Scattering Approach to Anderson Localization

Area of Science:

• Condensed Matter Physics
• Disordered Systems
• Quantum Mechanics

Background:

• Anderson localization describes the suppression of electron wave function propagation in disordered materials.
• Understanding electron transport in disordered systems is crucial for developing novel electronic devices.

Purpose of the Study:

• To develop a novel theoretical framework for analyzing Anderson localization.
• To investigate the dimensional dependence of electron localization in disordered samples.

Main Methods:

• Derivation of evolution equations for scattering and Wigner-Smith time-delay matrices.
• Formulation of a Fokker-Planck equation for proper delay times.
• Mapping to a nonlinear partial differential equation (Burgers type) with analytical solutions.

Main Results:

• Analytical solution for the density of delay times for arbitrary sample length L.
• Identification of distinct localization behaviors below and above d=2 dimensions.
• Explicit results for delay time density in localized (d<2) and metallic (d>2) regimes.

Conclusions:

• The developed approach provides a comprehensive analytical solution for Anderson localization.
• The study elucidates the critical role of dimensionality in determining localization phenomena.
• This work offers insights into electron transport in disordered systems across different dimensions.