Properties of topological insulators and superconductors under relativistic gravity

TL;DR

This paper investigates how relativistic gravity influences topological phases in quantum systems, revealing that topological states are generally robust but can experience energy shifts and phase transitions due to gravitational effects.

Contribution

It provides the first analysis of relativistic gravity's impact on topological quantum systems, showing robustness and identifying gravitationally induced phase transitions.

Findings

Topological states remain robust under relativistic gravity.

Gravitational redshift shifts the energy of topological states.

Possible gravitationally induced topological phase transition.

Abstract

The interplay between the curved spacetimes of general relativity and quantum mechanical systems is an active field of research. However, analysis of relativistic gravitation on extended quantum systems remains understudied. To this end, we study here the effects of a general relativistic curved spacetime on the topological phases of the Su-Schrieffer-Heeger model and Kitaev superconducting wire. We find that the topological states remain robust and well localized. In the topological insulator we find that the energy level of the topological state becomes shifted away from zero according to the gravitational redshift, breaking the system's chiral symmetry. In contrast, the Majorana zero mode of the topological superconductor remains at zero energy. Furthermore, within the topological superconductor, we identify the possibility of a gravitationally induced topological phase transition leading to the formation of a domain wall, shifting one of the boundary Majorana zero modes into the bulk.