Envelope-function theory of inhomogeneous strain in semiconductor nanostructures

Strain represents an ubiquitous feature in semiconductor heterostructures, and can be engineered by different means in order to improve the properties of various devices, including advanced metal-oxide-semiconductor field-effect transistors and spin-based qubits. However, its treatment within the envelope function framework is well established only for the homogeneous case, thanks to the theory of Bir and Pikus. Here, we generalize this theory to the case of inhomogeneous strain. By fully accounting for the relativistic effects and metric aspects of the problem, we derive a complete envelope-function Hamiltonian, including the terms that depend on first and second spatial derivatives of the strain tensor.