Electrostatic superlattices on scaled graphene lattices

Abstract

A scalable tight-binding model is applied for large-scale quantum transport calculations in clean graphene subject to electrostatic superlattice potentials, including two types of graphene superlattices: moiré patterns due to the stacking of graphene and hexagonal boron nitride (hBN) lattices, and gate-controllable superlattices using a spatially modulated gate capacitance. In the case of graphene/hBN moiré superlattices, consistency between our transport simulation and experiment is satisfactory at zero and low magnetic field, but breaks down at high magnetic field due to the adopted simple model Hamiltonian that does not comprise higher-order terms of effective vector potential and Dirac mass terms. In the case of gate-controllable superlattices, no higher-order terms are involved, and the simulations are expected to be numerically exact. Revisiting a recent experiment on graphene subject to a gated square superlattice with periodicity of 35 nm, our simulations show excellent agreement, revealing the emergence of multiple extra Dirac cones at stronger superlattice modulation. arXiv:1907.03288v1 [cond-mat.mes-hall]

Long-range ballistic transport of Brown-Zak fermions in graphene superlattices

“…A special case of encapsulated graphene heterostructures is graphene superlattices, where crystallographic axes of graphene and hBN are intentionally aligned. A small (1.8%) mismatch between graphene and hBN crystal lattices results in a periodic moiré potential acting on charge carriers in graphene and leading to the formation of electronic minibands [1][2][3][8][9][10][11][12][13][14][15][16][17] .…”

Moiré effects in graphene--hBN heterostructures

“…However, the effective continuum model cannot be used to simulate the transport for realistic experimental conditions, while results for the tight-binding models with empirical parameters must be carefully scrutinized to ascertain their reliability. For a large device transport simulation Chen et al [31] applied a scaled graphene lattice with a triangular periodic scalar moiré potential, and successfully reproduced the main features of the secondary Dirac point. However, as we show below, this sim-ple moiré potential does not lead to particle-hole asymmetry.…”

“…To emphasize the importance of full relaxation, we plot in Fig. 1(d) the band structure of graphene with a scalar moiré potential [31]: the band degeneracy at high symmetry points is lifted and one finds secondary Dirac points at ±0.225eV. However, in this case the DOS around the two secondary Dirac points are equal and obey particle-hole symmetry (Fig.…”

Biperiodic superlattices and transparent states in graphene

“…For instance, graphene nanoribbons with different edge orientations exhibit edge-dependent electronic and optical properties 11 – 14 . Here, it is also important to mention that there are recent breakthroughs in the fabrication of the so-called gated (electrostatic) graphene superlattices (GGSLs) 15 , 16 . One of the most attractive aspects of this type of superlattice is the tunability that can be achieved through electrostatic gating in contrast to moiré graphene superlattices.…”