Bilayer graphene with single and multiple electrostatic barriers: Band structure and transmission

Abstract

We evaluate the electronic transmission and conductance in bilayer graphene through a finite number of potential barriers. Further, we evaluate the dispersion relation in a bilayer graphene superlattice with a periodic potential applied to both layers. As model we use the massless Dirac-Weyl equation in the continuum model. For zero bias the dispersion relation shows a finite gap for carriers with zero momentum in the direction parallel to the barriers. This is in contrast to single-layer graphene where no such gap was found. A gap also appears for a finite bias. Numerical results for the energy spectrum, conductance, and the density of states are presented and contrasted with those pertaining to single-layer graphene.

Kronig-Penney model on bilayer graphene: Spectrum and transmission periodic in the strength of the barriers

“…We have L → Lt ⊥ / v F ≡ 0.59261L/nm which for L = 10 nm, v F = 10 6 m/s, and t ⊥ = 0.39 eV equals 5.9261 in dimensionless units. The wave functions in the different regions are related as follows (15) where S = GM(1)G −1 represents a shift from x=0 to x=L and the matrices S 1 and S 2 are equal to the matrix N of Eq. (B3) with P = P 1 and P = P 2 , respectively.…”

“…In singlelayer graphene already a number of papers relate their work to the theoretical understanding of such periodic structures [8][9][10][11][12][13][14] . Much less experimental and theoretical work has been done on bilayer graphene 14,15 .…”

The electronic properties of bilayer graphene

“…The characteristics of bilayer graphene in the presence of short-ranged defects and long-ranged chargedimpurities have been calculated [54,163,164,166,[171][172][173][174][175] and it is predicted that the conductivity has an approximately linear dependence on density at typical experimental densities [172]. At interfaces and potential barriers, conservation of the pseudospin degree of freedom may influence electronic transmission [178,179], as in monolayer graphene [178,180], including transmission at monolayer-bilayer interfaces [181][182][183][184], through multiple electrostatic barriers [185], or magnetic barriers [186,187]. Inducing interlayer asymmetry and a band gap using an external gate [9,17], described in section III, may be used to tune transport properties [181,188].…”

Hysteresis modeling in graphene field effect transistors

“…¼ 0. Taking the total density of states to be the sum of the low and high energy approximations gives the following: [21][22][23] …”