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Localization behavior induced by asymmetric disorder for the one-dimensional Anderson model
Delong Feng1,2, Yang Cui1,2, Kai Kang3
1CAS Key Laboratory Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Physical Review. E
|November 28, 2019
Summary
Asymmetric disorder slightly enhances Anderson localization near the band center in 1D systems. This effect is negligible for finite energies, explaining why it
Area of Science:
- Condensed Matter Physics
- Disordered Systems
Background:
- The Anderson model describes electron localization in disordered materials.
- Lyapunov exponents quantify localization length.
Purpose of the Study:
- Investigate the impact of asymmetric disorder on the Lyapunov exponent.
- Analyze localization behavior near the band center and for finite energies.
Main Methods:
- Perturbation calculation for Lyapunov exponent.
- Analysis of the one-dimensional Anderson model.
Main Results:
- Asymmetric disorder causes a small, quadratic enhancement of localization near the band center.
- Zero correction to the Lyapunov exponent for finite in-band energies.
- Quantitative behavior of the Lyapunov exponent under asymmetric disorder.
Conclusions:
- Asymmetric disorder effects are often negligible in weakly disordered systems.
- Asymmetry must be considered for high-accuracy localization studies in specific energy regimes.
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