Calculation of current density for graphene superlattice in a constant electric field

Farhad Sattari

doi:10.1007/s40094-015-0165-9

Abstract

Based on the transfer-matrix method, this paper has investigated the electrical transport properties in monolayer and bilayer graphene superlattices modulated by a homogeneous electric field. It is found that the angular range of the transmission probability can be efficiently controlled by the number of barriers. In addition, current density has an oscillatory behavior with respect to external field and Fermi energy. In other words, the current density in monolayer and bilayer graphene superlattices can be controlled by changing either the external field or the Fermi energy. Meanwhile, in the bilayer system unlike monolayer structure the value of current density can be zero. So, for designing electronic devices, bilayer graphene is more efficient.

Highlights

Model and methodWe consider two kinds of systems, MGS and BGS
Based on the transfer-matrix method, this paper has investigated the electrical transport properties in monolayer and bilayer graphene superlattices modulated by a homogeneous electric field
The charge carriers in graphene superlattice are described by the Dirac equation in which Homiltonian of carriers is written as H^ 1⁄4 H^0 þ V0ðxÞ, where H^0 1⁄4 "hvFr^ Á ~k. ~k represents wave vector of quasiparticles, r^ is 2D Pauli matrix and vF % 106 m/s is Fermi velocity

Summary

Model and method

We consider two kinds of systems, MGS and BGS. Where MGS and BGS indicate monolayer and bilayer graphene superlattices, respectively. Each system includes N square barriers modulated by a homogeneous electric field. The potential profile of the systems along the growth direction (the x-axis) has the multiple quantum well structure which is given by: V. V0 À eE0x ÀeE0x for barrier elsewhere, where, V0 represents height of the potential barrier. To neglect the strip edges, we focus on the case where the width of the graphene strip in the y-direction is much larger than the width of barriers, namely b

Tunnelign in MGS

Kiy qy ky

Tunnelign in BGS

Numerical results and discussion

Summary