Two band tunneling for a pnp junction in tetralayer graphene

Abstract

We investigate the band structure and the tunneling of ABCA-tetralayer graphene (ABCA-TTLG) subjected to an external potential U 0 applied between top and bottom layers. Using the tight-binding model, including the nearest t and next-nearest-neighbor t ′ hopping, low-energy model and two-band approximation model we study the band structure variation along the lines Γ − M − K − Γ in the first Brillouin zone , electronic band gap near Dirac point K , transmission properties and conductance, respectively. Our results reveal that ABCA-TTLG exhibits markedly different properties as functions of t ′ and U 0 . We show that the hopping parameter t ′ changes the energy dispersion, the position of K and breaks sublattice symmetries. A sizable band gap is created at K , which could be opened and controlled by the applied potential U 0 . This gives rise to 1D-like van Hove singularities (VHS) in the density of states (DOS). Resonant electronic transmission through graphene-based a p n p junction is studied as a function of the incident wave vector, the width and height of the barrier with and without U 0 . The resonant features in the transmission result from resonant hole states in the barrier and strongly influence the conductance. Our results are numerically discussed and compared with the literature. • Quantum tunneling of ABCA-tetralayer graphene in an potential applied between top and bottom layers is investigated. • The hopping parameter acts by changing the energy dispersion and the position of Dirac point K, also breaks the sublattice symmetries. • A sizable band gap is created at K, which could be opened and controlled by the potential giving rise to 1D-like van Hove singularities (VHS) in the density of states. • The resonant features in the transmission result from resonant hole states in the barrier and strongly influence the conductance.