  We investigate how the presence of a single-particle mobility edge in a
system can generate strong heat current rectification. Specifically, we study a
quadratic bosonic chain subject to a quasi-periodic potential and coupled at
its boundaries to spin baths of differing temperature. We find that
rectification increases by orders of magnitude depending on the spatial
position in the chain of localized eigenstates above the mobility edge. The
largest enhancements occur when the coupling of one bath to the system is
dominated by a localized eigenstate, while the other bath couples to numerous
delocalized eigenstates. By tuning the parameters of the quasi-periodic
potential it is thus possible to vary the amplitude, and even invert the
direction, of the rectification.
