Chirality-Dependent Hall Effect in Weyl Semimetals

We generalize a semiclassical theory and use the argument of angular momentum conservation to examine the ballistic transport in lightly doped Weyl semimetals, taking into account various phase-space Berry curvatures. We predict universal transverse shifts of the wave-packet center in transmission and reflection, perpendicular to the direction in which the Fermi energy or velocities change adiabatically. The anomalous shifts are opposite for electrons with different chirality, and they can be made imbalanced by breaking inversion symmetry. We discuss how to utilize local gates, strain effects, and circularly polarized lights to generate and probe such a chirality-dependent Hall effect.

Figure 1

(a) Schematic figure showing the transverse shifts $\delta y^{T,R}$ in transmission and refection for an incident Weyl electron wave packet in the $x-z$ plane scattered by a potential step. (b),(c) $\delta y^{T,R}$ plotted as functions of the incident angle ${\theta }_I$ and the potential step height $V_0$, respectively. The shaded regions mark the range of total reflection. (d) Schematic figure showing the Fermi surfaces and momenta ($k_y=0$) of the reflected and/or transmitted wave packets in normal, total reflection, and Klein tunneling regimes. The behaviors in (a)–(c) are for left-handed Weyl electrons, whereas the behaviors for right-handed ones (not shown) are the opposite; the features in (d) do not distinguish chirality. We have chosen the parameter values as ${\mathcal{E}}_I=0.01\mathrm{eV}$, $V_0=0.014\mathrm{eV}$, $v_z={10}^6\mathrm{m}/\mathrm{s}$, and $v_{x,y}=3\times {10}^5\mathrm{m}/\mathrm{s}$ in (b), and ${\theta }_I=\pi /4$, ${\mathcal{E}}_I=0.05\mathrm{eV}$, $v_z={10}^6\mathrm{m}/\mathrm{s}$, and $v_{x,y}=8\times {10}^5\mathrm{m}/\mathrm{s}$ in (c).

Figure 2

(a) Top view of an electron undergoing multiple (total) reflections in a cylindric potential well of WSMs. (b) Side view of the enhanced CHE in (a). (c) The chirality accumulation on the top and bottom surfaces in transmission through the green interface, which is detectable by the imbalanced absorbance of the left and right circularly polarized lights.