Hydrodynamics in generalized electronic two-band systems

In this paper, we derive the Euler and Navier-Stokes equations for electronic two-band systems in arbitrary dimension and with generic power-law dispersion relations. We focus on the hydrodynamic transport regime, where such systems offer a unique tunability between a Fermi-liquid type regime at high doping and the inherent two-band physics of the low-density system close to the Dirac-type band-touching point. For a generic dispersion, the absence of Euclidean or Lorentzian invariance leads to novel types of hydrodynamic equations. We characterize these novel hydrodynamic regimes through dimensionless numbers, such as the Prandtl and Lorenz numbers, or the ratio between shear viscosity and entropy density. In all cases, we provide a derivation of the physics of the long-wavelength plasmonic modes.