A Bound on Topological Gap from Newton's Laws*

A striking general bound on the energy gap in topological matter was recently discovered in Ref. [Onishi and Fu, Phys. Rev. X 14, 011052 (2024)]. A non-trivial indirect derivation builds on the properties of optical conductivity at an arbitrary frequency. The derivation by Onishi and Fu is rather unintuitive as the complexity of the derivation contrasts with the simplicity of the bound itself, which is focused solely on low-energy physics. 

In this talk, we propose a simpler derivation, allowing multiple generalizations, such as a universal bound on a gap in anisotropic systems, systems with multiple charge carrier types, and topological systems with zero Hall conductance. The derivation builds on the observation that the bound equals reduced Plank's constant times the ratio of the force by the external electric field on the charge carriers and their total kinematic momentum in the direction perpendicular to the force.