Non-saturating magnetoresistance in heavily disordered semiconductors

The resistance of a homogeneous semiconductor increases quadratically with magnetic field at low fields and, except in very special cases, saturates at fields much larger than the inverse of the carrier mobility, a number typically of the order of 1 T (refs 1, 2). A surprising exception to this behaviour has recently been observed in doped silver chalcogenides, which exhibit an anomalously large, quasi-linear magnetoresistive response that extends down to low fields and survives, even at extreme fields of 55 T and beyond. Here we present a simple model of a macroscopically disordered and strongly inhomogeneous semiconductor that exhibits a similar non-saturating magnetoresistance. In addition to providing a possible explanation for the behaviour of doped silver chalcogenides, our model suggests potential routes for the construction of magnetic field sensors with a large, controllable and linear response.