Quantum Formulation of Chiral Vortical Effect in Weyl Semi-metals

Abstract

The chiral vortical effect (CVE) is the generation of an axial current in a rotating Weyl fermion; its description is presently based on semiclassical frameworks. In this work, we develop a fully quantum formulation for CVE, solving the exact evolution of microscopic spinful wavefunctions, which enables a bottom-up quantitative test of semi-classical theories and postulated distributions $f_{\text{CVE}}$ in different reference frames. Notably, it shows that $f_{\text{CVE}}$ is over a ground-state-free Floquet spectrum, qualitatively distinct from a thermal equilibrium distribution (i.e., fermi form $f_F$), underscoring CVE as a non-equilibrium phenomenon, distinguished from other chiral transports. The $f_F$ only approximately holds when three conditions are simultaneously fulfilled: (1) slow rotation $\omega R/v_F\ll 1$, (2) high chemical potential $\mu/(\hbar v_F R)\gg 1$, (3) isotropic symmetry, where $R$ is the size, $v_F$ is fermi velocity. In these conditions, the theory recovers established semiclassical results, including the current-response coefficients and the magnetization contribution; otherwise, it uncovers quantum phenomena such as ``void states", deviation from the semiclassical formula $j_{\text{CVE}} \sim \mu^2$, a $v_F$-independent charge pumping. The theory is based on semimetals, providing more experimentally accessible detection than fundamental Weyl particles.