Commensurability Oscillations in One-Dimensional Graphene Superlattices

Abstract

We report the experimental observation of commensurability oscillations (COs) in 1D graphene superlattices. The widely tunable periodic potential modulation in hBN-encapsulated graphene is generated via the interplay of nanopatterned few-layer graphene acting as a local bottom gate and a global Si back gate. The longitudinal magnetoresistance shows pronounced COs when the sample is tuned into the unipolar transport regime. We observe up to six CO minima, providing evidence for a long mean free path despite the potential modulation. Comparison to existing theories shows that small-angle scattering is dominant in hBN/graphene/hBN heterostructures. We observe robust COs persisting to temperatures exceeding T=150 K. At high temperatures, we find deviations from the predicted T dependence, which we ascribe to electron-electron scattering.

Lithographic band structure engineering of graphene

“…Patterning through vdW heterostructures not only provides protection of the graphene channel, but also the edges [19], which obviously become increasingly important at higher pattern densities. While these nanostructured heterostructures displayed clear commensurability oscillations [19,20,33,34], vdW heterostructures with stronger confinement (higher pattern density) are needed to reach the quantum regime, as apparent from Fig. 1.…”

Periodically Gated Bilayer Graphene as an Electronic Metamaterial

“…Due to its atomic-scale perfection and unique electronic structure, monolayer graphene (MLG) has emerged as an ideal 2D material to study charge transport [24]. Much attention has been paid to ballistic transport of electrons and suppression of backscattering by Klein tunneling in MLG, including the effect of p − n junctions, local and periodic gating, interaction with the substrate and presence of magnetic field [25][26][27][28][29][30][31][32][33][34][35][36][37]. The band structure of MLG at the six Fermi points in the Brillouin zone is characterized by Dirac cones, formally describing massless particles with constant v F independent of doping.…”

Magnetoconductivity in quasiperiodic graphene superlattices

“…It was shown theoretically that the Weiss oscillations in monolayer graphene are enhanced relative to those of ordinary 2D electron gas, and are more robust against temperature damping in the small magnetic field regime 10 . The experimental observation of commensurability oscillations in 1D-graphene superlattices (GSLs) was reported for the first time very recently 14 . The study of magnetoconductivity oscillations has been also carried out for other periodically modulated two-dimensional (2D) systems, such as bilayer graphene 15 and phosphorene 16 .…”

“…In particular, it was found that the diagonal conductivity displays a strong anisotropy reversal when the magnetic field go from weak to intermediate strength, whereas the Hall conductivity exhibit plateaux for weak fields, which tend to disappear for intermediate ones. In the second description, most of the work focusses on the oscillations with B of the magnetoconductivity, especially on the Shubnikov-de Haas (SdH) and Weiss or commensurability oscillations [10][11][12][13][14] . It was shown theoretically that the Weiss oscillations in monolayer graphene are enhanced relative to those of ordinary 2D electron gas, and are more robust against temperature damping in the small magnetic field regime 10 .…”