Valley-dependent topological phase transition and quantum anomalous valley Hall effect in single-layer RuClBr

Quantum anomalous valley Hall effect (QAVHE), which combines both the features of QAHE and AVHE, is both fundamentally intriguing and practically appealing, but is experimentally challenging to realize in two-dimensional (2D) intrinsic magnetic materials to date. Here, based on first-principles calculations with the density functional theory $+U$ approach, we predicted the electronic correlation-driven valley-dependent quantum phase transition from ferrovalley (FV) to half-valley-semiconductor (HVS) to QAVHE to HVS to FV phase in single-layer RuClBr. Remarkably, the QAVHE phase with an integer Chern number ($C=1$) and chiral spin-valley locking, which is induced by sign-reversible Berry curvature or band inversion between ${d}_{xy}/{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals, can achieve complete spin and valley polarizations for low-dissipation electronics devices. We also find that the electron valley polarization can be switched by reversing magnetization direction, providing a route of magnetic control of the valley degree of freedom. An effective $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model is proposed to clarify valley-dependent quantum phenomena. Additionally, electronic correlation has an important effect on the variations of the Curie temperature of single-layer RuClBr. These findings shed light on the possible role of correlation effects on valley-dependent physics in 2D materials and open alternative perspectives for multifunctional spin-valley quantum devices in valleytronics.