the so-called Superconductor-Insulator-Transition, which is a hot topic in condensed matter physics. (ii) On an even more fundamental level our work will help paving the way for studying a new type of random-matrix ensembles – self-consistent random Hamiltonians – that may exhibit unusual properties related to the self-consistency property. The numerical analysis of self-consistent random-matrix ensembles is computationally very expensive. (i) The self-consistency conditions require an iterative scheme to find the proper Hamiltonian for a given realization of disorder. (ii) Many large systems need to be treated so that the computed ensemble averages acquire the typical (system-size independent) properties that dominate the experimental behavior. Computational details: Typically, we will consider systems with up to N=10^5 sites (sparse hermitian matrices of dimension NxN) and 10^5-10^6 disorder realizations. In order to avoid a repeated diagonalization of large matrices, we employ stochastic trace evaluations and standard sparse matrix routines.

Impressum, Conny Wendler