  Motivated by evidence of local electron-electron attraction in experiments on
disordered insulating films, we propose a new two-component Coulomb glass model
that combines strong disorder and long-range Coulomb repulsion with the
additional possibility of local pockets of a short-range inter-electron
attraction. This model hosts a variety of interesting phenomena, in particular
a crucial modification of the Coulomb gap previously believed to be universal.
Tuning the short-range interaction to be repulsive, we find non-monotonic humps
in the density of states within the Coulomb gap. We further study
variable-range hopping transport in such systems by extending the standard
resistor network approach to include the motion of both single electrons and
local pairs. In certain parameter regimes the competition between these two
types of carriers results in a distinct peak in resistance as a function of the
local attraction strength, which can be tuned by a magnetic field.
