Ballistic transport experiment detects Fermi surface anisotropy of graphene

Abstract

Monolayer graphene and bilayer graphene have strikingly different properties. One such difference is the shape of the Fermi surface. Although anisotropic band structures can be detected in optical measurements, they have so far been difficult to detect in transport experiments on twodimensional materials. Here we describe a ballistic transport experiment using high-quality graphene that revealed Fermi surface anisotropy in the magnetoresistance. The shape of the Fermi surface is closely related with the cyclotron orbit in real space. Electron trajectories in samples with triangular lattices of holes depend on the anisotropy of the Fermi surface. We found that this results in the magnetoresistance which are dependent on crystallographic orientation of the antidot lattice, which indicates the anisotropic Fermi surface of bilayer graphene which is a trigonally-warped circle in shape. While in monolayer, shape of magnetoresistance was approximately independent of the orientation of antidot lattice, which indicates that the Fermi surface is a circle in shape. The ballistic transport experiment is a new method of detecting anisotropic electronic band structures in two-dimensional electron systems.

Multiband Ballistic Transport and Anisotropic Commensurability Magnetoresistance in Antidot Lattices of AB-stacked Trilayer Graphene

“…Low-field magnetoresistance traces of the bilayer graphene showed commensurability magnetoresistance indicating anisotropy depending on the relative angle between crystallographic axes and the antidot lattice, while, in monolayer graphene, no such effects were observed. These results indicate that Fermi surface is significantly warped in bilayer graphene, but approximately isotropic in monolayer graphene [41].…”

“…1(a)). Recently, such anisotropy in the band structure was observed by making ballistic transport measurements on graphene antidot samples [41]. Low-field magnetoresistance traces of the bilayer graphene showed commensurability magnetoresistance indicating anisotropy depending on the relative angle between crystallographic axes and the antidot lattice, while, in monolayer graphene, no such effects were observed.…”

Evidence of Lifshitz transition in thermoelectric power of ultrahigh mobility bilayer graphene

“…Previous reports on the observation of LT in the transport properties of BLG have been scarce because of its relatively low energy scale (∼ 1 meV), rendering these effects negligible at higher temperatures (> 10 K) [13][14][15]. Furthermore, the density required to shift the chemical potential to E L is very small (n L ∼ 5 × 10 10 cm −2 ).…”

Robustness of ballistic transport in antidot superlattices

“…They were first fabricated by ion-beam implantation [1] or by etching periodic arrays of holes with periods of a few hundred nanometers into the 2DEG of AlGaAs/GaAs heterostructures [2] and by modulation of the 2DEG by nanostructured lateral metal gates [3]. Since then antidots were realized in many different materials [4][5][6], and recently also in graphene [7][8][9] and topological insulators [10]. They are a prime example of devices showing features of ballistic transport: when the typical length scales of a device become smaller than the mean free path of the electrons, transport is no longer dominated by diffusion due to impurity, phonon or electron-electron scattering.…”