相关论文: Topological effects, index theorem and supersymmet…
Graphene is a monoatomic layer of graphite with Carbon atoms arranged in a two dimensional honeycomb lattice configuration. It has been known for more than sixty years that the electronic structure of graphene can be modelled by…
Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is…
We investigate the emergence of geometric phases in graphene-based nanostructures through the lens of the Atiyah-Singer index theorem. By modeling low-energy quasiparticles in curved graphene geometries as Dirac fermions, we demonstrate…
We present a unified description of the quantum Hall effect in graphene on the basis of the 8-component Dirac Hamiltonian and the supersymmetric (SUSY) quantum mechanics. It is remarkable that the zero-energy state emerges because the…
We consider a graphene sheet folded in an arbitrary geometry, compact or with nanotube-like open boundaries. In the continuous limit, the Hamiltonian takes the form of the Dirac operator, which provides a good description of the low energy…
The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically…
Skyrmions are topologically protected spin textures, characterized by a topological winding number N , that occur spontaneously in some magnetic materials. Recent experiments have demonstrated the capability to grow graphene on top Fe/Ir, a…
The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a…
Armchair and zigzag edge terminations in planar hexagonal and trigonal graphene nanorings are shown to underlie one-dimensional topological states associated with distinctive energy gaps and patterns (e.g., linear dispersion of the energy…
We demonstrate theoretically that the topology of energy bands and Fermi surface in bilayer graphene undergoes a very sensitive transition when extremely tiny lateral interlayer shift occurs in arbitrary directions. The phenomenon…
Anomalous quantum Hall effects in single-layer and bilayer graphene are related with nontrivial topological properties of electron states (Berry phases $\pi$ and 2$\pi$, respectively). It was known that the Atiyah-Singer index theorem…
Dirac fermions have a central role in high energy physics but it is well known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the…
A topological concern is addressed in view of the extensively and intensively studied topological phases of condensed matter. In this realm, the phases with topological order cannot be characterized by symmetry alone. Moreover, the relevant…
We derive the single-particle eigenenergies and eigenfunctions for massless Dirac fermions confined to the surface of a sphere in the presence of a magnetic monopole, i.e., we solve the Landau level problem for electrons in graphene on the…
We discuss topological aspects of electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i) Appearance of the pairn of massless Dirac…
This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…
Unlike regular electron spin, the pseudospin degeneracy of Fermi points in graphene does not couple directly to magnetic field. Therefore, graphene provides a natural vehicle to observe the integral and fractional quantum Hall physics in an…
The quantum Hall effect is studied in a spherical geometry using the Dirac operator for non-interacting fermions in a background magnetic field, which is supplied by a Wu-Yang magnetic monopole at the centre of the sphere. Wave functions…
We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moir\'e pattern. The two low-energy flat bands from each monolayer…
Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy…