相关论文: Topological Phase Transitions from Harper to Fibon…

Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In…

One-dimensional quasiperiodic systems, such as the Harper model and the Fibonacci quasicrystal, have long been the focus of extensive theoretical and experimental research. Recently, the Harper model was found to be topologically…

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…

Here, the frequency degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic…

We report on a study of topological properties of Fibonacci quasicrystals. Chern numbers which label the dense set of spectral gaps, are shown to be related to the underlying palindromic symmetry. Topological and spectral features are…

The topological properties of the quantum Hall effect in a crystalline lattice, described by Chern numbers of the Hofstadter butterfly quantum phase diagram, are deduced by using a geometrical method to generate the structure of…

In crystalline systems, higher-order topology, characterized by topological states of codimension greater than one, typically arises from the mismatch between Wannier centers and atomic sites, leading to filling anomalies. However, this…

Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…

The redistribution of energy levels between energy bands is studied for a family of simple effective Hamiltonians depending on one control parameter and possessing axial symmetry and energy-reflection symmetry. Further study is made on the…

We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology and energetics, we show that for a generic normal state band…

We investigate the topological properties of Fibonacci quasicrystals using cavity polaritons. Composite structures made of the concatenation of two Fibonacci sequences allow investigating generalized edge states forming in the gaps of the…

Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological…

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 distinctive electronic properties of quasicrystals stem from their long range structural order, with invariance under rotations and under discrete scale change, but without translational invariance. d-dimensional quasicrystals can be…

Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…

Spatial profile of the Majorana fermion wave function in a one-dimensional $p$-wave superconductors ($\cal{PWS}$) with quasi periodic disorder is shown to exhibit spatial oscillations. These oscillations damp out in the interior of the…

Topological invariants govern many important physical properties in condensed matter systems. In this work, we obtain the complete set of topological invariants for a family of one-dimensional quasicrystals. The first and best-studied…

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…

The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with no counterparts in topological Hermitian…

We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time.…