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We investigate the phase diagram of moir\'e double bilayer transition metal dichalcogenides with ABBA stacking as a function of twist angle and applied pressure. At hole filling $\nu = 2$ per moir\'e unit cell, the noninteracting system…
Topologically protected chiral states at a mass-inverted quantum dot in graphene are studied by analyzing both tight-binding and kernal polynomial method calculations. The mass-inverted quantum dot is introduced by considering a…
Bilayer graphene cavities where electrons are confined within finite graphene flakes provide an alluring platform not only for the future nanoelectronic devices owing to the tunable energy gap but also for investigating the quantum nature…
When monolayer graphene is crystallographically aligned to hexagonal boron nitride (BN), a moir\'e superlattice is formed, producing characteristic satellite Dirac peaks in the electronic band structure. Aligning a second BN layer to…
The realization of fractional Chern insulators in moir\'e materials has sparked the search for further novel phases of matter in this platform. In particular, recent works have demonstrated the possibility of realizing quantum anomalous…
Topological semimetals with massless Dirac and Weyl fermions represent the forefront of quantum materials research. In two dimensions (2D), a peculiar class of fermions that are massless in one direction and massive in the perpendicular…
Spin-1/2 particles such as the electron are described by the Dirac equation, which allows for two spin eigenvalues (up or down) and two types of energy eigenvalues (positive or negative, corresponding to the electron and the positron). A…
The properties of a two-dimensional electron are investigated in the presence of a circular step magnetic field profile. Both electrons with parabolic dispersion as well as Dirac electrons with linear dispersion are studied. We found that…
In topological quantum materials the conduction and valence bands are connected at points (Dirac/Weyl semimetals) or along lines (Line Node semimetals) in the momentum space. Numbers of studies demonstrated that several materials are indeed…
We study the effects of insulating oxides in their crystalline forms on the energy band structure of monolayer and bilayer graphene using a \textit{first principles} density functional theory based electronic structure method and a local…
Twisted bilayer graphene develop quasi-flat bands at specific "magic" interlayer rotation angles through an unconventional mechanism connected to carrier chirality. Quasi-flat bands are responsible for a wealth of exotic,…
We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits…
Graphene is known as a two-dimensional Dirac semimetal, in which electron states are described by the Dirac equation of relativistic quantum mechanics. Three-dimensional analogues of graphene are characterized by Dirac points or lines in…
This study is devoted to the profound implications of tilted Dirac cones on the quantum transport properties of two-dimensional (2D) Dirac materials. These materials, characterized by their linear conic energy dispersions in the vicinity of…
A novel two-dimensional carbon allotrope, rectangular graphyne (R-graphyne) with tetra-rings and acetylenic linkages, is proposed by first-principles calculations. Although the bulk R-graphyne exhibits metallic property, the nanoribbons of…
Two-dimensional (2D) carbon materials play an important role in nanomaterials. We propose a new carbon monolayer, named hexagonal-4,4,4-graphyne (H4,4,4-graphyne), which is a nanoporous structure composed of rectangular carbon rings and…
The material termed three-dimensional (3D) Dirac semimetal has attracted great interests recently, since it is an electronic analogue to two-dimensional graphene. Starting from this novel phase, various topologically distinct phases may be…
In many of three-dimensional metals with the inversion symmetry and a weak spin-orbit interaction, Dirac points of the electron energy spectrum form band-contact lines in the Brillouin zones of these crystals, and electron topological…
Dirac materials, starting with graphene, have drawn tremendous research interest in the past decade. Instead of focusing on the $p_z$ orbital as in graphene, we move a step further and study orbital-active Dirac materials, where the orbital…
The study of moir\'e engineering started with the advent of van der Waals heterostructures in which stacking two-dimensional layers with different lattice constants leads to a moir\'e pattern controlling their electronic properties. The…