Spatial variation of the two-dimensional electron gas density induced by an increasing Hall electric field

The local properties of a high-mobility, two-dimensional electron gas (2DEG) subjected to an increasing Hall electric field are studied by imaging photoluminescence spectroscopy. It is observed that as the Hall electric field increases, the distribution of a 2DEG density across the sample becomes spatially nonuniform. This nonuniformity is associated with the ``gating effect'' of the Hall electric field that is screened by low-mobility charges accumulating in the layers parallel to the 2DEG. We consider two mechanisms to explain the 2DEG density redistribution induced by the Hall electric field. The first involves in-plane electron transport that results in a linear 2DEG density variation across the Hall bar. The second is activated at a high Hall voltage ($g50$ mV) and involves vertical electron tunneling out of the 2DEG layer. We conclude that the 2DEG density redistribution can affect the nonlinear magnetotransport phenomena recently studied in GaAs/Al${}_{x}$Ga${}_{1\ensuremath{-}x}$As heterostructures containing a high-mobility 2DEG.