Multiband k·p theory of monolayer XSe ( X=In,

Multiband $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Hamiltonians near the high symmetric points in the Brillouin zones of two-dimensional (2D) materials are widely used to predict and understand the unique transport and optical properties of 2D materials. Based on the crystal symmetry of 2D materials, the authors develop a multiband $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Hamiltonian for monolayer GaSe and InSe using the theory of invariants. The authors establish the relationship between the crystal lattice symmetry and the Hamiltonian matrix elements, accounting for spin-orbit interaction and strain. The work provides a systematic way to construct the relevant multiband $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Hamiltonian for various monolayer and few-layer materials.