Related papers: Chern number in Ising models with spatially modula…
We extend Kitaev's real-space formulation of the first Chern number to the second Chern number and establish a computational framework for its evaluation. To test its validity, we apply the derived formula to the disordered Wilson-Dirac…
In this paper, we formulate the real-space Chern number in a supercell framework. In this framework, the overlap matrix between two corners of the Brillouin zone (BZ) is derived from diagonalizing the real-space Hamiltonian with periodic…
In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable $C^*$-algebra by a twisted $\mathbb{R}^d$-action. The…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…
We evaluate the real-space second Chern number of four-dimensional Chern insulators using the kernel polynomial method. Our calculations are performed on a four-dimensional system with $30^4$ sites, and the numerical results agree well with…
Chern number is usually characterized by Berry curvature. Here, by investigating the Dirac model of even-dimensional Chern insulator, we give the general relation between Berry curvature and quantum metric, which indicates that the Chern…
Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states.…
The Chern number has been widely used to describe the topological properties of periodic structures in the momentum space. Here, we introduce a real-space spin Chern number for the optical near fields of finite-sized structures. This new…
We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing…
We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase (EGP) introduced for one-dimensional lattice models to two dimensions. In contrast to the geometric phase for density matrices…
Chern numbers are gaining traction as they characterize topological phases in various physical systems. However, the resilience of the system topology to external perturbations makes it challenging to experimentally investigate transitions…
Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological…
The Chern number is a crucial topological invariant for distinguishing the phases of Chern insulators. Here we find that for Chern insulators with inversion symmetry, the Chern number alone is insufficient to fully characterize their…
The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…
This work explores the topological properties of altermagnets, a novel class of collinear magnetic materials. We employ equivariant K-theory of magnetic groups and Hamiltonian models to formulate a robust $C^z_4 \mathbb{T}$ topological…
Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first…
To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension,…
The Chern number is often used to distinguish between different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline…
The coupling between the spin and momentum degrees of freedom due to spin-orbit interactions (SOI) suggests that the strength of the latter can be modified by controlling the motion of the charge carriers. In this paper, we investigate how…
We present models of topological insulating Hamiltonians exhibiting intrinsic altermagnetic features, protected by combined three-fold or four-fold rotational symmetries with time-reversal. We demonstrate that the spin Chern number serves…