Quantum mechanics with coordinate-dependent mass

TL;DR

This paper investigates quantum particles with coordinate-dependent properties, deriving a Hamiltonian for interface states in semiconductors, predicting localized electron states at interfaces, and analyzing their scattering behavior.

Contribution

It introduces a rotationally-symmetric Hamiltonian for coordinate-dependent quantum particles and predicts new localized interface electron states in semiconductors.

Findings

Localized electron states appear at semiconductor interfaces.

States occur at intersections of bulk dispersions.

Scattering behavior of carriers at the interface is analyzed.

Abstract

We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed between two semiconductors. We predict a new type of electron states, localized at the interface. They appear whenever the two bulk dispersions intersect. These shallow states lie near the point of intersection and are restricted to a finite range of perpendicular momentum. The scattering of carriers by the interface is discussed.