Related papers: Measuring topological invariants in polaritonic gr…

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems…

We present a general scheme for measuring the bulk properties of non-interacting tight-binding models realized in arrays of coupled photonic cavities. Specifically, we propose to implement a single unit cell of the targeted model with…

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…

The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength.…

Topological insulators represent a new state of matter where the topological nature of the bulk bands dictates the existence of a surface state with unique properties. These materials are predicted to host exotic states such as Majorana…

We address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function…

The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling…

We investigate -- through simulations and analytical calculations -- the consequences of uniaxial lateral compression applied to the upper layer of few-layer graphene. The simulations of compressed graphene show that strains larger than 2.8…

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…

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…

Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…

Over the past few years, topological insulators have taken center stage in solid state physics. The desire to tune the topological invariants of the bulk and thus control the number of edge states has steered theorists and experimentalists…

We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the…

We study edge-states in graphene systems where a bulk energy gap is opened by inversion symmetry breaking. We find that the edge-bands dispersion can be controlled by potentials applied on the boundary with unit cell length scale. Under…

Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structure. The ability to tune such a material through a topological…

This thesis studies how the rudimentary attributes of graphene's charge carriers, and local moments on its surface, can be directly manipulated and controlled with electrostatic potentials. We first consider bilayer graphene subject to a…

Rhombohedral multilayer graphene has emerged as an extraordinary platform for investigating exotic quantum states, such as superconductivity and fractional quantum anomalous Hall effects, mainly due to the existence of topological surface…

Systems with engineered flatband spectra are a postulate of high-capacity transmission links and a candidate for high-temperature superconductivity. However, their operation relies on the edge or surface modes susceptible to fluctuations…

We theoretically introduce a quasi-1D magnetic heterostructure of alternating 2D topological and normal insulator strips. Its low-energy physics is governed by a hybrid Hamiltonian intertwining the Su-Schrieffer-Heeger and Shockley models,…

In this paper we study the topology of the bands of a plasmonic crystal composed of graphene and of a metallic grating. Firstly, we derive a Kronig-Penney type of equation for the plasmonic bands as function of the Bloch wavevector and…