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Two-dimensional atomic crystals can radically change their properties in response to external influences such as substrate orientation or strain, resulting in essentially new materials in terms of the electronic structure. A striking…
The relative orientation (twist) of successive layers of stacked two-dimensional (2D) materials creates variations in the interlayer atomic registry. The variations often form a super lattice, called a moir\'e pattern, which can alter…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
Moir\'e superlattices in stacked 2D crystals are powerful platforms for engineering correlated and topological quantum phases, with twisted graphene and transition metal dichalcogenides (TMDs) as prominent examples. Their angle-sensitive…
Two-dimensional multi-layer materials with an induced moir\'e pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these…
We study the electronic band structure and the topological property of the twisted double bilayer graphene, or a pair of AB-stacked bilayer graphenes rotationally stacked on top of each other. We consider two different arrangements, AB-AB…
We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous…
A computationally efficient workflow for obtaining the low-energy symmetric tight-binding Hamiltonians for twisted multilayer systems is presented in this work. We apply this scheme to twisted bilayer graphene at the first magic angle. As…
In this review, we present recent works on materials whose common point is the presence of electronic bands of very low dispersion, called "flat bands", which are due to specific atomic order effects without electron interactions. These…
A general method is presented to unfold band structures of first-principles super-cell calculations with proper spectral weight, allowing easier visualization of the electronic structure and the degree of broken translational symmetry. The…
The eigenstates of an electron in the chiral two-dimensional electron gas (C2DEG) formed in an AB-stacked bilayer or an ABC-stacked trilayer graphene is a spinor with $4$ or $6$ components respectively. These components give the amplitude…
Moir\'e superlattices formed at the interface between stacked two-dimensional atomic crystals offer limitless opportunities to design materials with widely tunable properties and engineer intriguing quantum phases of matter. However,…
According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moir\'e patterns produced by small misalignments between its individual layer honeycomb lattices. We have…
In this paper, the 2D band structure of a mixed-mode metamaterial resonator array for in-plane waves is investigated. The band structure in the interior and on the boundary of the irreducible Brillouin zone as well as 1D dispersion diagrams…
A twist between two systems offers the possibility to drastically change the underlying physical properties. To that end, we study the bandstructure of twisted moir\'e potentials in detail. At sets of commensurate twisting angles, the low…
The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone. Since the discovery of topological insulators, much attention has been paid to the…
Moir\'e-pattern based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly…
Twisted double bilayer graphene has recently emerged as an interesting moir\'e material that exhibits strong correlation phenomena that are tunable by an applied electric field. Here we study the atomic and electronic properties of three…
A moire pattern is formed when two copies of a periodic pattern are overlaid with a relative twist. We address the electronic structure of a twisted two-layer graphene system, showing that in its continuum Dirac model the moire pattern…
The electronic structure of materials is fundamentally governed by their crystal symmetry. While most research on two-dimensional materials has focused on hexagonal lattices, such as graphene, hexagonal boron nitride, and transition metal…