相关论文: Topological Spectral Bands with Frieze Groups

We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie…

We call a set $K \subset {\mathbb R}^s$ with positive Lebesgue measure a {\it spectral set} if $L^2(K)$ admits an exponential orthonormal basis. It was conjectured that $K$ is a spectral set if and only if $K$ is a tile (Fuglede's…

This dissertation is about rearrangement groups: a class of groups of homeomorphisms of fractal topological spaces. Introduced in 2019 by J. Belk and B. Forrest, this class generalizes the famous trio of Thompson groups $F$, $T$ and $V$ and…

Motivated by the indications of high-Tc superconductivity in natural graphite enriched in the rhombohedral phase, we study the band structure of several stacking configurations that combine two of the three graphite structures as well as…

Topological insulators (TIs) are an important family of quantum materials that exhibit a Dirac point (DP) in the surface band structure but have a finite band gap in bulk. A large degree of spin-orbit interaction and low bandgap is a…

Recent work of An, Drummond-Cole, and Knudsen, as well as the author, has shown that the homology groups of configuration spaces of graphs can be equipped with the structure of a finitely generated graded module over a polynomial ring. In…

Systems hosting flat bands offer a powerful platform for exploring strong correlation physics. Theoretically topological degeneracy rising in systems with non-trivial topological orders on periodic manifolds of non-zero genus can generate…

In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. We also introduce some generalization of the Brauer group in the topological context and show that any its element…

Let $T_1$ and $T_2$ be homogeneous trees of even degree $\ge 4$. A BM group $\Gamma$ is a torsion free discrete subgroup of $\aut (T_1) \times \aut (T_2)$ which acts freely and transitively on the vertex set of $T_1 \times T_2$. This…

When granular mixtures of different sizes are fluidized, each species spontaneously separates and condenses to form patterns. Although granular segregation has been extensively studied, the inability to directly observe the time evolution…

Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…

In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the…

Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter…

We study bounded operators defined in terms of the regular representations of the $C^*$-algebra of an amenable, Hausdorff, second countable locally compact groupoid endowed with a continuous $2$-cocycle. We concentrate on spectral…

We give a survey of the theory of surface braid groups and the lower algebraic K-theory of their group rings. We recall several definitions and describe various properties of surface braid groups, such as the existence of torsion,…

We present a rigorous and fully consistent $K$-theoretic framework for studying gapped topological phases of free fermions such as topological insulators. It utilises and profits from powerful techniques in operator $K$-theory. From the…

Insulating, atomically flat transition metal dichalcogenides (TMDs) like WSe2 are ideal substrates for probing intrinsic graphene properties. Conventionally, their influence on graphene's band structure is assumed negligible, particularly…

Periodically driven quantum systems can exhibit subharmonic response, usually characterized through physical observables and often discussed in interacting settings. Here we show that a sharp subharmonic signature already appears in the…

Ternary tetradymites Bi2Te2S, Bi2Te2Se and Bi2Se2Te are found to be stable, bulk topological insulators via theory, showing band inversion between group V and VI pz orbitals. We identify Bi2Se2Te as a good candidate to study massive Dirac…