Helical magnetic effect and the chiral anomaly
Naoki Yamamoto, Di-Lun Yang
Abstract
In the presence of the fluid helicity $\mathbit{v}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{\ensuremath{\omega}}$, the magnetic field induces an electric current of the form $\mathbit{j}={C}_{\mathrm{HME}}(\mathbit{v}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{\ensuremath{\omega}})\mathbit{B}$. This is the helical magnetic effect (HME). We show that for massless Dirac fermions with charge $e=1$, the transport coefficient ${C}_{\mathrm{HME}}$ is fixed by the chiral anomaly coefficient $C=1/(2{\ensuremath{\pi}}^{2})$ as ${C}_{\mathrm{HME}}=C/2$ independently of interactions. We show the conjecture that the coefficient of the magnetovorticity coupling for the local vector charge, $n={C}_{B\ensuremath{\omega}}\mathbit{B}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{\ensuremath{\omega}}$, is related to the chiral anomaly coefficient as ${C}_{B\ensuremath{\omega}}=C/2$. We also discuss the condition for the emergence of the helical plasma instability that originates from the HME.