We report measurements of transport in a two-dimensional electron gas in a spatially random magnetic field in which the average magnetic field extends from the classical regime ͗ c ͘Ͻ1 into the quantum Hall regime.Experiments make use of a rough Nd-Fe-B permanent magnet on the surface of a GaAs heterostructure. Effective mass, transport and total scattering times, and g-factor-enhancement values ͑all measured from Shubnikov-de Haas oscillations͒ are comparable to those found for potential scattering in a uniform magnetic field.Magnetotransport in a two-dimensional ͑2D͒ electron system with a spatially random magnetic field has generated recent interest for a number of reasons. First, several recent experimental realizations using high-mobility heterostructure materials and overlayers of superconductors or ferromagnets 1-4 have yielded interesting classical transport results. Second, a theoretical debate has arisen concerning the existence of extended states analogous to quantum Hall edge states in a two-dimensional electron gas ͑2DEG͒ in a spatially random field with zero average ͑͗B͘ϭ0, ͗B 2 ͘ 0͒. 5
We investigate theoretically and experimentally classical advective transport in a 2D electron gas in a random magnetic field. For uniform external perpendicular magnetic fields large compared to the random field we observe a strong enhancement of conductance compared to the ordinary Drude value. This can be understood as resulting from advection of cyclotron guiding centers. For low disorder this enhancement shows non-trivial scaling as a function of scattering time, with consistency between theory and experiment.
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