Non-saturating magnetoresistance in heavily disordered semiconductors

Abstract

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 chalcogenides3,4,5, 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.

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Figure 1: Four-terminal network resistor unit, and a schematic diagram of an N × M resistor network.
Figure 2: Normalized magnetoresistance ΔR(H)/R(0) as a function of dimensionless magnetic field β for different sized N × N uniform networks.
Figure 3: Visualization of currents and voltages at large magnetic field in a 10 × 10 random network of disks with radii 1 (arbitrary units), where the potential difference U = -1 V.
Figure 4: Average normalized magnetoresistance ΔR(H)/R(0) as a function of dimensionless magnetic field H/H0 of 20 × 20 random resistor networks for different mobility distributions, where H0 = 1 kOe is a typical field scale.

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Acknowledgements

P.B.L. thanks the NHMFL for hospitality during the final drafting of this Letter. The NHMFL is supported by the National Science Foundation, the state of Florida and the US Department of Energy. This work was supported by the Association of Commonwealth Universities and the Cambridge Commonwealth Trust.

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Correspondence to M. M. Parish.

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Parish, M., Littlewood, P. Non-saturating magnetoresistance in heavily disordered semiconductors. Nature 426, 162–165 (2003). https://doi.org/10.1038/nature02073

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