  The recent discovery of 2D superconductivity at the interface of BaPbO$_3$
(BPO) and BaBiO$_3$ (BBO) has motivated us to study in depth the electronic and
structural properties and the relation between them in this particular
heterostructure, by means of first-principles calculations. Our results
indicate that the breathing distortions, the charge ordering and the
semiconducting behaviour that characterize the parent compound BBO in its bulk
form, are preserved at the innermost layers of the BBO side of the BPO/BBO
bilayer. On the other hand, at the interface, there is a partial breaking of
the breathing distortions with a concomitant charge transfer between the
interfacial Bi ions and the on top BPO layer. We show that two types of
carriers coexist at the interface, the delocalized 3D like sp states coming
from Pb ions and the quasi 2D s states from the Bi ones. We obtain a
substantial electron-phonon coupling between the 2D Bi states with the
interfacial stretching phonon mode and a large density of states that can
explain the critical temperature experimentally observed bellow 3.5 K. We hope
these findings will motivate future research to explore different interfaces
with charge ordered semiconductors as BBO in order to trigger this fascinating
2D behavior.
