Electron Optics in Phosphorene pn Junctions: Negative Reflection and Anti-Super-Klein Tunneling

Abstract

Ballistic electrons in phosphorene pn junctions show optical-like phenomena. Phosphorene is modeled by a tight-binding Hamiltonian that describes its electronic structure at low energies, where the electrons behave in the zigzag direction as massive Dirac fermions and in the orthogonal armchair direction as Schrödinger electrons. Applying the continuum approximation, we derive the electron optics laws in phosphorene pn junctions, which show very particular and unusual properties. Due to the anisotropy of the electronic structure, these laws depend strongly on the orientation of the junction with respect to the sublattice. Negative and anomalous reflection are observed for tilted junctions, while the typical specular reflection is found only, if the junction is parallel to the zigzag or armchair edges. Moreover, omni-directional total reflection, called anti-super Klein tunneling, is observed if the junction is parallel to the armchair edge. Applying the nonequilibrium Green's function method on the tight-binding model, we calculate numerically the current flow. The good agreement of both approaches confirms the atypical transport properties, which can be used in nano-devices to collimate and filter the electron flow, or to switch its direction.

Quenching effect of oscillating potential on anisotropic resonant transmission through a phosphorene electrostatic barrier

“…The structural anisotropy [12][13][14][15] along the armchair and zigzag directions of phosphorene, e.g., the puckered arrangement in the former, where the low energy massive quantum particles obey Dirac like linear spectrum, while, a bilayer structure in the latter obeying Schrödinger like quadratic spectrum, has made the material much more favorable than many other recently observed 2D materials for the next generation electronic and opto electronic world. In particular, the aforesaid unique anisotropic electronic structure makes phosphorene very attractive for fundamental research as well as for many technological applications 16 , e.g., transistor, detectors and sensors etc. The present work mainly addresses the ballistic resonant tunneling of electrons through quasi-bound state of phosphorene n-p-n junction (barrier) particularly at below barrier electron energies.…”

Black Phosphorus n-type doping by Cu: a microscopic surface investigation

“…Our results indicate a route towards ultra-sharp p-n junctions in bP, which would be exciting to explore in transport measurements on high-mobility bP and might enable observation of electro-optical effects in this material. 57…”

Electronic cloaking of confined states in phosphorene junctions

“…The electronic transport in GPJs can be modeled with the tight-binding low-energy effective Hamiltonian [12,15,[18][19][20]…”

“…As we can see in Fig. In the case of the ZZ direction, the electronic transport has been overestimated due to the charge carriers in this direction have been regarded as Schrödinger particles [15,20].…”

“…These characteristics rise the prospects of phosphorene from both the fundamental and technological standpoint. In fact, several exotic phenomena [14,15] and possible applications [11,13] have been reported. Regarding gated phosporene junctions (GPJs), they can be fabricated by placing electrostatic gates over the phosphorene layer as shown in Fig.…”