Abstract
Two-dimensional (2D) materials are well-known to exhibit interesting phenomena due to quantum confinement. Here, we show that quantum confinement, together with structural anisotropy, result in an electric-field-tunable Dirac cone in 2D black phosphorus. Using density functional theory calculations, we find that an electric field, Eext, applied normal to a 2D black phosphorus thin film, can reduce the direct band gap of few-layer black phosphorus, resulting in an insulator-to-metal transition at a critical field, Ec. Increasing Eext beyond Ec can induce a Dirac cone in the system, provided the black phosphorus film is sufficiently thin. The electric field strength can tune the position of the Dirac cone and the Dirac-Fermi velocities, the latter being similar in magnitude to that in graphene. We show that the Dirac cone arises from an anisotropic interaction term between the frontier orbitals that are spatially separated due to the applied field, on different halves of the 2D slab. When this interaction term becomes vanishingly small for thicker films, the Dirac cone can no longer be induced. Spin-orbit coupling can gap out the Dirac cone at certain electric fields; however, a further increase in field strength reduces the spin-orbit-induced gap, eventually resulting in a topological-insulator-to-Dirac-semimetal transition.
Highlights
Two-dimensional (2D) layered materials, where interlayer interactions are dominated by weak van der Waals forces, has attracted tremendous attention in nanoelectronics[1]
Similar to the Stark effect previously predicted for boron nitride nanotubes, two-dimensional transition metal dichalcogenides, and other 1D and 2D materials[8,9,10,11,12,13] we find that the electric field localizes the valence band maximum (VBM) and conduction band minimum (CBM) states at opposite surfaces of the slab
We show that the emergent Dirac cone physics arises from anisotropic interaction terms between the electric-field-induced quantum-confined VBM and CBM states in few layer black phosphorus
Summary
Two-dimensional (2D) layered materials, where interlayer interactions are dominated by weak van der Waals (vdW) forces, has attracted tremendous attention in nanoelectronics[1]. A layered semiconductor material, is the thermodynamically stable form of phosphorus Different experimental techniques, such as mechanical[3] and liquid[4] exfoliation, have been employed to thin down the bulk to a monolayer. The resulting potential difference between the VBM and CBM states results in a decrease in the band gap, eventually leading to an insulator-to-metal transition at a critical applied field, Ec. in contrast to other materials, we find that for black phosphorus films below a certain critical thickness, a further increase in applied field strength results in a highly anisotropic opening in the band gap that leads to a formation of a Dirac cone. We show that the emergent Dirac cone physics arises from anisotropic interaction terms between the electric-field-induced quantum-confined VBM and CBM states in few layer black phosphorus
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