Topological Fermi-liquid theory for interacting Weyl metals with time reversal symmetry breaking

Abstract

Introducing both the Berry curvature and the chiral anomaly into Landau's Fermi-liquid theory, we construct a topological Fermi-liquid theory, applicable to interacting Weyl metals in the absence of time reversal symmetry. Following the Landau's Fermi-liquid theory, we obtain an effective free-energy functional in terms of the density field of chiral fermions, where the band structure is modified, involved with an emergent magnetic dipole moment due to the Berry curvature. The density field of chiral fermions is determined by a self-consistent equation, minimizing the effective free-energy functional with respect to the order-parameter field. Beyond these thermodynamic properties, we construct a Boltzmann transport theory to encode both the Berry curvature and the chiral anomaly in the presence of forward scattering of a Fermi-liquid state, essential for understanding dynamic correlations in interacting Weyl metals. This generalizes the Boltzmann transport theory for the Landau's Fermi-liquid state in the respect of incorporating the topological structure and extends that for noninteracting Weyl metals in the sense of introducing the forward scattering. Finally, we justify this topological Fermi-liquid theory, generalizing the first-quantization description for noninteracting Weyl metals into the second-quantization representation for interacting Weyl metals. First, we introduce a topological Fermi-gas theory, integrating over high-energy electronic degrees of freedom deep inside a pair of chiral Fermi surfaces. As a result, we reproduce a topologically modified Drude model with both the Berry curvature and the chiral anomaly, given by the first-quantization description. Second, we take into account interactions between such low-energy chiral fermions on the pair of chiral Fermi surfaces. Following the Landau's Fermi-liquid theory, we perform the renormalization group analysis. We find that only forward scattering turns out to be marginal above possible superconducting transition temperatures, justifying the topological Fermi-liquid theory of interacting Weyl metals with time reversal symmetry breaking. The topological Fermi-liquid theory serves a theoretical platform for us to investigate the role of Fermi-liquid interactions in anomalous transport phenomena of interacting Weyl metals such as anomalous Hall effects, chiral magnetic and vortical effects, and negative longitudinal magnetoresistivity properties. In addition, it allows us to study how thermodynamic properties such as the Wilson's ratio and spectra of collective excitations such as zero sound modes in the Landau's Fermi-liquid state are modified due to the Berry curvature and the chiral anomaly.