相关论文: Unification of topological invariants in Dirac mod…

Dirac semimetal is a class of semi-metallic phase protected by certain types of crystalline symmetries, and its low-energy effective Hamiltonian is described by Dirac equations in three dimensions (3D). Despite of various theoretical…

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting…

Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states.…

Topological invariants, such as the winding number, the Chern number, and the Zak phase, characterize the topological phases of bulk materials. Through the bulk-boundary correspondence, these topological phases have a one-to-one…

Topological non-trivial band structures are the core problem in the field of topological materials. In this paper, we investigate the topological band structure in a system with controllable Dirac points from the perspective of wave packet…

Topological invariants play a key role in the characterization of topological states. Due to the existence of exceptional points, it is a great challenge to detect topological invariants in non-Hermitian systems. We put forward a dynamic…

The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I…

In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum…

The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…

We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…

The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical…

Topological materials are characterized by integer invariants that underpin their robust quantized electronic features, as famously exemplified by the Chern number in the integer quantum Hall effect. Yet, in most candidate systems, the…

Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…

We consider the analogy between the topological phase transition which occurs as a function of spatial coordinate on a surface of a non-trivial insulator, and the one which occurs in the bulk due to the change of internal parameters (such…

A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. We uncover a correspondence between the curvature function that…

We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…

Recently, a moir\'e material has been proposed in which multiple domains of different topological phases appear in the moir\'e unit cell due to a large moir\'e modulation. Topological properties of such moir\'e materials may differ from…

At the heart of the study of topological insulators lies a fundamental dichotomy: topological invariants are defined in infinite systems, but surface states as their main footprint only exist in finite systems. In the slab geometry, namely…

In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a…

The topological properties of a material depend on its symmetries, parameters, and spatial dimension. Changes in these properties due to parameter and symmetry variations can be understood by computing the corresponding topological…