Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride (1202.2870v1)

Abstract: The Schr\"odinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of band gaps near points of the reciprocal lattice known as Brillouin zone boundaries. However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a band gap and instead new Dirac points appear in the electronic structure of the material. Graphene on hexagonal boron nitride (hBN) exhibits a rotation dependent Moir\'e pattern. In this letter, we show experimentally and theoretically that this Moir\'e pattern acts as a weak periodic potential and thereby leads to the emergence of a new set of Dirac points at an energy determined by its wavelength. The new massless Dirac fermions generated at these superlattice Dirac points are characterized by a significantly reduced Fermi velocity. The local density of states near these Dirac cones exhibits hexagonal modulations indicating an anisotropic Fermi velocity.

• The paper demonstrates that a Moiré-induced superlattice potential in graphene on hBN gives rise to additional Dirac points in its electronic band structure.
• The study employs STM and STS techniques to validate theoretical predictions by observing significant local density of states modulations and reduced Fermi velocities.
• It reveals energy asymmetry and anisotropic carrier propagation, offering insights for engineering tunable graphene-based electronic devices.

Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride

The paper entitled "Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride" examines the phenomenon of new Dirac points forming in the electronic structure of graphene when placed on a hexagonal boron nitride (hBN) substrate. This investigation is grounded in both theoretical predictions and experimental observations, providing significant insight into the behavior of massless Dirac fermions under the influence of a superlattice potential.

Overview

Graphene's electronic properties are typically described by the massless Dirac equation, which inhibits the traditional band gap opening seen in materials with periodic potentials. Instead, a periodic potential on graphene can result in the emergence of new Dirac points rather than band gap openings. This paper explores how graphene on hBN can exhibit such behavior due to the Moiré pattern that arises from the slight lattice mismatch and relative rotation between the graphene and the substrate.

Key Findings

1. Moiré-Induced Superlattice Potential: The paper identifies that a Moiré pattern, formed due to the rotational misalignment and lattice mismatch between graphene and hBN, acts as a weak periodic potential. This periodic potential leads to the emergence of new Dirac points at energies correlated with the superlattice's reciprocal lattice vectors.
2. Experimental Validation: Scanning tunneling microscopy (STM) and spectroscopy (STS) are used to confirm the theoretical predictions. Calculated and observed local density of states (LDOS) modulations provide evidence for the existence of these new Dirac points. Notably, the Fermi velocity is significantly reduced at these new Dirac points, with a decrease from approximately $1.1 \times 10^6$ m/s to values as low as $0.64 \times 10^6$ m/s.
3. Energy Asymmetry and Anisotropy: The research highlights an asymmetry in energy dependence, where the emergence of superlattice Dirac points shows different strengths in the conduction and valence bands. Additionally, the anisotropy of particle propagation, indicated by hexagonal modulations in the LDOS, reflects variations in the Fermi velocity.

Theoretical and Practical Implications

The formation of additional Dirac points opens avenues for controlling electron transport in graphene through engineered periodic potentials. The demonstrated spatial modulation of carrier velocities suggests potential applications in creating graphene-based devices with tunable electronic properties. This paper also deepens the theoretical understanding of massless Dirac fermions in periodic potentials and the unique role of chirality preventing band gap formation.

Speculation on Future Developments

Potential future research directions include exploring how these superlattice Dirac points can be harnessed or controlled in practical device applications. Further theoretical work could extend these observations to other 2D materials and heterostructures, potentially facilitating the development of next-generation nanoelectronic and optoelectronic devices with customized electronic properties.

This paper provides a detailed exploration of graphene's interaction with a periodic potential arising from an hBN substrate, offering valuable insights into both fundamental physics and practical device engineering.