Paper
Self-consistent inclusion of disorder in the BCS-BEC crossover near $T_c$
Authors
M. Iskin
Abstract
We develop a systematic theoretical approach to incorporate the effects of a static white-noise disorder into the BCS-BEC crossover near the critical temperature () of the superfluid transition. Starting from a functional-integral formulation in momentum-frequency space, we derive an effective thermodynamic potential that fully accounts for Gaussian fluctuations of the order-parameter field and its coupling to the disorder potential. The effective action, expanded to second order in both the disorder potential and the bosonic field, naturally involves third- and fourth-order terms arising from the logarithmic expansion near . This formalism, valid across the entire BCS-BEC crossover, reproduces the well-established BCS and BEC limits and yields self-energy expressions consistent with previous analyses for non-interacting point bosons and tightly bound fermion pairs. The approach applies equally to continuum and lattice systems and provides a natural framework for generalizations to multiband models.