Collective dynamics of Fermi surface fluctuations in an interacting Weyl metal phase

Instabilities in a Landau's Fermi-liquid state occur, increasing the strength of interaction parameters in the Landau's Fermi-liquid theory. Introducing both the Berry curvature and chiral anomaly into this theoretical framework, we investigate collective dynamics of Fermi surface fluctuations and reveal their instabilities in an interacting Weyl metal phase with broken time reversal symmetry. Recently, a topological Fermi-liquid theory has been proposed to describe this interacting Weyl metal phase, where not only the Berry curvature but also the chiral anomaly is introduced into the Landau's Fermi-liquid theory [Phys. Rev. B 95, 205113 (2017)]. Based on the Boltzmann-equation framework, we find criteria for the stability of the topological Fermi-liquid state as a function of forward-scattering Landau's interaction parameters and the distance of a pair of Weyl points given by an external magnetic field. In addition to these instability criteria for general angular momentum channels, we investigate the dispersion relation of the zero-sound mode as the simplest example of such Fermi surface fluctuations. Zero-sound modes are well-defined collective excitations in a Landau's Fermi-liquid state, given by the collective dynamics of Fermi surface deformations in the spin-singlet channel with zero angular momentum, where their instability is related with phase separation. We find that the role of the Berry curvature changes the instability criteria of the Landau's Fermi-liquid state. Even if the zero-sound mode is stable in the region of the forward-scattering amplitude, the Berry curvature gives rise to Landau damping beyond the Landau's Fermi-liquid theory. Based on the instability criterion of the zero-sound mode, we propose a phase diagram for a topological Fermi-liquid state against the phase separation in the plane of Landau's interaction parameter and effective Berry curvature, which generalizes the one-dimensional phase diagram of the Landau's Fermi-liquid theory.