Related papers: Edge-following topological states
In recent years, the study of topologically non-trivial structures in one-dimensional models has been dominated by the Su--Schrieffer--Heeger model due to its simplicity in design and its ability to support edge states with robustness to…
Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components…
We construct and investigate a family of two-band unitary systems living on a cylinder geometry and presenting localized edge states. Using the transfer matrix formalism, we solve and investigate in details such states in the thermodynamic…
Magic-angle twisted bilayer graphene is the best studied physical platform featuring moire potential induced narrow bands with non-trivial topology and strong electronic correlations. Despite their significance, the Chern insulating states…
Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. Using scanning…
Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream…
Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner…
Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index.…
The Chern index characterizes the topological phases of nonreciprocal photonic systems. Unlike in electronic systems, the photonic Chern number has no clear physical meaning, except that it determines the net number of unidirectional edge…
Twisted double bilayer graphene (tDBG) has emerged as an especially rich platform for studying strongly correlated and topological states of matter. The material features moir\'e bands that can be continuously deformed by both perpendicular…
We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it…
We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well-defined and nontrivial in the $D \to \infty$ limit. Dynamical mean-field theory…
Topological insulators are new states of matter in which the topological phase originates from symmetry breaking. Recently, time-reversal invariant topological insulators were demonstrated for classical wave systems, such as acoustic…
The topic of photonic topological insulators and scattering-protected edge states bridges concepts from condensed matter physics and electromagnetics, and necessitates understanding the Berry potential and related concepts. These notes are…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically…
Systems that exhibit topologically protected edge states are interesting both from a fundamental point of view as well as for potential applications, the latter because of the absence of back-scattering and robustness to perturbations. It…
Bulk-edge correspondence is one of the most distinct properties of topological insulators. In particular, the 1D winding number $\n$ has a one-to-one correspondence to the number of edge states in a chain of topological insulators with…
The propagation of linear and nonlinear edge modes in bounded photonic honeycomb lattices formed by an array of rapidly varying helical waveguides is studied. These edge modes are found to exhibit strong transmission (reflection) around…
Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge…