Related papers: Universal topological marker
We study solutions of $2 \times 2$ systems $(h D_t + \mathcal{D}) \Psi_t = 0$ on $\mathbb{R}^2$ in the semiclassical regime $h \rightarrow 0$. Our Dirac operator $\mathcal{D}$ is a standard model for interfaces between topological…
We propose a way -- universal wave function overlap -- to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data should fully characterize the topological orders…
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 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…
The concept of topological fermions, including Weyl and Dirac fermions, stems from the quantum Hall state induced by a magnetic field, but the definitions and classifications of topological fermions are formulated without using magnetic…
It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on…
We study topological superconductor in one-dimensional (1D) mosaic lattice whose on-site potentials are modulated for equally spaced sites. When the system is topologically nontrivial, Majorana zero modes appear at the two ends of the 1D…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
Gapless Dirac surface states are protected at the interface of topological and normal band insulators. In a binary superlattice bearing such interfaces, we establish that valley-dependent dimerization of symmetry-unrelated Dirac surface…
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…
The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…
Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is…
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…
We study superconductors with $n$-fold rotational invariance both in the presence and in the absence of spin-orbit interactions. More specifically, we classify the non-interacting Hamiltonians by defining a series of $Z$-numbers for the…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
We show that time-reversal invariant superconductors in d=2 (d=3) dimensions can support topologically stable Fermi points (lines), characterized by an integer topological charge. Combining this with the momentum space symmetries present,…
We propose a general construction of commuting projector lattice models for 2D and 3D topological phases enriched by U(1) symmetry, with finite-dimensional Hilbert space per site. The construction starts from a commuting projector model of…
Tridiagonal $k$-Toeplitz operators provide a natural framework for modelling one-dimensional $k$-periodic lattice systems. A fundamental connection is obtained between Coburn's lemma for tridiagonal $k$-Toeplitz operators and the existence…
The index, which is given in terms of the number of zero modes of the Dirac operator with definite chirality, plays a central role in various topological aspects of gauge theories. We investigate its properties in non-commutative geometry.…
The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to…