Abstract
We provide a universal tight bound on the energy gap of topological insulators by exploring relationships between topology, quantum geometry, and optical absorption. Applications of our theory to infrared absorption near topological band inversion, magnetic circular dichroism in Chern insulators, and topological gap in moiré materials are demonstrated.
- Received 25 August 2023
- Revised 15 November 2023
- Accepted 15 December 2023
DOI:https://doi.org/10.1103/PhysRevX.14.011052
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Insulating states are not all equivalent but can be distinguished by the topology of their ground state wave function. Topologically nontrivial insulators cannot be smoothly deformed to trivial atomic insulators while preserving a finite energy gap. While the ground state topology has been extensively studied in the past, the size of the energy gap has not been studied in relation to the topology. In this work, we show that there is an upper bound on the energy gap of topological insulators.
Specifically, we focus on Chern insulators, topologically nontrivial insulators that exhibit the quantum Hall effect. We derive a general tight bound on the energy gap of Chern insulators by considering the optical absorption of linear and circularly polarized light. Our derivation uses only two basic principles of physics: non-negative dissipation and causality of optical response.
Our bound is universally applicable to all Chern insulators, including those exhibiting the fractional quantum Hall effect. Our work also reveals direct connections among topology, geometry, and energy in quantum materials, opening up new research directions.
