Post on 28-Dec-2015
Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines
by Michaël Barbier, Panagiotis Vasilopoulos, and François M. Peeters
Philosophical Transactions AVolume 368(1932):5499-5524
December 13, 2010
©2010 by The Royal Society
(a) A one-dimensional potential barrier of height Vb and width Wb. (b) A single unit of a potential well next to a potential barrier.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
(a) Contour plot of the transmission through a single barrier with μ = 0, Wb = L and ub = 10.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
(a) Conductance G versus strength P of a δ-function barrier in single-layer graphene; the conductance is independent of the energy.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
(a) Four different regions for a single unit of figure 1b with ub = 24, uw = 16, Wb = 0.4 and Ww = 0.6.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
The lowest conduction band of the spectrum of graphene near the K point (a,b) in the absence of SL potential and (c,d) in its presence with u = 4π.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
The spectrum of graphene near the K point (a) in the absence of an SL and (b) in its presence with u = 4.5π.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
The group velocity components vy and vx at the Dirac point j = 0 (shown, respectively, by the solid and the double dotted-dashed curve), and at the extra Dirac points j = 1,2,3 (shown,
respectively, by the dotted-dashed and the dashed curves) as a function ...
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
Conductivities (a) σxx and (b) σyy, versus Fermi energy for an SL on single-layer graphene with u = 4π and 6π shown by, respectively, the dashed and solid curves.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
(a) Schematics of Kronig–Penney SL on single-layer graphene.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
(a) Spectrum for a Kronig–Penney SL with P = 0.4π.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
Four different types of band alignments in bilayer graphene.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
(a) Contour plot of the transmission for the potential of figure 1b in bilayer graphene with Wb = Ww = 40 nm, Vb = −Vw = 100 meV and zero bias.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
Contour plot of the transmission through a single barrier in (a,b), for width Wb = 50 nm, and through double barriers in (c–f) of equal widths Wb = 20 nm that are separated by Ww = 20 nm.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
Two-terminal conductance of four equally spaced barriers versus energy for Wb = Ww = 10 nm and different SL types I–IV.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
(a) Bound states of the antisymmetric potential profile (type IV) with bias Δw = −Δb = 200 meV.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society
Lowest conduction and highest valence band of the spectrum for a square SL with period L = 20 nm and Wb = Ww = 10 nm.
Michaël Barbier et al. Phil. Trans. R. Soc. A 2010;368:5499-5524
©2010 by The Royal Society