Related papers: Non-Commutative Tools for Topological Insulators
The hallmark feature of topological insulators renders edge transport virtually impervious to scattering at defects and lattice disorder. In our work, we experimentally demonstrate a topological system, using a photonic platform, in which…
We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…
Integrated plasmonics is advancing rapidly, enabling a wide range of functionalities to be incorporated onto a single chip. Applications span information processing, computation, quantum sensing, and dark-matter detection. This progress has…
In this paper topological $K$-group calculations for fiber bundles with structure group $SO(3)$ over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is…
To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for…
Fractional topological insulators are electronic systems that carry fractionally charged excitations, conserve charge and are symmetric to reversal of time. In this review we introduce the basic essential concepts of the field, and then…
We use the N-terminal scheme for studying the edge state transportin in two-dimensional topological insulators. We find the universal nonlocal response in the ballistic transport approach. This macroscopic exhibition of the topological…
Nonlinear topological insulators have garnered substantial recent attention as they have both enabled the discovery of new physics due to interparticle interactions, and may have applications in photonic devices such as topological lasers…
The class of topological insulator materials is one of the frontier topics of condensed matter physics. The great success of this field is due to the conceptual breakthroughs in theories for topological electronic states and is strongly…
Higher-order topological insulators are unusual materials that can support topologically protected states, whose dimensionality is lower than the dimensionality of the structure at least by 2. Among the most intriguing examples of such…
Time-reversal invariant three-dimensional topological insulators can be defined fundamentally by a topological field theory with a quantized axion angle theta of zero or pi. It was recently shown that fractional quantized values of theta…
Floquet topological insulators describe independent electrons on a lattice driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In dimension two such systems are characterized by integer-valued…
Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a…
Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review work completed over the last few years, including our own, regarding…
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field…
Topology is central to understanding and engineering materials that display robust physical phenomena immune to imperfections. Different topological phases of matter are characterised by topological invariants. In energy-conserving…
Topological quantum phases of quantum materials are defined through their topological invariants. These topological invariants are quantities that characterize the global geometrical properties of the quantum wave functions and thus are…
We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…
Topological insulators are unique physical structures that are insulators in their bulk, but support currents at their edges which can be unidirectional and topologically protected from scattering on disorder and inhomogeneities. Photonic…
Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to…