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The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small `magic' twist angles has been linked to the existence of nearly-flat bands, which make TBG a fresh playground to…
The recent experimental observations of designer Dirac Fermions and topological phases in molecular graphene are addressed theoretically. Using scattering theory we calculate the electronic structure of finite lattices of scattering centers…
Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton…
The emergent concept of magnetic charge quasi-particle provides a new realm to study the evolution of magnetic properties in two-dimensional artificially frustrated magnets. We report on the exploration of magnetic phases due to various…
Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix…
We have performed large-scale density-matrix renormalization group studies of the lightly doped Hubbard model on the honeycomb lattice on long three and four-leg cylinders. We find that the ground state of the system upon lightly doping is…
The experimental study of edge states in atomically-thin layered materials remains a challenge due to the difficult control of the geometry of the sample terminations, the stability of dangling bonds and the need to measure local…
The propagation of linear and nonlinear edge modes in bounded photonic honeycomb lattices formed by an array of rapidly varying helical waveguides is studied. These edge modes are found to exhibit strong transmission (reflection) around…
Elastic wave dispersion is studied in an octet truss lattice and compared with a designed rib lattice known to exhibit strong Cosserat elastic effects. Dispersion entails variation of wave speed with frequency. The phenomenon is…
We study numerically the nature of the diffusion process on a honeycomb and a quasi-lattice, where a point particle, moving along the bonds of the lattice, scatters from randomly placed scatterers on the lattice sites according to strictly…
This article presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders which are arranged in a triangular lattice. First, we present transmission…
In this article we develop an effective medium model to characterize the electron wave propagation in graphene based nanostructures with an electrostatic and magnetic vector potentials imposed on their surface. We use a numerical algorithm…
Engineering the electromagnetic environment of a quantum emitter gives rise to a plethora of exotic light-matter interactions. In particular, photonic lattices can seed long-lived atom-photon bound states inside photonic band gaps. Here we…
We study the rare-earth magnets on a honeycomb lattice, and are particularly interested in the experimental consequences of the highly anisotropic spin interaction due to the spin-orbit entanglement. We perform a high-temperature series…
Pair-density-wave (PDW) is a long-sought exotic state with oscillating superconducting order without external magnetic field. So far it has been rare in establishing a 2D microscopic model with PDW long-range order in its ground state. Here…
We present an analytical method of studying "extended" electronic eigenstates of a diamond hierarchical lattice, which may be taken as the simplest of the hierarchical models recently proposed for stretched polymers. We use intuitive…
We use a functional renormalization group approach to study the instabilities due to electron-electron interactions in a bilayer honeycomb lattice model with AA stacking, as it might be relevant for layered graphene with this structure.…
The effect of weak potential and bond disorder on the density of states of graphene is studied. By comparing the self-consistent non-crossing approximation on the honeycomb lattice with perturbation theory on the Dirac fermions, we…
Strong Coulomb repulsion is predicted to open a many-body charge gap at the Dirac point of graphene, transforming the semimetal into a Mott insulator. However, this correlated insulating phase has remained inaccessible in pristine graphene,…
We investigate higher-order plasmons in graphene nanoribbons, and present how electronic edge states and wavefunction fine structure influence the graphene plasmons. Based on nearest-neighbor tight-binding calculations, we find that a…