Group theory and density functional theory (DFT) methods are combined to obtain compact and accurate k · p Hamiltonians that describe the bandstructures around the K and points for the 2D material hexagonal boron arsenide predicted to be an important low-bandgap material for electric, thermoelectric, and piezoelectric properties that supplements the well-studied 2D material hexagonal boron nitride. Hexagonal boron arsenide is a direct bandgap material with band extrema at the K point. The bandgap becomes indirect with a conduction band minimum at the point subject to a strong electric field or biaxial strain. At even higher electric field strengths (approximately 0.75 V Å−1) or a large strain (14%) 2D hexagonal boron arsenide becomes metallic. Our k · p models include to leading orders the influence of strain, electric, and magnetic fields. Excellent qualitative and quantitative agreement between DFT and k · p predictions are demonstrated for different types of strain and electric fields.
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