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  • Open Access

Berry Curvature and Nonlocal Transport Characteristics of Antidot Graphene

Jie Pan1, Ting Zhang1,2, Haijing Zhang1,2, Bing Zhang1, Zhen Dong1, and Ping Sheng1,2,*

  • 1Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
  • 2Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

  • *sheng@ust.hk
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Phys. Rev. X 7, 031043 – Published 12 September, 2017

DOI: https://doi.org/10.1103/PhysRevX.7.031043

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.

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Popular Summary

Graphene is a transparent, flexible conductor with potential for many novel applications from solar cells to wearable electronics. It consists of a sheet, just one atom thick, of carbon atoms laid out in a honeycomb pattern. Some of the unique properties of graphene come from the fact that electrons traveling within the sheet behave as if they have no mass. By creating holes (known as antidots) in the graphene sheet, the electronic properties can be significantly changed. Electrons in such “antidot graphene” recover the mass that appears to be absent in pristine graphene. One key to understanding the behavior of electrons in graphene is a mathematical concept known as Berry curvature. Nonzero Berry curvature, for example, manifests a weak magnetic field that acts on the electrons. In pristine graphene, the Berry curvature is zero; it is widely assumed that the same is true for antidot graphene. We present a mathematical analysis, and experimental verification, that shows the antidot Berry curvature is actually nonzero, which can lead to intriguing electronic effects.

Specifically, we derive, for the first time, an effective Hamiltonian—a mathematical construct that describes the total energy—for antidot graphene in the form of a 4×4 matrix. Based on this Hamiltonian, we predict a nonzero Berry curvature that can give rise to interesting nonlocal transport effects that are absent in pristine graphene. We measure the electronic properties of three samples of antidot graphene, each with a different hole size, and find an excellent match to our theoretical predictions.

Our derived effective Hamiltonian can greatly facilitate the study of electronic properties of antidot graphene precisely at energies where it differs from pristine graphene.

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Phys. Rev. X 7, 031043– Published 12 September, 2017
  • Received 20 January 2017
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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