Strain-induced half-valley metals and topological phase transitions in M Br 2 monolayers ( M = Ru , Os )

The target of valleytronics developments is to manipulate the valley degree of freedom and utilize it in microelectronics as charge and spin degrees of freedom. Based on first-principles calculations, we demonstrate that $M{\\mathrm{Br}}_{2}$ $(M=\\mathrm{Ru},\\phantom{\\rule{4pt}{0ex}}\\mathrm{Os})$ monolayers are intrinsically ferrovalley materials with large valley polarization up to 530 meV. Compressive strain can induce phase transitions in the materials from ferrovalley insulators to complete valley-polarized metals, called half-valley metals, in analogy to the concept of half metals in spintronics. With the increase of the strain, the materials become Chern insulators, whose edge states are chiral-spin-valley locking. The phase transition is caused by sequent band inversions of the ${d}_{xy}/{d}_{{x}^{2}\\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals at $K\\ensuremath{-}$ and $K+$ valleys, analyzed based on a strained $\\mathbit{k}\\ifmmode\\cdot\\else\\textperiodcentered\\fi{}\\mathbit{p}$ model. Our work provides a pathway for carrying out low-dissipation electronics devices with complete spin and valley polarizations.