Electric spin and valley tunneling Hall effects

The electric Hall effect (EHE) is a newly identified Hall effect characterized by a perpendicular electric field inducing a transverse charge current in two-dimensional (2D) systems. Here, we propose a spin and valley version of EHE. We demonstrate that the transverse spin and valley currents can be generated in an all-in-one tunnel junction based on a buckled 2D hexagonal material in response to a perpendicular electric field, referred to as the electric spin Hall effect and electric valley Hall effect, respectively. These effects arise from the perpendicular-electric-field-induced backreflection phase of electrons in the junction spacer, independent of Berry curvature. The valley Hall conductance exhibits an odd response to the perpendicular electric field, whereas the spin Hall conductance shows an even one. The predicted effects can further enable the transverse separation of a pair of pure spin-valley-locked states with full spin-valley polarization while preserving time-reversal symmetry, as manifested by equal spin and valley Hall angles. Our findings present a new mechanism for realizing the spin and valley Hall effects and provide a novel route to the full electric-field manipulation of spin and valley degrees of freedom, with significant potential for future applications in spintronics and valleytronics.