Related papers: Hierarchical Topological States without Dimension …
Topological phases feature robust edge states that are protected against the effects of defects and disorder. The robustness of these states presents opportunities to design technologies that are tolerant to fabrication errors and resilient…
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…
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…
High-order topological insulators (TIs) develop the conventional bulk-boundary correspondence theory and rise the interest in searching innovative topological materials. To realize a high-order TI with a wide passband of 1D and 2D…
The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner…
Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken,…
Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges.…
Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond…
The discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the $d$-dimension insulating bulk is confined to ($d-1$)-dimensions, led to several potential applications. Recently, it…
Topological insulators are a new class of materials which have gapped spectra in the bulk, but are accompanied by topologically protected gapless excitations at the surface (edge) of the system. These phenomena have a close relationship…
Topological insulators in the Bi$_2$Se$_3$ family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band…
In this tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focussing on the low energy description of higher-order topological insulators in terms of the Dirac equation. Our aim…
Topological phases of matter are generally characterized by topological properties of energy bands of a system. Their transitions under preserved symmetries occur through closing a gap of energy bands, leading to topologically protected…
Three-dimensional (3D) topological insulators in general need to be protected by certain kinds of symmetries other than the presumed $U(1)$ charge conservation. A peculiar exception is the Hopf insulators which are 3D topological insulators…
Topological Insulators are a novel state of matter where spectral bands are characterized by quantized topological invariants. This unique quantized non-local property commonly manifests through exotic bulk phenomena and corresponding…
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…
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…
We have performed a systematic investigation of the formation of topologically protected boundary states (TPBS) in topological/normal insulators (TI/NI) heterostructures. Using a recently developed scheme to construct {\it ab-initio}…
We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…