Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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 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.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.


  1. Kittel, C. Quantum Theory of Solids (Wiley, New York, 1963)

    MATH  Google Scholar 

  2. Smith, R. A. Semiconductors 2nd edn (Cambridge Univ. Press, Cambridge, 1978)

    MATH  Google Scholar 

  3. Xu, R. et al. Large magnetoresistance in non-magnetic silver chalcogenides. Nature 390, 57–60 (1997)

    ADS  CAS  Article  Google Scholar 

  4. Lee, M., Rosenbaum, T. F., Saboungi, M.-L. & Schnyders, H. S. Band-gap tuning and linear magnetoresistance in the silver chalcogenides. Phys. Rev. Lett. 88, 066602 (2002)

    ADS  CAS  Article  Google Scholar 

  5. Husmann, A. et al. Megagauss sensors. Nature 417, 421–424 (2002)

    ADS  CAS  Article  Google Scholar 

  6. Dalven, R. & Gill, R. Energy gap in β-Ag2Se. Phys. Rev. 159, 645–649 (1967)

    ADS  CAS  Article  Google Scholar 

  7. Tokura, Y. (ed.) Colossal Magnetoresistive Oxides (Gordon and Breach Science, New York, 2000)

  8. Kapitza, P. L. The change of electrical conductivity in strong magnetic fields. Proc. R. Soc. Lond. A 123, 292–372 (1929)

    ADS  Article  Google Scholar 

  9. Abrikosov, A. A. Quantum magnetoresistance. Phys. Rev. B 58, 2788–2794 (1998)

    ADS  CAS  Article  Google Scholar 

  10. Büttiker, M. Magnetoresistance of very pure simple metals. Phys. Rev. B 42, 3197–3200 (1990)

    ADS  Article  Google Scholar 

  11. Bruls, G. J. C. L., Bass, J., van Gelder, A. P., van Kempen, H. & Wyder, P. Linear magnetoresistance caused by sample thickness variations. Phys. Rev. Lett. 46, 553–555 (1981)

    ADS  Article  Google Scholar 

  12. Beer, A. C. Solid State Physics Supplement 4: Galvanomagnetic Effects in Semiconductors (Academic, New York, 1963)

    Google Scholar 

  13. Reynolds, J. A. & Hough, J. M. Formulae for dielectric constant of mixtures. Proc. Phys. Soc. Lond. B 70, 769–775 (1957)

    ADS  Article  Google Scholar 

  14. Balagurov, B. Ya. Conductivity of inhomogeneous media in strong magnetic fields. Sov. Phys. Solid State 28, 1694–1698 (1986)

    Google Scholar 

  15. Stroud, D. & Pan, F. P. Effect of isolated inhomogeneities on the galvanomagnetic properties of solids. Phys. Rev. B 13, 1434–1438 (1976)

    ADS  CAS  Article  Google Scholar 

  16. Bergman, D. J. & Stroud, D. G. High-field magnetotransport in composite conductors: Effective medium approximation. Phys. Rev. B 62, 6603–6613 (2000)

    ADS  CAS  Article  Google Scholar 

  17. Herring, C. Effect of random inhomogeneities on electrical and galvanomagnetic measurements. J. Appl. Phys. 31, 1939–1953 (1960)

    ADS  Article  Google Scholar 

  18. Dreizin, Yu. A. & Dykhne, A. M. Anomalous conductivity of inhomogeneous media in a strong magnetic field. Sov. Phys. JETP 36, 127–136 (1973)

    ADS  Google Scholar 

  19. Solin, S. A., Thio, T., Hines, D. R. & Heremans, J. J. Enhanced room-temperature geometric magnetoresistance in inhomogeneous narrow-gap semiconductors. Science 289, 1530–1532 (2000)

    ADS  CAS  Article  Google Scholar 

  20. Solin, S. A., Thio, T. & Hines, D. R. Controlled GMR enhancement from conducting inhomogeneities in non-magnetic semiconductors. Physica B 279, 37–40 (2000)

    ADS  CAS  Article  Google Scholar 

  21. Ogorelec, Z., Hamzic, A. & Basletic, M. On the optimisation of the large magnetoresistance of Ag2Se. Europhys. Lett. 46, 56–61 (1999)

    ADS  Article  Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to M. M. Parish.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Parish, M., Littlewood, P. Non-saturating magnetoresistance in heavily disordered semiconductors. Nature 426, 162–165 (2003).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing