Related papers: Topological junctions for one-dimensional systems
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…
Helical edge modes are characteristic of topological insulators in two dimensions. This paper demonstrates that helical edge modes remain across transitions to ordinary insulators or to semimetals under certain condition. Straight and…
Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in…
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 work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts…
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…
Symmetry is one of the cornerstones of modern physics and has profound implications in different areas. In symmetry-protected topological systems, symmetries are responsible for protecting surface states, which are at the heart of the…
Spectrum and wave function of gapless edge modes are derived analytically for a tight-binding model of topological insulators on square lattice. Particular attention is paid to dependence on edge geometries such as the straight (1,0) and…
The abstract notion of topology has led to profound insights into real materials. Notably, the surface and edges of topological materials can host physics, such as unidirectional charge or spin transport, that is unavailable in isolated…
We investigate and experimentally observe the existence of topologically protected interface modes in a one-dimensional mechanical lattice, and we report on the effect of nonlinearities on topological protection. The lattice consists of a…
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 mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial…
Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet…
We construct and analyze a class of one-dimensional boundary Hamiltonians arising from two-dimensional symmetry-protected topological phases with $\mathbb{Z}_N^{\times 3}$ symmetry on a triangular lattice. Using a cohomology-based…
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 materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
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…