Thank you for visiting nature.com. 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

## 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.

This is a preview of subscription content

## Access options

\$32.00

All prices are NET prices.

## References

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

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

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

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)

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

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

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)

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

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

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)

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

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

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

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

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

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

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

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)

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)

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

## 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.

## Author information

Authors

### 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

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

• Accepted:

• Issue Date:

• DOI: https://doi.org/10.1038/nature02073

• ### Electron–phonon coupling in copper intercalated Bi$$_{2}$$Se$$_{3}$$

• Maciej Wiesner
• Kristie Koski
• Pertti Hakonen

Scientific Reports (2022)

• ### Giant linear magnetoresistance in half-metallic Sr2CrMoO6 thin films

• Zhao-Cai Wang
• Lei Chen
• Ren-Kui Zheng

npj Quantum Materials (2021)

• ### Gate-tunable linear magnetoresistance in molybdenum disulfide field-effect transistors with graphene insertion layer

• Hao Huang
• Hongming Guan
• Ning Tang

Nano Research (2021)

• ### Modeling of magneto-conductivity of bismuth selenide: a topological insulator

• Yogesh Kumar
• Rabia Sultana
• V. P. S. Awana

SN Applied Sciences (2021)

• ### Observation of Landau Level-Dependent Aharonov-Bohm-Like Oscillations in a Topological Insulator

• Shiu-Ming Huang
• Chien Lin
• Mitch M. C. Chou

Nanoscale Research Letters (2020)