  We demonstrate the existence of novel interaction effects in hole-doped
semiconductor quantum wells which are connected to dramatic changes in the
Fermi surface geometry occurring upon variation of the doping. We present band
structure calculations showing that quantum wells formed in $p$-type cubic
semiconductors develop nested Fermi surfaces at a critical hole density set by
the width $d$ of the quantum well $k_F\sim \pi/d$. Nesting gives rise to
competing superconducting and charge or spin density wave order, which we
analyze using the perturbative renormalization group method. The correlated
phases may be created or destroyed by tuning the hole density towards or away
from the critical density. Our results establish $p$-type semiconductor quantum
wells as a platform for novel correlated phases, which may be precisely
controlled using electrostatic gating and external magnetic fields.
