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/Al_1-x{Ga}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 (VH) and the magnetoconductance (σₓₓ) reflect the irreversible motion of flux in the gate in complementary ways. In particular, σₓₓ 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.