Magnus Hall Effect

A new type of a linear response Hall effect is predicted in time-reversal-invariant systems with a built-in electric field at zero magnetic field. The Hall response results from a quantum Magnus effect where a self-rotating Bloch electron wave packet moving under an electric field develops an anomalous velocity in the transverse direction. We show that in the ballistic limit the Magnus Hall conductance measures the distribution of the Berry curvature on the Fermi surface.

Figure 1

(a) Geometry of the device for the Magnus Hall effect. Source and drain regions are separated by a segment with a built-in electric field. An electron that exits the source exhibits a Magnus shift $\mathrm{\Delta }{y}_A$. Potential energy $U(x)$ profile in the central region determines the position of the band bottom. (b) The direction of the Hall current is preserved under inversion of both the direction of the potential drop and the electrochemical potential bias.

Figure 2

Magnus Hall conductance $G_H$ as a function of the chemical potential $\mu$ at $T=0.01$ and $\mathrm{\Delta }U=0.05$ from Eq. (11) (dashed) and Landauer-Buttiker simulation (solid). The inset shows the distribution of Berry curvature of the valence bands in the Brillouin zone. The green line shows the Fermi surface for $E=-0.35$ (solid for $v_x>0$ and dashed for $v_x<0$).

Figure 3

Hall conductance for the bilayer graphene model for $\mathrm{\Delta }U=10\mathrm{meV}$. Inset: Berry curvature distribution around the $K$ and $K^{\prime }$ valley of the valence band of bilayer graphene. The green line shows the Fermi surface at $\mu =-60\mathrm{meV}$ (solid for $v_x>0$ and dashed for $v_x<0$).