Related papers: Edge-following topological states
A recently-proposed class of photonic topological insulators is shown to map onto Chalker-Coddington-type networks, which were originally formulated to study disordered quantum Hall systems. Such network models are equivalent to the Floquet…
We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $\mathbb{Z}_K$ or $\mathbb Z_K \times \mathbb Z_K $ symmetry. We argue that modular…
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field…
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…
Topological insulators are currently of considerable interest due to peculiar electronic properties originating from helical states on their surfaces. Here we demonstrate that the sound excited by helical particles on surfaces of…
Two-dimensional non-interacting fermions without any anti-unitary symmetries generically get Anderson localized in the presence of disorder. In contrast, topological superconductors with their inherent particle-hole symmetry can host a…
We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing…
The topological insulators have a gap in the bulk but extended states at the edge that can carry current. We study a geometry in which such edge states will manifest themselves through periodic oscillations in the magnetoconductance of a…
We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moir\'{e} pattern, and the emergence of these moir\'{e} edge states is…
Symmetry and topology are essential principles in topological physics. Recently, the idea of sub-symmetry-protected topology -- where some of the original symmetries are broken while a remaining subset, called sub-symmetries, continues to…
We suggest that exotic sphere fibrations can be mapped to band topologies in condensed matter systems. These fibrations can correspond to geometric phases of two double bands or state vector bases with second Chern numbers m+n and -n…
In condensed matter physics, symmetry profoundly governs the fundamentals of topological matter. The emergence of new topological phase is typically linked to the enrichment of symmetries. Different parity-time symmetry relations…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
Recent theoretical works have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed…
Topological materials can host edge and corner states that are protected from disorder and material imperfections. In particular, the topological edge states of mechanical structures present unmatched opportunities for achieving robust…
We study the scattering of edge states of 2D topological insulator (TI) in the uniform external magnetic field due to edge imperfections, common in realistic 2D TI samples. The external magnetic field breaks time reversal (TR) symmetry,…
Three-dimensional topological crystalline insulators were recently predicted and observed in the SnTe class of IV-VI semiconductors, which host metallic surface states protected by crystal symmetries. In this work, we study thin films of…
A topological insulator and its spin analogue as a gapped spin liquid have characteristic low energy excitations (edge states) within the gap when the systems have boundaries. This is the bulk-edge correspondence, which implies that the…
Three-dimensional (3D) topological materials exhibit much richer phenomena than their lower-dimensional counterparts. Here, we propose self-localized topological states (i.e., topological solitons) in a 3D nonlinear photonic Chern…
We report direct imaging of standing waves of the nontrivial surface states of topological insulator Bi$_2$Te$_3$ by using a low temperature scanning tunneling microscope. The interference fringes are caused by the scattering of the…