Upper critical field for electrons in two-dimensional lattice

We address a problem of the upper critical field in a lattice described by a two-dimensional tight-binding model with the on-site pairing. We develop a finite-system-approach which enables investigation of magnetic and superconducting properties of electrons on clusters, consisting of a few thousand sites. We discuss how the quasiparticle density of states changes with the applied external magnetic field and present the temperature dependence of the upper critical field. We also briefly discuss possible extension of the model to account for the properties of high-temperature superconductors.