Vortical effects in chiral band structures using Kubo's formula

Recently, transport phenomena in Weyl semimetals have attracted much research attention in condensed matter physics. The chiral vortical effect -- a chiral anomaly-induced transport phenomenon characterized by an axial current in a rotating chiral fluid -- is well-studied in high energy physics, but its realization in condensed matter is much less understood. In this work, we derive the response of electrons in a general band structure to rotation at non-zero temperature T, wavevector q, and frequency Ω. Unlike the hydrodynamic and Boltzmann-equation-based approaches used in high-energy physics, we use the Kubo formula which is more quantum-mechanical and easier to extend to finite q and Ω and general band structures. For a Weyl fermion at T=0, we recover the high-energy physics results in the static limit (Ω→0 before q→0$) but not in the uniform limit (q→0 before Ω→0), and trace the difference in results to vanishing contribution from intraband terms in the latter limit.