Related papers: Theory for constructing effective models for elect…
Multilayer graphene systems with a rhombohedral stacking order harbor nearly flat bands in their single-particle spectrum. We propose ansatz states to describe the surface-localized states of flat band electrons. The absence of kinetic…
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…
Band structure determines the motion of electrons in a solid, giving rise to exotic phenomena when properly engineered. Drawing an analogy between electrons and photons, artificially designed optical lattices indicate the possibility of a…
We consider graphene bilayer in a constant magnetic field of arbitrary orientation (i.e. tilted with respect to the graphene plane). In the low energy approximation to tight binding model with Peierls substitution, we find the exact…
Starting from an atomistic approach we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. The descriptions are validated by…
Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half-filling and in the…
A numerical scheme is proposed to identify low energy configurations of a F\"oppl-von K\'arm\'an model for bilayer plates. The dependency of the corresponding elastic energy on the in-plane displacement $u$ and the out-of-plane deflection…
Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models taking into…
Theoretical progress in graphene physics has largely relied on the application of a simple nearest-neighbor tight-binding model capable of predicting many of the electronic properties of this material. However, important features that…
Magic-angle ($\theta=1.05^\circ$) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We…
We give a concise account on the derivation of hybrid quantum-classical models for stationary electron transport in graphene, in presence of sharp potential steps of barriers. A quantum region (an asymptotically thin strip around the…
Here we present a flexible strategy to realize robust nanomaterials exhibiting valence electronic structures whose fundamental physics is described by the SSH-Hamiltonian. These solid-state materials are realized using atomically precise…
We study the electronic properties of twisted bilayers graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function, which depends not only on the distance between two carbon atoms, but also on the…
A nano-stitching method is proposed and investigated to modify graphene bilayers. Based this method, four types of low energy carbon allotropes, "wormhole graphene" allotropoes, are obtained and their structures, stabilities and electronic…
We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\R^n$, $n \in \{1, 2, 3\}$. Standard homogenization theory provides, for the limit of a small periodicity length…
We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an…
This paper investigates the mathematical properties of independent-electron models for twisted bilayer graphene by examining the density-of-states of corresponding single-particle Hamiltonians using tools from semiclassical analysis. This…
A novel effective Hamiltonian in the subspace of singly occupied states is obtained by applying the Gutzwiller projection approach to a generalized Hubbard model with the interactions between two nearest- neighbor sites. This model provides…
We present a non-perturbative framework for deriving effective Hamiltonians that describe low-energy excitations in quantum many-body systems. The method combines block diagonalization based on the Cederbaum--Schirmer--Meyer transformation…
The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of…