Berry Curvature and Nonlocal Transport Characteristics of Antidot Graphene

Abstract

Antidot graphene denotes a monolayer of graphene structured by a periodic array of holes. Its energy dispersion is known to display a gap at the Dirac point. However, since the degeneracy between the A and B sites is preserved, antidot graphene cannot be described by the 2D massive Dirac equation, which is suitable for systems with an inherent A=B asymmetry. From inversion and time-reversal-symmetry considerations, antidot graphene should therefore have zero Berry curvature. In this work, we derive the effective Hamiltonian of antidot graphene from its tight-binding wave functions. The resulting Hamiltonian is a 4 × 4 matrix with a nonzero intervalley scattering term, which is responsible for the gap at the Dirac point. Furthermore, nonzero Berry curvature is obtained from the effective Hamiltonian, owing to the double degeneracy of the eigenfunctions. The topological manifestation is shown to be robust against randomness perturbations. Since the Berry curvature is expected to induce a transverse conductance, we have experimentally verified this feature through nonlocal transport measurements, by fabricating three antidot graphene samples with a triangular array of holes, a fixed periodicity of 150 nm, and hole diameters of 100, 80, and 60 nm. All three samples display topological nonlocal conductance, with excellent agreement with the theory predictions.

Absence of a giant spin Hall effect in plasma-hydrogenated graphene

“…Large nonlocal resistances in the H-bar structure were also observed in graphene decorated with heavy atoms 30 , hBN/graphene heterostructures 31 and in graphene structured with an antidot array 32 . These were attributed to the occurrence of a valley-Hall effect 30,31 , a nonzero Berry curvature, due to the presence of a band gap 32 and transport through evanescent waves 33,34 . However none of these effects can sufficiently explain the observed behavior 12 .…”

Lithographic band structure engineering of graphene

“…Curabitur consectetuer. EBL BCP [25] EBL [26] NIL [27] NSL [28] EBL [29] EBL [19] EBL [20] EBL [31] EBL [30] This work Minimum feature size, w (nm)…”

“…This has led to more than a decade of research into ways of archiving dense nanostructuring of graphene without compromising the transport properties, but so far disorder at edges increasingly dominate transport measurements as pattern densities increase [22][23][24]. Figure 1 summarise a subset of key experimental works [19,20,[25][26][27][28][29][30][31] featuring twodimensional (2D) nanostructured graphene as well as microscale Hall bars for reference [31], with the reported charge carrier mobility, µ, plotted against the minimum feature size of the system. Here the mobility is calculated from the Drude model of conductivity, σ = neµ, where e is the electron charge.…”

“…Here the mobility is calculated from the Drude model of conductivity, σ = neµ, where e is the electron charge. In early devices fabricated from non-encapsulated graphene, extremely small and dense features have indeed been achieved with block copolymer (BCP) [25] masks, electron-beam lithography (EBL) [26,29,30], nanosphere lithography (NSL) [28], and nano-imprint lithography (NIL) [27]. However, the resulting charge carrier mobilities and associated mean free paths in these works were too low to support quantum transport of the charge carriers beyond semiclassical transport.…”

Floquet Graphene Antidot Lattices

“…We conclude with some ideas for future research. One immediate question that we have not answered is whether the Floquet graphene antidot lattice features non-trivial topology [71][72][73]. More precisely, this system combines two gapping mechanisms, the time-reversalsymmetry-breaking circularly polarized light and the chiral-symmetry-breaking antidot lattice, both of which retain the particle-hole (charge-conjugation) symmetry.…”