Efficient finite-temperature generalization of the propagator method

Develop a similarly efficient generalization of the real-space lattice-propagator calculation method to finite temperature, where the sharp Fermi-sea occupation step is replaced by a Fermi function.

Background

The paper presents an efficient method for calculating real-space particle-addition and particle-removal propagators at zero temperature and finite carrier concentration. Its key simplifications rely on the sharp separation at the Fermi energy between occupied and unoccupied states, which allows selected real or imaginary parts of finite-concentration propagators to be obtained directly from the corresponding empty-system propagators and the remaining parts to be recovered through Kramers–Kronig relations.

At finite temperature, occupations are described by a smooth Fermi function rather than a sharp step. Consequently, the zero-temperature identities used by the method no longer apply directly, and the paper leaves unresolved whether an equally efficient computational generalization can be constructed.