Topological quantization of boundary forces and the integrated density of states

TL;DR

This paper demonstrates that for certain quantum systems, the boundary force per unit area and energy is topologically quantized and equals the integrated density of states when the Fermi energy is in a bulk spectral gap.

Contribution

It establishes a topological quantization of boundary forces and their equality to the integrated density of states in half-space Schrödinger operators.

Findings

Boundary force per unit area and energy is topologically quantized.

Boundary force equals the integrated density of states at the Fermi energy.

Quantization holds when the Fermi energy lies in a bulk spectral gap.

Abstract

For quantum systems described by Schr\"odinger operators on the half-space $\RR^{d-1}\times\RR^{leq 0}$ the boundary force per unit area and unit energy is topologically quantised provided the Fermi energy lies in a gap of the bulk spectrum. Under this condition it is also equal to the integrated density of states at the Fermi energy.