Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors

The interplay of disorder and magnetic vortices is a recurrent topic of research in the theory of superconductivity. In most of previous approaches, disorder enters in a phenomenological way, namely, it is not the random potential felt by the electrons. Here we address this problem in a fully microscopic model: a two-dimensional disordered superconductor at zero temperature described by the Bogoliubov-de Gennes (BdG) formalism for lattices of sizes up to $100\times100$ where the magnetic field is introduced by the Peierls's substitution. For a not too strong disorder strength, we identify a rich phase diagram in Fourier space as a function of the magnetic field strength. Initially, we observe the expected Abrikosov triangular vortex lattice slightly distorted by disorder. Intriguingly, an increase in the magnetic field leads to an unexpected rectangular lattice which is followed by a vortex glass with only traces of Bragg's peaks but strong vortex repulsion. Finally, a further increases of the field leads to a fully disordered phase where even vortex repulsion is suppressed. We show that these phases can coexist with global phase coherence. Disorder also enhances the critical magnetic field with respect to the clean limit with a maximum for strong disorder strength on the metallic side of the transition.Comment: 34 pages, 11 figure