Related papers: Evaluation of real-space second Chern number using…
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…
Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete symmetries and are characterized by topological…
We report a study of a disorder-dependent real-space representation of the quantum geometry in topological systems. Thanks to the development of an efficient linear-scaling numerical methodology based on the kernel polynomial method, we can…
Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which…
The atomic-scale influence of disorder on the topological order can be quantified by a universal topological marker, although the practical calculation of the marker becomes numerically very costly in higher dimensions. We propose that for…
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…
Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index.…
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…
As an important figure of merit for characterizing the quantized collective behaviors of the wavefunction, Chern number is the topological invariant of quantum Hall insulators. Chern number also identifies the topological properties of the…
The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions…
The discovery of topological states of matter has profoundly augmented our understanding of phase transitions in physical systems. Instead of local order parameters, topological phases are described by global topological invariants and are…
Two-dimensional Euler insulators are novel kind of systems that host multi-gap topological phases, quantified by a quantised first Euler number in their bulk. Recently, these phases have been experimentally realised in suitable…
Modern technological advances allow for the study of systems with additional synthetic dimensions. Using such approaches, higher-dimensional physics that was previously deemed to be of purely theoretical interest has now become an active…
In disordered two dimensional Chern insulators, a single bulk extended mode is predicted to exist per band, up to a critical disorder strength; all the other bulk modes are localized. This behavior contrasts strongly with topologically…
We propose an efficient numerical method to compute the $k$-space second Chern number in four-dimensional (4D) topological systems. Our approach employs an adaptive mesh refinement scheme to evaluate the Brillouin-zone integral, which…
A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has…
We study an one-dimensional transverse field Ising model with additional periodically modulated real and complex fields. It is shown that both models can be mapped on a pseudo spin system in the k space in the aid of an extended Bogoliubov…
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.…
We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states…