Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions

Robustness of ballistic transport in antidot superlattices

“…The slow decay rate is therefore almost zero in comparison and the portion of trapped chaotic orbits is just a (small) correction to the portion of pinned orbits. The main contribution to the CPs stems from the change in the fast decay, which reflects the dynamics of the highly chaotic part of the phase space, a finding which is also reported by recent quantum simulations on graphene antidots by Power et al [14]. This is also in accordance with the magnetic focusing mechanism between successive collisions with an antidot and its neighbors that has been argued to increase the diffusivity of chaotic orbits in [29].…”

“…At even lower temperatures, when the coherence length of the electrons grows, quantization of periodic orbits manifests itself in additional resistivity oscillations [11][12][13]. CPs in graphene have also been reproduced recently in tight-binding simulations of small antidot systems [14]. In the following we will consider the incoherent ballistic transport, which can be analyzed in terms of quasi-classical dynamics [15].…”

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.…”

An order N numerical method to efficiently calculate the transport properties of large systems: An algorithm optimized for sparse linear solvers

“…Since in our Hall bar we consider leads along both the x and y directions, we avoid discontinuities in the magnetic field by smoothly varying the vector potential according to Ref. [44,29]. We calculate the system longitudinal and transverse resistances using the Landauer-Büttiker formula, Eq.…”

“…The corresponding Green's functions are recursively combined using the Dyson equation to obtain matrix elements of the full system Green's function that are relevant for transport calculations. The RGF method is robust, accurate, has a simple implementation, and has been widely used [23,24,25,26,27,28,29].…”