Large valley splitting under biaxial strain in Janus SHfAX₂ (A = Si, Ge; X = N, P, As)

The exploration of valley physics in 2D materials exhibiting strong spin-orbit coupling (SOC) holds fundamental significance. In this work, we demonstrate that the 2D Janus SHfAX₂ (A = Si, Ge; X = N, P, As) family emerges as a promising 2D valley material from first-principles calculations. We find that there is a large valley splitting at the K and K' points in the 2D SHfAX₂. This splitting predominantly originates from its strong SOC effect and the built-in electric field in the Janus structure. The spin states of valley splitting remain stable under biaxial strain ranging from -4% to 4%. In this study, the conduction band exhibits a peak in the Berry curvature related to valley splitting at the K/K' points. Consequently, the carriers in the K/K' valleys accumulate at the opposite edges of the nanoribbons, generating the valley Hall effect. The 2D SHfAX₂ has high mechanical and dynamic stability, thus providing an emerging family of 2D materials targeting real-world valley-based devices.