Third-Generation TB-LMTO

TL;DR

This paper introduces the third-generation TB-LMTO method, extending the KKR approach to more accurately solve the Schrödinger equation for complex potentials, with applications to superconductors and silicon.

Contribution

It develops a generalized formalism for the TB-LMTO method that includes downfolding, corrections, and proper treatment of potential overlaps, improving accuracy and applicability.

Findings

Effective downfolding to low-energy Hamiltonians demonstrated on superconductors.

First-principles TB Hamiltonians for silicon derived.

Correct treatment of potential overlap enables elimination of empty spheres.

Abstract

We describe the screened Korringa-Kohn-Rostoker (KKR) method and the third-generation linear muffin-tin orbital (LMTO) method for solving the single-particle Schroedinger equation for a MT potential. The simple and popular formalism which previously resulted from the atomic-spheres approximation (ASA) now holds in general, that is, it includes downfolding and the combined correction. Downfolding to few-orbital, possibly short-ranged, low-energy, and possibly orthonormal Hamiltonians now works exceedingly well, as is demonstrated for a high-temperature superconductor. First-principles sp3 and sp3d5 TB Hamiltonians for the valence and lowest conduction bands of silicon are derived. Finally, we prove that the new method treats overlap of the potential wells correctly to leading order and we demonstrate how this can be exploited to get rid of the empty spheres in the diamond structure.