  We present piezoresistance measurements in modulation doped AlAs quantum
wells where the two-dimensional electron system occupies two conduction band
valleys with elliptical Fermi contours. Our data demonstrate that, at low
temperatures, the strain gauge factor (the fractional change in resistance
divided by the sample's fractional length change) in this system exceeds
10,000. Moreover, in the presence of a moderate magnetic field perpendicular to
the plane of the two-dimensional system, gauge factors up to 56,000 can be
achieved. The piezoresistance data can be explained qualitatively by a simple
model that takes into account intervalley charge transfer.
