Observation of geometry-dependent conductivity in two-dimensional electron systems
Physical Review B - Condensed Matter and Materials Physics
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Backes, D., Hall, R., Pepper, M., Beere, H., Ritchie, D., & Narayan, V. (2015). Observation of geometry-dependent conductivity in two-dimensional electron systems. Physical Review B - Condensed Matter and Materials Physics, 92 (23)https://doi.org/10.1103/PhysRevB.92.235427
We report electrical conductivity σ measurements on a range of two-dimensional electron gases (2DEGs) of varying linear extent. Intriguingly, at low temperatures (T) and low carrier density (n_s) we find the behaviour to be consistent with σ ∼ L^α , where L is the length of the 2DEG along the direction of transport. Importantly, such scale-dependent behaviour is precisely in accord with the scaling hypothesis of localization [Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)] which dictates that in systems where the electronic wavefunction ξ is localized, σ is not a material-specific parameter, but depends on the system dimensions. From our data we are able to construct the ‘β- function’ ≡ (h/e²)d ln σ/d lnL and show this to be strongly consistent with theoretically predicted limiting values. These results suggest, remarkably, that the electrons in the studied 2DEGs preserve phase coherence over lengths ∼ 10 µm. This suggests the utility of the 2DEGs studied towards applications in quantum information as well as towards fundamental investigations into many-body localized phases.
We acknowledge funding from the Leverhulme Trust, UK and the Engineering and Physical Sciences Research Council (EPSRC), UK. We also acknowledge D. Joshi for assistance with device fabrication. DB and VN acknowledge useful discussions with Margarita Tsaousidou, Chris Ford, Charles Smith, Moshe Kaveh and Richard Berkovits.
UNIVERSITY COLLEGE LONDON (FB EPSRC) (EP/K004077/1)
External DOI: https://doi.org/10.1103/PhysRevB.92.235427
This record's URL: https://www.repository.cam.ac.uk/handle/1810/252559