Related papers: Non-Commutative Tools for Topological Insulators
The surface states of a topological insulator in a fine-tuned magnetic field are ideal candidates for realizing a topological metal which is protected against disorder. Its signatures are (1) a conductance plateau in long wires in a finely…
For conventional topological phases, the boundary gapless modes are determined by bulk topological invariants. Based on developing an analytic method to solve higher-order boundary modes, we present $PT$-invariant $2$D topological…
The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require…
Using exact diagonalization and quantum Monte Carlo calculations we investigate the effects of disorder on the phase diagram of both non-interacting and interacting models of two-dimensional topological insulators. In the fermion sign…
Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
Topological insulators (TIs) are renowned for their remarkable electronic properties: quantised bulk Hall and edge conductivities, and robust edge wave-packet propagation, even in the presence of material defects and disorder. Computations…
We aim at reducing the uncertainties inherent in the analysis of the topological structure by using scale controlled smoothing and observables independent on the "microscopic" description of the instanton ensemble.
Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification…
In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear non-modal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the non-trivial time evolution of non-modal…
Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward an ordering unique…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
Bulk boundary correspondence in topological materials allows to study their bulk topology through the investigation of their topological boundary modes. However, for classes that share similar boundary phenomenology, the growing diversity…
Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations.…
The Letter is analyzing bulk spin (moment) currents and spin (moment) accumulation at edges of a 2D topological insulator taking into account reflection from edges. Accumulation occurs only at edge states, which distinguish topological…
The criteria for strong correlations on surfaces of three-dimensional topological insulators are discussed. Usually, the Coulomb repulsion at such surfaces is too weak for driving a phase transition to a strongly correlated regime. I…
We report on the measurement of topological invariants in an electromagnetic topological insulator analog formed by a microwave network, consisting of the winding numbers of scattering matrix eigenvalues. The experiment can be regarded as a…
The studies of topological insulators and topological semimetals have been at frontiers of condensed matter physics and material science. Both classes of materials are characterized by robust surface states created by the topology of the…