The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day. There have been numerous reviews of a more or less specialized nature. The present review aims to fill the niche for a non-specialized review of this very active area of research. The basic concepts behind the theory are introduced with more detailed sections covering experimental results, one-dimensional localization, scaling theory, weak localization, magnetic field effects and fluctuations.

https://iopscience.iop.org/article/10.1088/0034-4885/56/12/001/pdf

Localization: theory and experiment

An overview of the integer quantum Hall effect is given. A mathematical framework using nonommutative geometry as defined by Connes is prepared. Within this framework, it is proved that the Hall conductivity is quantized and that plateaux occur when the Fermi energy varies in a region of localized states.

The noncommutative geometry of the quantum Hall effect

We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hall conductivity is quantized and that plateaux occur when the Fermi energy varies in a region of localized states.

The Non-Commutative Geometry of the Quantum Hall Effect

An effective-mass theory of the properties of excitons in isolated GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum wells is presented. The phenomenon of exciton mixing induced by the complicated valence-band structure is emphasized. The effects of external perturbations such as electric and magnetic fields and uniaxial pressure normal to quantum wells grown in different crystal directions are calculated. Exciton mixing is found to cause many observable effects on transition energies and oscillator strengths.

Exciton mixing in quantum wells

Electronic States in Semiconductor Heterostructures

Theory of magnetoexcitons in quantum wells.

Connection rule of envelope functions at heterointerface

http://link.springer.com/content/pdf/10.1007/978-3-642-73554-7_1.pdf

Anderson Localization: An Introduction

http://link.springer.com/content/pdf/10.1007/978-3-642-73554-7_45.pdf

Numerical Study of Localization in 2D Systems: Effects of Magnetic Field and Spin-Orbit Interaction

Localization in two-dimensional square lattices: Effects of magnetic field and spin-orbit interaction

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