Forms of transport lifetimes satisfying Peierls’ argument for general band structures

Characterize the form of the transport lifetime τ_{n,k} that satisfies Peierls’ argument—yielding non-dissipative stationary solutions of the coupled Boltzmann equations in the absence of Umklapp and anharmonicity—for electronic band dispersions more complicated than parabolic or Dirac-cone graphene.

Background

The authors demonstrate that, for a single parabolic band, a constant-in-energy relaxation time leads to Peierls-type solutions that nullify the collisional integral, and for graphene’s Dirac cones a lifetime proportional to |k| does the same. This reflects momentum conservation in the absence of Umklapp and anharmonic scattering.

They note that more complex band structures will require different lifetime forms to satisfy Peierls’ argument, but do not derive them here.