Related papers: Continuous bulk and interface description of topol…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
We consider topologically non-trivial interface Hamiltonians, which find several applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence of topologically protected,…
A central property of (Chern) topological insulators is the presence of robust asymmetric transport along interfaces separating two-dimensional insulating materials in different topological phases. A Topological Anderson Insulator is an…
We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant,…
This paper presents a fast algorithm for computing transport properties of two-dimensional Dirac operators with linear domain walls, which model the macroscopic behavior of the robust and asymmetric transport observed at an interface…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
This paper analyzes Floquet topological insulators resulting from the time-harmonic irradiation of electromagnetic waves on two dimensional materials such as graphene. We analyze the bulk and edge topologies of approximations to the…
This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…
Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on…
Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac…
This monograph offers an overview on the topological invariants in fermionic topological insulators from the complex classes. Tools from K-theory and non-commutative geometry are used to define bulk and boundary invariants, to establish the…
Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined…
Topological insulators (TIs) are novel materials that manifest spin-polarized Dirac states on their surfaces or at interfaces made with conventional matter. We have measured the electron kinetics of bulk doped TI Bi$_2$Se$_3$ with angle…
This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic…
This paper concerns the asymmetric transport observed along interfaces separating two-dimensional bulk topological insulators modeled by (continuous) differential Hamiltonians and how such asymmetry persists after numerical discretization.…
At the heart of the study of topological insulators lies a fundamental dichotomy: topological invariants are defined in infinite systems, but surface states as their main footprint only exist in finite systems. In the slab geometry, namely…
The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models…
In this chapter, criteria for existence of propagating optical modes which are transversely bound at the interface of two materials are studied. In particular, quite general cases are considered, where the materials involved are assumed to…
We show how to engineer a chiral spectral flow of interface states in a gapless system. Although the bulk bands touch -- thus making the topological indices of the bands ill-defined -- this spectral flow has a topological origin that makes…
This paper proposes a classification of elliptic (pseudo-)differential Hamiltonians describing topological insulators and superconductors in Euclidean space by means of domain walls. Augmenting a given Hamiltonian by one or several domain…