  There have recently been several experiments studying induced
superconductivity in semiconducting two-dimensional electron gases that are
strongly coupled to thin superconducting layers, as well as probing possible
topological phases supporting Majorana bound states in such setups. We show
that a large band shift is induced in the semiconductor by the superconductor
in this geometry, thus making it challenging to realize a topological phase.
Additionally, we show that while increasing the thickness of the
superconducting layer reduces the magnitude of the band shift, it also leads to
a more significant renormalization of the semiconducting material parameters
and does not reduce the challenge of tuning into a topological phase.
