标题： 量子限制和结构各向异性导致少层黑磷中出现电可调的狄拉克锥 显示英文标题

标题： Quantum-confinement and Structural Anisotropy result in Electrically-Tunable Dirac Cone in Few-layer Black Phosphorous

摘要： 二维材料因其量子限制效应而广为人知，表现出有趣的物理现象。在这里，我们表明，量子限制效应与结构各向异性相结合，会在二维黑磷中产生一个电场可调的狄拉克锥。通过密度泛函理论计算，我们发现一个外加电场E_ext垂直作用于二维黑磷薄膜时，可以减小少层黑磷的直接带隙，导致在临界电场E_c时发生绝缘体到金属的转变。当E_ext超过E_c时，如果黑磷薄膜足够薄，可以在系统中诱导出狄拉克锥。电场强度可以调节狄拉克锥的位置和狄拉克-费米速度，后者在大小上与石墨烯中的类似。我们证明，狄拉克锥来源于由于施加的电场在二维晶格不同半部分的空间分离而产生的前沿轨道之间的各向异性相互作用项。当这种相互作用项在较厚的薄膜中变得微不足道时，就无法再诱导出狄拉克锥。自旋-轨道耦合可以在某些电场下使狄拉克锥出现能隙；然而，进一步增加电场强度会减小自旋-轨道引起的能隙，最终导致拓扑绝缘体到狄拉克半金属的转变。 显示英文摘要

摘要： 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, E_ext, 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, E_c. Increasing E_ext beyond E_c 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-semi-metal transition.