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Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the two-dimensional material, enhance electron correlations, and give rise to novel condensed-matter phases such as superconductors, Mott insulators, Wigner crystals and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different twisted graphene layers. In this work, we propose a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates. We take graphene/SiC heterostructure as a prototypical example and demonstrate experimentally that the substrate modulation leads to Dirac fermion cloning and consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Our theoretical modeling captures the cloning mechanism of Dirac states and indicates that Moiré flat bands can emerge at certain magic lattice constants of the substrate, specifically when the period of modulation becomes nearly commensurate with the (√3×√3)𝑅30∘ supercell of graphene. The results show that epitaxial single monolayer graphene on suitable substrates is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons.
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Graphene quantum dots, graphene non-circular n{p{n-junctions: Quasi-relativistic pseudopotential approach
We have constructed a continuous model of graphene quantum dot (GQD) as the hydrodynamic limit of the discrete model of n{p{n graphene junction in the form of a rhombic supercell on the graphene plane. The topological type of the proposed GQD-model corresponds bijectively to the GQD-edge topology and can be similar to a sphere or torus. The Hamiltonian of the discrete model of n{p{n graphene junction is chosen to be the Dirac{Weyl type with one Dirac point and 6 pairs of Weyl nodes{antinodes in the folding-zone approximation. The bending-band structure of the proposed GQD-model is ensured by a GQD pseudopotential barrier, which is given by a set of well pseudopotentials for individual carbon atoms of the GQD. The main speci c feature of the structure of electron levels of both spherical and toroidal GQDs is the self-similar energy bands located subsequently one behind another on the energy scale. The atom-like distribution of the electron density is realized from the geometric viewpoint only for toroidal GQDs due to the absence of the curvature for a torus. Though the quasi-zero-energy band exists for spherical and toroidal GQDs, no electron density is present on this band for toroidal GQDs. This causes the formation of a pseudogap between the hole and electron bands, because of the absence of the electron density at the quantum dot center like the case of an ordinary atom. However, the confinement of the electron density is observed for both spherical and toroidal GQDs.
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- Award ID(s):
- 1829245
- PAR ID:
- 10099804
- Date Published:
- Journal Name:
- NATO science for peace and security series. A, Chemistry and biology
- ISSN:
- 1874-6489
- Page Range / eLocation ID:
- 47-58
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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