Theory of the electronic and transport properties of graphene under a periodic electric or magnetic field

Abstract

We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar potential, owing to the linear dispersion and the chiral (pseudospin) nature of the electronic states, the group velocity of its carriers is renormalized highly anisotropically in such a manner that the velocity is invariant along the periodic direction but is reduced the most along the perpendicular direction. Under a periodic scalar potential, new massless Dirac fermions are generated at the supercell Brillouin zone boundaries. Also, we show that if the strength of the applied scalar potential is sufficiently strong, new zero-energy modes may be generated. With the periodic scalar potential satisfying some special conditions, the energy dispersion near the Dirac point becomes quasi one-dimensional. On the other hand, for graphene under a one-dimensional periodic vector potential (resulting in a periodic magnetic field perpendicular to the graphene plane), the group velocity is reduced isotropically and monotonically with the strength of the potential.

The electronic structure and intervalley coupling of artificial and genuine graphene superlattices

“…Figure 13 shows the electronic structure of such a superlattice, in which 𝑣 f , the group velocity along the periodic direction of the superlattice potential, vanishes while 𝑣 e remains finite. This result is exactly the opposite of what is expected in the previous studies adopting single-valley approximation [46,53]: finite 𝑣 f and vanishing 𝑣 e . In the sections below, we confine our discussion to Kronig-Penneytype graphene superlattices (Eq.…”

Localization behavior of Dirac particles in disordered graphene superlattices

“…If, however, the potential strength of a scalar GSL is greater than a certain critical value, new Dirac points emerge. 28 The resulting, strongly anisotropic dispersion relation then collimates the wave packet.…”

“…GSL refers to graphene under external periodic scalar [20][21][22][23][24][25][26][27][28] or vector potentials. [28][29][30][31][32][33][34][35][36] Because GSLs further tailor the band dispersion relation of graphene, they may be used to construct graphene-based quantum devices.…”

“…GSL refers to graphene under external periodic scalar [20][21][22][23][24][25][26][27][28] or vector potentials. [28][29][30][31][32][33][34][35][36] Because GSLs further tailor the band dispersion relation of graphene, they may be used to construct graphene-based quantum devices. Theoretical studies of GSLs and graphene under periodic corrugation [37][38][39] have been highly fruitful, with remarkable findings such as electron beam supercollimation 23 and the emergence of extra Dirac points.…”

Electron transmission through a periodically driven graphene magnetic barrier

“…On the other hand, the use of an inhomogeneous magnetic field introduces the concept of graphene magnetic barrier 6 that totally reflects an incoming electron (thereby suppressing the Klein effect) with energy less than a threshold value related to the total magnetic flux through the barrier 6,8 . Now, when such graphene magnetic barrier is made to be driven by an external oscillating scalar or vector field, many exotic properties could stem from the nano scale multiple field coupling [15][16][17][18][19][20][21][22][23] and is therefore quite worth studying particularly in the perspective of its high demand in designing electric field (A.C.) tunable graphene based digital nano-devices.…”