Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations.

Tessellations of the hyperbolic spaces by regular polygons support discrete quantum and classical models with unique spectral and topological characteristics. Resolving the true bulk spectra and the thermodynamic response functions of these models requires converging periodic boundary conditions and our Letter delivers a practical and rigorous solution for this open problem on generic {p,q}-tessellations. This enables us to identify the true spectral gaps of bulk Hamiltonians and construct all but one topological models that deliver the topological gaps predicted by the K theory of the lattices.

Noncollinear Spin Current for Switching of Chiral Magnetic Textures.

We propose a concept of noncollinear spin current, whose spin polarization varies in space even in nonmagnetic crystals. While it is commonly assumed that the spin polarization of the spin Hall current is uniform, asymmetric local crystal potential generally allows the spin polarization to be noncollinear in space. Based on microscopic considerations, we demonstrate that such noncollinear spin Hall currents can be observed, for example, in layered Kagome Mn_{3}X (X=Ge, Sn) compounds.

Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach.

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry.