Monte Carlo studies of thermalization of electron–hole pairs in spin-polarized degenerate electron gas in monolayer graphene

Monte Carlo method is applied to the study of relaxation of excited electron–hole (e–h) pairs in graphene. The presence of background of spin-polarized electrons, with high density imposing degeneracy conditions, is assumed. To such system, a number of e–h pairs with spin polarization parallel or antiparallel to the background is injected. Two stages of relaxation: thermalization and cooling are clearly distinguished when average particles energy \(\langle E\rangle\) and its standard deviation \(\sigma _E\) are examined. At the very beginning of thermalization phase, holes loose energy to electrons, and after this process is substantially completed, particle distributions reorganize to take a Fermi–Dirac shape. To describe the evolution of \(\langle E \rangle\) and \(\sigma _E\) during thermalization, we define characteristic times \(\tau _\text {th}\) and values at the end of thermalization \(E_\text {th}\) and \(\sigma _\text {th}\). The dependence of these parameters on various conditions, such as temperature and background density, is presented. It is shown that among the considered parameters, only the standard deviation of electrons energy allows to distinguish between different cases of relative spin polarizations of background and excited electrons.