Strain and electric field modulation of the electronic structure of bilayer graphene

Abstract

We study how the electronic structure of the bilayer graphene ͑BLG͒ is changed by electric field and strain from ab initio density-functional calculations using the linear muffin-tin orbital and the linear augmented plane wave methods. Both hexagonal and Bernal stacked structures are considered. We only consider interplanar strain where only the interlayer spacing is changed. The BLG is a zero-gap semiconductor like the isolated layer of graphene. We find that while strain alone does not produce a gap in the BLG, an electric field does so in the Bernal structure but not in the hexagonal structure. The topology of the bands leads to Dirac circles with linear dispersion in the case of the hexagonally stacked BLG due to the interpenetration of the Dirac cones, while for the Bernal stacking, the dispersion is quadratic. The size of the Dirac circle increases with the applied electric field, leading to an interesting way of controlling the Fermi surface. The external electric field is screened due to polarization charges between the layers, leading to a reduced size of the band gap and the Dirac circle. The screening is substantial in both cases and diverges for the Bernal structure for small fields as has been noted by earlier authors. As a biproduct of this work, we present the tight-binding parameters for the free-standing single layer graphene as obtained by fitting to the density-functional bands, both with and without the slope constraint for the Dirac cone and keeping the hopping integral up to four near neighbors.

Analytical expression for the RKKY interaction in doped graphene

“…is the tight-binding Hamiltonian, ij denotes summation over distinct pairs of nearest neighbors, t ≈ 2.56 eV, 17 σ is the spin index, and the interaction term between the localized spins S p TABLE I: Summary of the RKKY interaction in graphene for both the doped (kF = 0) and the undoped case (kF = 0), given as a product of the terms: J αβ = αC αDαF . The long-distance behavior is obtained by replacing αF with α 1 + cos xD…”

Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer

“…Compared with single-layer graphene, graphene bilayers, including AA stacked, AB stacked (Bernal) and twisted graphene bilayer, display even more complex electronic band structures and intriguing properties because of the interplay of quasiparticles between the Dirac cones on each layer [16][17][18][19][20][21][22][23][24][25][26][27][28] . Recently, several groups addressed the physics of the strained graphene bilayer (either AA-or AB-stacked graphene bilayer) theoretically and obtained many interesting results [29][30][31][32][33][34] . Despite many suggestive findings and potential applications, there have unfortunately been no experimental studies of the effect of strain on the electronic band structures of the graphene bilayer.…”

Intra- and inter-layer charge redistribution in biased bilayer graphene

“…39 In contrast, E k g always linearly increase from 0.00 to 0.93 eV as the electric field increases from 0 to 10 V/nm. This is because that E g and E and ∆, respectively.…”

“…37 Moreover, we have checked other first-principles, tight-binding and experimental studies and find that our results are consist with those values. [38][39][40] For example, in Ref. 38, they get E g around 100 meV when the electric field is 1 V/nm, while our calculated E g is ∼94 meV.…”