Two-dimensional electron gas as a flux detector for a type-II superconducting film

Thin type-II superconducting films have been prepared on top of the two-dimensional electron gas (2DEG) in a GaAs/${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ga}}_{\mathit{x}}$As heterostructure. The type-II gate and the 2DEG are so close to one another that the magnetic field distribution at the superconductor, consisting of a lattice of flux vortices, is projected intact onto the electronic system below. We show that the 2DEG acts as a very sensitive flux detector for the superconducting film. Both the Hall voltage (${\mathit{V}}_{\mathit{H}}$) and the magnetoconductance (${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$) reflect the irreversible motion of flux in the gate in complementary ways. In particular, ${\mathrm{\sigma }}_{\mathit{x}\mathit{x}}$ is a probe of magnetic-field inhomogeneities on a scale of the inelastic scattering length in the 2DEG. A method of measuring the spatial dependence of the magnetic field at a flux vortex is proposed that exploits this property.