  Interference represents one of the most striking manifestation of quantum
physics in low-dimensional systems. Despite evidences of quantum interference
in charge transport have been known for a long time, only recently signatures
of interference induced thermal properties have been reported, paving the way
for the phase-coherent manipulation of heat in mesoscopic devices. In this work
we show that anomalous thermoelectric properties and efficient heat
rectification can be achieved by exploiting the phase-coherent edge states of
quantum Hall systems. By considering a tunneling geometry with multiple quantum
point contacts, we demonstrate that the interference paths effectively break
the electron-hole symmetry, allowing for a thermoelectric charge current
flowing either from hot to cold or viceversa, depending on the details of the
tunnel junction. Correspondingly, an interference induced heat current is
predicted, and we are able to explain these results in terms of an intuitive
physical picture. Moreover, we show that heat rectification can be achieved by
coupling two quantum Hall systems with different filling factors, and that this
effect can be enhanced by exploiting the interference properties of the tunnel
junction.
