Related papers: Emergent quasiparticles in Euclidean tilings
We investigate the physics of quasicrystalline models in the presence of a uniform magnetic field, focusing on the presence and construction of topological states. This is done by using the Hofstadter model but with the sites and couplings…
Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two- and few-layer configurations of graphene have been realized and…
Spinless systems exhibit unique topological characteristics compared to spinful ones, stemming from their distinct algebra. Without chiral interactions typically linked to spin, an intriguing yet unexplored interplay between topological and…
We show that graphene, in its simplest form and settings, is a practical table-top realization of the analog of exotic quantum gravity scenarios, which are speculated to lead to certain generalized Heisenberg algebras. In particular, we…
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
The phenomenon of spin-dependent quantum scattering in two-dimensional (2D) pseudospin-1/2 Dirac materials leading to a relativistic quantum chimera was recently uncovered. We investigate spin-dependent Dirac electron optics in 2D…
Tiling models can reveal unexpected ways in which local constraints give rise to exotic long-range spatial structure. The recently discovered Hat monotile (and its mirror image) has been shown to be aperiodic~[Smith et al., arXiv:2303.10798…
Topological quantum materials have emerged as a frontier in condensed matter physics as well as in materials science, with intriguing electronic states that are robust to perturbations. Among the diverse structural motifs, kagome, chiral,…
Flat bands and Dirac cones in materials are at the source of the exotic electronic and topological properties. The Lieb lattice is expected to host these electronic structures, arising from quantum destructive interference. Nevertheless,…
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…
The discovery of correlated phases in twisted moir\'e superlattices accelerated the search for low-dimensional materials with exotic properties. A promising approach uses engineered substrates to strain the material. However, designing…
Strongly interacting electrons in layered materials give rise to a plethora of emergent phenomena, such as unconventional superconductivity. heavy fermions, and spin textures with non-trivial topology. Similar effects can also be observed…
We present a real-space view of one-dimensional (1D) to three-dimensional (3D) topological materials with 13 representative samples selected from each class, including 1D trans-polyacetylene, two-dimensional (2D) graphene, and 3D…
In this work we analyze a class of Moir\'e models consisting of an active honeycomb monolayer such as graphene or a hexagonal transition-metal dichalcogenide (TMD) on top of a substrate, in which the K and K' valleys of the active layer are…
We present a thorough tight-binding analysis of the band structure of a wide variety of lattices belonging to the class of honeycomb and Kagome systems including several mixed forms combining both lattices. The band structure of these…
Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative…
Equilateral triangle-shaped graphene nanoislands with a lateral dimension of $n$ benzene rings are known as $[n]$triangulenes. Individual $[n]$triangulenes are open-shell molecules, with single-particle electronic spectra that host $n-1$…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
Initiated by the discovery of topological insulators, topologically non-trivial materials have attracted immense interest in the physics community in the past decade. One of the latest additions to the field, the material class of…
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen…