1205.0132 (Partha Goswami)

Change in Stacking Order and Lifshitz transition in Bi-layer Graphene    [PDF]

Partha Goswami

The AB-stacking for the bi-layer graphene (BLG) system, which is the elementary building block of 3D graphite with the A-carbon of the upper sheet lying on top of the B-carbon of the lower one, corresponds to a certain number of hopping parameters that also occur in the slightly shifted AA-stacked system where the A atoms of the two layers are over each other and the B atoms of the layers are displaced with respect to each other. Notwithstanding the two important facts, that (i) the choice of the basis A1, B2,A2, B1 in the valley K (for the valley K' the basis is B2, A1, B1,A2) for the former and A1, B1,A2, B2 for the latter ensures real energy eigenvalues of the corresponding Hamiltonians and (ii) the systems are invariant under the parity inversion and the time reversal, one obtains intrinsically different single-particle excitation spectrum in the two cases. To clarify, in the former case there is trigonal warping,that is, the Fermi energy density of states (on the kx - ky plane) splits, with the application of a tunable perpendicular electric field produced by the external gates deposited on the BLG surface, into four pockets comprising of the central part and three legs. This topological change is called the Lifshitz transition induced by the electric field and the skew interlayer hopping between A1 - B2 (and a concurrent velocity v3 in addition to the Fermi velocity vF). In the latter also the skew interlayer hopping between A1 - B2 (and A2 - B1)introduces an additional velocity, but causes a bias-tunable impact in the density of states comprising of different topology. Finally, we find that the activation energy necessary to destroy this AA-stacked phase is over one of magnitude less than that of the AB-stacked system to make it meta-stable at room temperature.

View original: http://arxiv.org/abs/1205.0132