Related papers: From orthogonal link to phase vortex in generalize…
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…
2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…
In this study, a tight-binding model on square octagon lattice with nearest-neighbour and next-nearest-neighbour hoppings is considered. The system is topologically trivial although it exhibits quadratic band-touching points in its…
We show that link concordance implies link homotopy for immersions of codimension at least two. As a consequence, we prove that every link $\sqcup^r S^n \hookrightarrow S^{n+2}$ is link homotopically trivial for $n\geq 2$, that is, there is…
We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. The novel feature of our network model is that in addition to a weak topological…
The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators,…
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as…
Topological theories have established a new set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by…
The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but…
Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological…
The search for robust examples of the magnetic version of topological insulators, referred to as quantum anomalous Hall insulators or simply Chern insulators, so far lacks success. Our groups have explored two distinct possibilities based…
The interplay among topology, disorder, and non-Hermiticity can induce some exotic topological and localization phenomena. Here we investigate this interplay in a two-dimensional non-Hermitian disordered Chern-insulator model with two…
We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…
The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wavefunction. Here we address the Chern number of a two-dimensional insulator and we show that the…
Two recent papers proved that complex index pairings can be calculated as the half-signature of a finite dimensional matrix, called the spectral localizer. This paper contains a new proof of this connection for even index pairings based on…
In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and…
We systematically investigate how static symmetry-breaking perturbations and dynamic Floquet terms via a polarized light manipulate the topological phase transitions in the two-dimensional quadratic-band-crossing-point (QBCP) materials. The…
This paper is a survey of the $\mathbb{Z}_2$-valued invariant of topological insulators used in condensed matter physics. The $\mathbb{Z}$-valued topological invariant, which was originally called the TKNN invariant in physics, has now been…
We detect the topological properties of Chern insulators with strong Coulomb interactions by use of cluster perturbation theory and variational cluster approach. The common scheme in previous studies only involves the calculation of the…
Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall…