Related papers: Corner states and topological transitions in two-d…
We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
Topological insulators are bulk semiconductors that manifest in-gap massless Dirac surface states due to the topological bulk-boundary correspondence principle [1-3]. These surface states have been a subject of tremendous ongoing interest,…
In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…
Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology of optical materials is characterized using the Berry phase defined by Bloch…
The phase transition from a topological insulator to a trivial band insulator is studied by angle-resoled photoemission spectroscopy on Bi$_{2-x}$In$_{x}$Se$_{3}$ single crystals. We first report the complete evolution of the bulk band…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
The bulk-edge correspondence principle, a cornerstone of topological physics, ensures that first-order topological systems host robust chiral edge states in two dimension. This was later extended to higher-order phases, where second-order…
The bulk-edge correspondence characterizes topological insulators and superconductors. We generalize this concept to the bulk-corner correspondence and the edge-corner correspondence in two dimensions. In the bulk-corner (edge-corner)…
This work reports topological extraordinary properties of sound transmission through topological states in sonic crystals denominated Suzuki phase, consisting of a rectangular lattice of vacancies created in a triangular lattice. These…
The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases and quantum information. While recent studies suggest that…
The presence or absence of topologically-produced edge states of a crystal are robust to disorder; their stability in the presence of decay is less clear. For topologically nontrivial bosonic systems with finite particle lifetimes, such as…
The bulk-boundary correspondence guarantees topologically protected edge states in a two-dimensional topological superconductor. Unlike in topological insulators, these edge states are, however, not connected to a quantized (spin) current…
By stacking PbTe layers there is a non-monotonic topological phase transition as a function of the number of monolayers. Based on first principles calculations we find that the proper stacked crystal symmetry determines the topological…
Topological insulators are characterized by insulating bulk states and robust metallic surface states. Band inversion is a hallmark of topological insulators: at time-reversal invariant points in the Brillouin zone, spin-orbit coupling…
Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimension lower than the bulk have significantly opened a new perspective for understanding of…
We address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function…
Recently, higher-order topological phases that do not obey the usual bulk-edge correspondence principle have been introduced in electronic insulators and brought into classical systems, featuring with in-gap corner/hinge states. So far,…