Static Electric Field in a 1D Systems without Boundaries

TL;DR

This paper investigates the influence of orbital positioning on the topological coefficient in 1D systems with doubled unit cells, revealing that static dielectric screening remains boundary-independent, contrary to prior assumptions.

Contribution

It demonstrates that orbital positions affect the topological $ heta$-term coefficient and clarifies the boundary independence of static dielectric screening in 1D systems.

Findings

Orbital position alters the $ heta$-term coefficient.

Static dielectric screening is boundary-independent.

Resolved a paradox in the SSH model.

Abstract

In this brief report, we show that in a 1D system with unit-cell doubling, the coefficient of the $\theta$-term is not only determined the topological index, $\int i\bra{u_k}\frac{\d}{\d k}\ket{u_k}{\rm d}k$. Specifically, the relative position between the electronic orbitals and the ions also alters the coefficient. This resolves a paradox when we apply our previous result to the Su-Shreiffer-Heeger model where the two ground states related by a lattice translation have $\theta$ differed by $\pi$. We also show that the static dielectric screening is the same with or without boundaries, on the contrary to what we have commented in our previous paper.