The conditions for the existence of collapsed states of an electron bound to an impurity on the surface of few-layer black phosphorus (BP) are theoretically determined by a model that combines tight-binding and continuum approximations. Under applied vertical bias, the quasiparticle gap of this material significantly decreases and eventually closes at sufficiently high bias. As the bias reduces the gap, the binding energy of an electron bound to a positively charged impurity may reach the energy range where it crosses the valence band, thus characterizing the collapsed impurity state. On the other hand, depending on its orientation, the applied bias may also pull the electron away from the impurity, thus reducing its binding energy and, consequently, preventing the collapse. We demonstrate that the competition between these two phenomena leads to a reentrant behavior of the impurity collapsed state as the applied bias increases. Also, in the case where the BP gap is closed by the bias, low-energy electrons in this material behave as massless Dirac fermions with highly anisotropic Fermi velocity, for which we use a semianalytical method to predict the conditions of applied bias and impurity charge that lead to the impurity collapsed state. The phase diagrams produced in our study will help guide future work towards the observation of such collapsed electron-impurity states in BP.

Close

PrevNext

View figure in article

• Dirac semimetal
• Layered semiconductors
• Nanostructures
• Phosphorene
• Effective mass theory
• Tight-binding model