Integer quantum Hall effect in Kekulé-patterned graphene

Abstract

Y-shaped Kekulé bond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed. In this paper, the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field. Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula. It is found that the Y-shaped Kekulé bond texture lifts the valley degeneracy of all Landau levels except that of the zero mode, leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity. Consequently, the Hall conductivity is quantized as ± ne 2/h for n = 2, 4, 6, 8, 10, …, excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones. These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulé bond texture amplitude.

Valley transport in Kekulé structures of graphene

“…This can lead to the disappearance of the valley degeneracy of Landau levels related to the magnetic field. The coupling of valley and momentum [40] can lead to the emergence of many novel physical properties in the Kekulé structures, such as valley precession, [30] the enhanced Andreev reflection, [47] and the valley supercurrent, [31] integer quantum Hall effect, [58] and supercurrent rectification effect. [59] In this work, we mainly review some recent progresses of valley transport in two-dimensional Kekulé graphene superlattices.…”

Crossed Andreev reflection in normal-superconductor-normal junction based on Kekulé-Y patterned graphene

“…The lattice scheme is shown in figure 1(a), the strong and weak bonds arrange to Y-shape periodically, and the unit cell is * Author to whom any correspondence should be addressed. enlarged to triple of the pristine graphene, correspondingly, the Brillouin zone folds into one-third of pristine graphene in the momentum space and the K and K ′ valley fold together at the Γ point [13][14][15][16]. Soon afterwards, Gamayun et al [17] have showed that the Kek-Y graphene breaks the inversion symmetry and produces two species of massless Dirac fermions with valley-pseudospin locked, which has changed the energy band to generate a new single Dirac cone phase, paving a new path for the control of the valley degree of freedom.…”

Kekulé Induced Valley Birefringence and Skew Scattering in Graphene

“…Kekulé-Y patterned graphene, breaks a valley degeneracy through valley-momentum locking which produces a low energy spectrum with two nested Dirac cones with different Fermi velocities 36 . The energy-momentum dispersion modification caused by Kekulé-Y patterning leads to drastic modifications in the magnetic and optical response of graphene [43][44][45][46][47][48] , and crucially aids the control of the valley degree of freedom in the electronic transport [49][50][51][52][53][54][55][56] . In this paper we study the scattering of Dirac fermions from circularly Kekulé-Y-patterned regions in the semiclassical limit and we explore the effects of this interaction on electron optics and the appearance of valley birefringence.…”