  Interacting two-component Fermi gases loaded in a one-dimensional (1D)
lattice and subject to harmonic trapping exhibit intriguing compound phases in
which fluid regions coexist with local Mott-insulator and/or band-insulator
regions. Motivated by experiments on cold atoms inside disordered optical
lattices, we present a theoretical study of the effects of a random potential
on these ground-state phases. Within a density-functional scheme we show that
disorder has two main effects: (i) it destroys the local insulating regions if
it is sufficiently strong compared with the on-site atom-atom repulsion, and
(ii) it induces an anomaly in the compressibility at low density from quenching
of percolation.
