Relativistic k.p Hamiltonians for centrosymmetric topological insulators from ab initio wave functions

TL;DR

This paper introduces a microscopic method to derive accurate k·p Hamiltonians from ab initio wave functions, effectively capturing topological properties of centrosymmetric insulators and correcting previous modeling inaccuracies.

Contribution

The authors develop a formalism that derives small-size k·p Hamiltonians directly from ab initio data without symmetry constraints, accurately determining topological invariants for 3D and 2D systems.

Findings

Effective models often mispredict topological character of thin films.

The method accurately computes topological invariants from ab initio wave functions.

Application to Bi2Se3, Bi2Te3, and Sb2Te3 demonstrates improved modeling.

Abstract

We present a method to microscopically derive a small-size k$\cdot$p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true $\mathbb{Z}_2$ topological invariant. We consider bulk crystals and thin films of Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$, and Sb$_{2}$Te$_{3}$. It turns out that the effective continuous k$\cdot$p models with open boundary conditions often incorrectly predict the topological character of thin films.