Related papers: Peierls Instability in Hexagonal Lattices
A high-frequency asymptotic scheme is generated that captures the motion of waves within discrete hexagonal and honeycomb lattices by creating continuum homogenised equations. The accuracy of these effective medium equations in describing…
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal's bonds. In particular, we show the…
The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated…
The possibility of intrinsic superconductivity in alkali-coated graphene monolayers has been recently suggested theoretically. Here, we derive the possible pairing symmetries of a carbon honeycomb lattice and discuss their phase diagram. We…
Scanning tunneling microscopy experiments have revealed an spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between…
We study the Lowest Landau Level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we study well-posedness and establish the existence of…
Periodicity is one of the most fundamental structural characteristics of systems occurring in nature. The properties of these systems depend strongly on the symmetry of the underlying periodic structure. In solid state materials - for…
We prove the existence of periodic tessellations of $\mathbb{R}^N$ minimizing a general nonlocal perimeter functional, defined as the interaction between a set and its complement through a nonnegative kernel, which we assume to be either…
In this work we revisit the existence, stability and dynamics of unstable traveling solitary waves in the context of lattice dynamical systems. We consider a nonlinear lattice of an $\alpha$-Fermi-Pasta-Ulam type with the additional feature…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
Recent experiments have revealed the possibility of precise electron beam manipulation of silicon impurities in graphene. Motivated by these findings and studies on metal surface quantum corrals, the question arises what kind of embedded Si…
The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively.…
We study in a semiclassical regime a two-dimensional magnetic periodic Schr\"odinger operator. We first review some results for the square (Harper), triangular and hexagonal (case of the graphene) lattices. Then we study the case considered…
We analytically evaluate the entanglement spectra of the superconductivity states in graphene, primarily focusing on the s-wave and chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity states. We demonstrate that the topology of the…
We study the transport properties of a tight-binding model of non-interacting fermions with random hopping on the honeycomb lattice. At the particle-hole symmetric chemical potential, the absence of diagonal disorder (random onsite…
Localization of electronic wave functions in modern two-dimensional (2D) materials such as graphene can impact drastically their transport and magnetic properties. The recent localization landscape (LL) theory has brought many tools and…
We study the plaquette valence bond solid phase in a XXZ type spin-1/2 model in the kagome lattice. The low energy theory for this phase is a U(1) lattice gauge theory on the honeycomb lattice. We find that there is an emergent 1-form U(1)…
Moir\'e superlattices have become an emergent solid-state platform for simulating quantum lattice models. However, in single moir\'e device, Hamiltonians parameters like lattice constant, hopping and interaction terms can hardly be…
Fermions moving in a two-dimensional honeycomb lattice (graphene) have, at low energies, chiral symmetry. Generalizing this construction to four dimensions potentially provides fermions with chiral symmetry and only the minimal fermion…
We present a method which provides a unified framework for most stability theorems that have been proved in graph and hypergraph theory. Our main result reduces stability for a large class of hypergraph problems to the simpler question of…