  Steady-state thermoelectric machines convert heat into work by driving a
thermally-generated charge current against a voltage gradient. In this work, we
propose a new class of steady-state heat engines operating in the quantum
regime, where a quasi-periodic tight-binding model that features a mobility
edge forms the working medium. In particular, we focus on a generalization of
the paradigmatic Aubrey-Andr\'e-Harper (AAH) model, known to display a
single-particle mobility edge that separates the energy spectrum into regions
of completely delocalized and localized eigenstates. Remarkably, these two
regions can be exploited in the context of steady-state heat engines as they
correspond to ballistic and insulating transport regimes. This model also
presents the advantage that the position of the mobility edge can be controlled
via a single parameter in the Hamiltonian. We exploit this highly tunable
energy filter, along with the peculiar spectral structure of quasiperiodic
systems, to demonstrate large thermoelectric effects, exceeding existing
predictions by several orders of magnitude. This opens the route to a new class
of highly efficient and versatile quasi-periodic steady-state heat engines,
with a possible implementation using ultracold neutral atoms in bichromatic
optical lattices.
