Anomalous valley Hall effect in two-dimensional <i>p</i>-orbital honeycomb lattice

Abstract

Anomalous valley Hall effect (AVHE) in two-dimensional materials represents a cornerstone phenomenon in condensed matter physics. While substantial research efforts have been predominantly concentrated on d-orbital systems, its realization in p-orbital platforms is rarely investigated. Here, taking monolayer XN (X = Ge and Sn) as prototypical systems, we demonstrate the existence of AVHE in two-dimensional p-orbital systems through first-principles calculations and symmetry analysis. Monolayer XN is a ferromagnetic semiconductor with a pair of valleys in the valence bands. The synergistic breaking of both inversion and time-reversal symmetries enables spin–orbit coupling to intrinsically lift the valley degeneracy, yielding spontaneous valley polarizations. Moreover, the emergent valley-contrasting Berry curvatures directly manifest measurable AVHE responses under in-plane electric fields. Crucially, we systematically elucidate the microscopic origin of these polarization phenomena, uncovering the essential role of in-plane px/y orbital contribution. These findings significantly expand the candidate materials for valleytronic research.