Related papers: Emergent quasiparticles in Euclidean tilings
The interplay of hopping parameters that can give rise to flat bands in consequence of quantum interference in electronic, photonic, and other interesting materials has become an extensively studied topic. Most of the recognized structures…
The study of graphene, since its discovery around 2004, is possibly the largest and fastest growing field of research in material science, because of its exotic mechanical, thermal, electronic, optical and chemical properties. The studies…
Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied properties. They range from metals and superconductors to strongly spin-orbit-coupled semiconductors and charge-density-wave systems, with their single-layer…
Quantum materials that host a flat band, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern…
The physics of graphene is acting as a bridge between quantum field theory and condensed matter physics due to the special quality of the graphene quasiparticles behaving as massless two dimensional Dirac fermions. Moreover, the particular…
We predict a new family of robust two-dimensional (2D) topological insulators in van der Waals heterostructures comprising graphene and chalcogenides BiTeX (X=Cl, Br and I). The layered structures of both constituent materials produce a…
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…
Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat.…
We describe the structure of quasiflats in two-dimensio\-nal Artin groups. We rely on the notion of metric systolicity developed in our previous work. Using this weak form of non-positive curvature and analyzing in details the combinatorics…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
The beginning of high interest in two-dimensional (2D) crystals is marked by the synthesis of graphene, which constitutes exemplary monolayer material. This is due to the multiple extraordinary properties of graphene, particularly in the…
We study the Dirac quasiparticles in $d$-dimensional lattice systems of electrons in the presence of domain walls ($d=1$), vortices ($d=2$), or hedgehogs ($d=3$) of superconducting and/or insulating, order parameters, which appear as mass…
After the discovery of Dirac fermions in graphene, it has become a natural question to ask whether it is possible to realize Dirac fermions in other two-dimensional (2D) materials as well. In this work, we report the discovery of multiple…
The discovery of graphene has spurred vigorous investigation of 2D materials, revealing a wide range of extraordinary properties and functionalities. 2D heterostructural materials have recently been fabricated by assembling isolated planes…
Unexpected hypersurfaces arise when vanishing in points of a set $Z$ and higher-order vanishing along a general linear subspace fails to impose the expected number of independent conditions on forms of a fixed degree. The phenomenon was…
The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of…
We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic…
Self-similar quasicrystals (like the famous Penrose and Ammann-Beenker tilings) are exceptional geometric structures in which long-range order, quasiperiodicity, non-crystallographic orientational symmetry, and discrete scale invariance are…
This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann-Beenker tilings 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…