Electronic Sound and Diffusion in Disordered Multiband Metals

Abstract

Multiband metals can host acoustic plasmons: gapless collective charge excitations involving out-of-phase motion of electrons in different bands, sometimes referred to as 'demons'. Using a hydrodynamic description valid at high temperatures, and a microscopic description with vertex corrections valid at low temperatures, we show, upon including disorder inevitably present in real materials, that the mode frequency becomes purely imaginary, resulting in diffusive behaviour over a finite range of small wave vectors $q\le q_c$. This framework provides a natural, parameter-free explanation for the anomalous nonlinear dispersion recently reported for the demon in Sr$_2$RuO$_4$, which deviates from the gapless behaviour predicted by the random phase approximation. Our results establish demons as fundamentally distinct from previously known acoustic excitations, such as phonons and photons, which exhibit inertial dynamics protected by symmetries or gauge redundancies.