Berry curvature contributions to the density fluctuation spectrum of Bloch electrons

Recent work has shown that the equations of motion (EOM) for semiclassical Bloch electrons must be modified in the presence of a non-zero Berry curvature [1]. These corrections to the EOM have implications for many physical quantities: effective mass, electron orbits in a magnetic field, de Haas-van Alphen oscillations, etc. In addition the Boltzmann transport equation is also modified with possible ramifications for calculations of transport phenomena. We investigate these issues for a gas of spinless Bloch electrons in an external electric field. We find modifications to the traditional dispersion relation for density fluctuations; in particular we find a shift in the plasma frequency and an anisotropic sound velocity. [1] M.-C. Chang and Q. Niu, Phys. Rev. B 53, 7010 (1996)