Mass-invariant universal optical conductivity from quantum geometry

Mass is a defining property of particles, shaping their fundamental nature and interactions. In condensed matter systems, the effective mass of electrons has long been regarded as a key factor influencing material properties, including their transport and optical responses. In this work, we challenge this conventional wisdom by unveiling a mass-invariant universal optical conductivity, purely derived from quantum geometry, in quadratic band–touching semimetals. Specifically, the optical conductivity simplifies to σ = ( e 2 / 8 ℏ ) d max 2 , independent of effective mass and other band structure details, where d max represents the maximum Hilbert-Schmidt quantum distance. Furthermore, under time-reversal and rotational symmetries, d max is restricted to discrete values of 0 or 1, leading to a quantized universal optical conductivity. We also use first-principles calculations to demonstrate the mass-invariant universal optical conductivity across multiple materials, including bilayer graphene, monolayer bismuth, monolayer kagome palladium thiophosphate, and other realistic material candidates. Our work establishes a previously unidentified class of universal quantities in quantum materials entirely governed by quantum geometry.