Universal bound on topological gap

          @misc{ pirsa_PIRSA:24050031,
            doi = {10.48660/24050031},
            url = {https://pirsa.org/24050031},
            author = {Fu, Liang},
            keywords = {Quantum Information},
            language = {en},
            title = {Universal bound on topological gap},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050031 see, \url{https://pirsa.org}}
          }
          

Abstract

I will show the existence of a universal upper bound on the energy gap of topological states of matter, such as (integer and fractional) Chern insulators, quantum spin liquids and topological superconductors. This gap bound turns out to be fairly tight for the Chern insulator states that were predicted and observed in twisted bilayer transition metal dichalcogenides. Next, I will show a universal relation between the energy gap and dielectric constant of solids. These results are derived from fundamental principles of physics and therefore apply to all electronic materials. I will end by outlining new research directions involving topology, quantum geometry and energy.