Related papers: Classification of topological invariants related t…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time…
This monograph offers an overview on the topological invariants in fermionic topological insulators from the complex classes. Tools from K-theory and non-commutative geometry are used to define bulk and boundary invariants, to establish the…
Topological insulators are new quantum states with helical gapless edge or surface states inside the bulk band gap.These topological surface states are robust against the weak time-reversal invariant perturbations, such as lattice…
We demonstrate that the presence of a localized state at the corner of an insulating domain is not always a predictor of a certain non-trivial higher-order topological invariant, even though they appear to co-exist in the same Hamiltonian…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order…
Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner…
A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these…
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we…
Recent formal classifications of crystalline topological insulators predict that the combination of time-reversal and rotational symmetry gives rise to topological invariants beyond the ones known for other lattice symmetries. Although the…
In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to…
We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
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…