Nontrivial interband effect: applications to magnetic susceptibility, nonlinear optics, and topological degeneracy pressure

TL;DR

This paper develops a theory of the nontrivial interband effect in solid-state physics, linking topological properties to magnetic, optical, and mechanical phenomena, and introduces new concepts like interband-induced degeneracy pressure.

Contribution

It introduces a comprehensive framework for the nontrivial interband effect, connecting topological band structures to diverse physical properties and proposing new measures like degeneracy pressure.

Findings

Calculated orbital magnetic susceptibility for topological Hamiltonians.

Defined and computed interband-induced degeneracy pressure, showing its negative tendency.

Linked topological band structures to mechanical and nonlinear optical properties.

Abstract

The interband effect is an important concept both in traditional and modern solid-state physics. In this paper, we present a theory of the nontrivial interband effect, which cannot be removed without breaking given rules. We define the general nontrivial interband effect by regarding a property of the set of the total bands of a tight-binding Hamiltonian as the triviality. As examples of the source of the nontrivial interband effect, we consider several topological concepts: stable topological insulator, symmetry-based indicator, fragile topological insulator, and multipole/higher-order topological insulator. As an application, we calculate the orbital magnetic susceptibility for tight-binding Hamiltonians with topological properties. In addition, we consider the mechanical properties induced by the nontrivial interband effect. We define interband-induced degeneracy pressure, which tends to take a negative value, and calculate it for the Chern insulator. This calculation demonstrates the importance of topological band structures in mechanical properties of solids. We also discuss the application to nonlinear optics characterized by the polarization difference and the generalization to interacting systems with entanglement. The framework of the nontrivial interband effect, which includes topological concepts as subsets, might be useful for finding unexplored concepts.