BaTiO$_3$/GaAs heterostructures: a possible route to reconfgurable III-V nanoelectronics*

Ferroelectric field effect device concepts have existed since the early days of the transistor.\footnote{J. F. Scott , \textit {Ferroelectric Memories}, Springer-Verlag , Berlin \textbf {2000}} The challenges have been more materials-based rather than conceptual. Recent advances in oxide-molecular-beam epitaxy have allowed high quality interfaces between complex oxides and compound semiconductors. Here we focus on heterostructures between GaAs and BaTiO$_3$, which are well lattice-matched and have atomically sharp interfaces. These structures can be configured both in the III-V layer, by growing GaAs/AlGaAs heterostructures and quantum wells; and they can be ferroelectrically patterned in the BaTiO$_3$ layer using a scanning probe microscope. We discuss current efforts to develop this material for both optical and transport-based experiments.