Quantum structure of the chiral vortical effect and boundary-induced vortical pumping

Abstract

The chiral vortical effect (CVE) -- an axial current driven by rotation in chiral matter -- appears in systems ranging from relativistic fluids to Weyl semimetals, yet its quantum origin remains unclear because existing derivations are semiclassical. We present an exact quantum solution of a rotating Weyl fermion in a finite cylinder. We show that the bulk vortical response is entirely a magnetization current while the current density on the rotation axis remains finite and matches semiclassical predictions. For spin-polarized boundary conditions, we uncover an additional effect beyond the known CVE: a robust family of chiral modes that transport axial charge, $ΔQ=χN^2\,Δθ/4π$, under rotation by angle $Δθ$, where $χ$ is the Weyl node chirality and $N$ is the number of chiral modes. The pump is independent of temperature, Fermi level and Weyl velocities, but depends on the UV-sensitive number $N$. These results establish a fully quantum picture of the CVE and reveal a boundary-enforced chiral spectral structure underlying vortical response in Weyl systems.

Figures (3)

• Figure 1: (a) Illustration of a rotating Weyl fermion on a cylinder with a spin-polarized boundary (red). (b) The spectrum of $H_\text{rot}$\ref{['eq:H-rot']}, consisting of subbands separated in energy by $\hbar\Omega$ (only $|n|{\le1}$ are demonstrated). For spin-polarized boundary conditions, the $n\ge0$ subbands host chiral modes (red) with $k_\perp\to0$ whose effective Fermi level changes by $(n+1/2)\hbar\Omega$ (green) under rotation, leading to quantized charge pumping. Other subbands contain only $k_\perp\neq0$ modes, which are non-chiral and lead to vanishing transport.
• Figure 2: Radial dependence of the current density $j_z$ (inset: 3D plot) and the chiral current density $j_z^{\text{ch}}$ (orange). At $\rho\to0$, the value of $j_z$, termed $j_z^\text{ax}$ here, equals the semiclassical value, while $j_z$ averages to zero over a cross-section in the thermodynamic limit due to its oscillatory nature. $N_{k_{\perp}}=11$ is adopted, and $N_{k_{\perp}}$-dependence is shown in App. \ref{['subsec:cross-section average']}
• Figure 3: (a) $j_z(\rho)$ from the bulk states for various cutoff choices $N_\text{max}$ on $n$. The contribution tends to locally vanish as $N_\text{max}$ grows due to cancellation between various oscillating functions. (b) The global cancellation (dashed) due to oddness of current density with respect to $k_z$, exemplified by $k_z={\pm}1$ modes. The dashed line is defined by $\int_0^{\rho}(j_{k_z=1}+j_{k_z=-1})$.