Axial Current Generation from Electric Field: Chiral Electric Separation Effect

We study a relativistic plasma containing charged chiral fermions in an external electric field. We show that with the presence of both vector and axial charge densities, the electric field can induce an axial current along its direction and thus cause chirality separation. We call it the Chiral Electric Separation Effect (CESE). On very general basis, we argue that the strength of CESE is proportional to $\mu_V\mu_A$ with $\mu_V$ and $\mu_A$ the chemical potentials for vector charge and axial charge. We then explicitly calculate this CESE conductivity coefficient in thermal QED at leading-log order. The CESE can manifest a new gapless wave mode propagating along the electric field. Potential observable of CESE in heavy-ion collisions is also discussed.