Anisotropic transport in ballistic bilayer graphene cavities

TL;DR

Bilayer graphene exhibits trigonal warping of its low-energy Fermi surface, yielding anisotropic group velocities and direction-dependent transport. The authors combine tight-binding simulations with semiclassical equations of motion to link triangular, stable orbits in a circular BLG cavity to enhanced quantum-state localization and to predict robust, anisotropic transport in gate-defined BLG cavities with six leads. They reveal Lifshitz-transition signatures in transport and demonstrate that a six-lead geometry provides orientation-independent detection of anisotropy while enabling gate-tunable, directionally selective transmission. This work establishes a practical framework for probing anisotropic quantum dynamics in 2D materials using gate-defined electronic cavities and highlights the potential of BLG for controlled, direction-dependent transport in nanoscale devices.

Abstract

Closing the gap between ray tracing simulations and experimentally observed electron jetting in bilayer graphene (BLG), we study all-electronic, gate-defined BLG cavities using tight-binding simulations and semiclassical equations of motion. Such cavities offer a rich playground to investigate anisotropic electron transport due to the trigonally warped Fermi surfaces. In this work, we achieve two things: First, we verify the existence of triangular modes (as predicted by classical ray tracing calculations) in the quantum solutions of closed circular BLG cavities. Then, we explore signatures of said triangular modes in transport through open BLG cavities connected to leads. We show that the triangular symmetry translates into anisotropic transport and present an optimal setup for experimental detection of the triangular modes as well as for controlled modulation of transport in preferred directions.

Figures (18)

• Figure 1: (a) Schematics of an electronic BLG cavity defined by a smooth, electrostatic confinement with local energy band offset $\mu_c$. (b) BLG band structure ($K^+$ valley) and Fermi contours for Fermi energy $E_F = 80$ meV (both valleys $K^\pm$). The flat sides of the triangular warped Fermi lines give rise to six dominant group velocities. (c) Conductance through the cavity for all lead combinations. Conductance between leads connectable via the dominant group velocities (red and blue arrows in (a) is strongly enhanced compared to other lead combinations.
• Figure 2: Probability density of selected eigenstates ($E_n = 100\pm 0.1$ meV) of a closed BLG cavity with $U = 40$ meV and $\mu_c = 100$ meV. We show examples for (a)-(b) regular quantum states, (c) a "bouncing ball" scar, and (d) an "ergodic state". Large plots show the LDOS when both valleys are included due to fermion doubling, the small insets show related probability densities when only one valley contributes.
• Figure 3: (a) Real space semiclassical trajectory of a stable periodic orbit (blue) in a circular BLG cavity with smooth boundaries. Propagation through the cavity is numbered $i)-vi)$. (b) Fermi lines ($K^-$ valley) and k-space trajectory of the stable periodic orbit in momentum space. The scattering events at the boundary are given by the (blue) lines connecting the stars, marking momenta propagation ($i)-vi)$). Straight lines in k-space imply the conservation of the momentum parallel to the local scattering area. (c) Trajectory that starts as a whispering gallery-like mode (blue) and transitions to a standard trajectory (orange). Propagation ($i)-ix)$) corresponds to the star marked points in k-space (d). For the k-space trajectory connecting $i)-v)$ the combination of the circular cavity and the locally rotational invariant k-space region (gray circle), results in a local conservation of angular momentum. Scattering events occurring over larger areas within the smooth boundary lead to curved k-space trajectories.
• Figure 4: Conductance through the BLG cavity for (a) neighboring lead pairs, (b) triangular connected lead pairs and (c) opposing lead pairs depending on the displacement field $U$ and the band offset $\mu_c$. The orange dashed line marks the Fermi wavelength $\lambda_F = 115$ nm. The white dashed line denotes the Lifshitz transition.
• Figure 5: Thermal broadened - 2 K - line cuts at (a) $U=10$ meV and (c) $U=150$ meV through the conductance map of Fig.\ref{['fig:ConductanceHeatmap']}. (b),(d) mode-averaged current densities for selected band offsets $\mu_c$. At the top of the outer right column the 2D-projections of the band-structure near the $K^+$ valley for the two different displacements fields, $U$, are displayed. The horizontal lines correspond to the dashed lines in the conductance plots. Below the band-structures we show the Fermi-lines and corresponding group velocities.