We propose an exact construction for atypical excited states of a class of non-integrable quantum many-body Hamiltonians in one dimension (1D), two dimensions (2D), and three dimensins (3D) that display area law entanglement entropy. These examples of many-body "scar" states have, by design, other properties, such as topological degeneracies, usually associated with the gapped ground states of symmetry protected topological phases or topologically ordered phases of matter.

A monolayer of WTe2 has been shown to display quantum spin Hall (QSH) edge modes persisting up to 100 K in transport experiments. Based on density-functional theory calculations and symmetry-based model building including the role of correlations and substrate support, we develop an effective electronic model for WTe2 which fundamentally differs from other prototypical QSH settings: we find that the extraordinary robustness of quantum spin Hall edge modes in WTe2 roots in a glide symmetry due to which the topological gap opens away from high-symmetry points in momentum space. While the indirect bulk gap is much smaller, the glide symmetry implies a large direct gap of up to 1 eV in the Brillouin zone region of the dispersing edge modes, and hence enables sharply boundary-localized QSH edge states depending on the specific boundary orientation.

We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y3Fe5O12) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.

We extend the scope of Kitaev spin liquids to non-Archimedean lattices. For the pentaheptite lattice, which results from the proliferation of Stone-Wales defects on the honeycomb lattice, we find an exactly solvable non-Abelian chiral spin liquid with spontaneous time reversal symmetry breaking due to lattice loops of odd length. Our findings call for potential extensions of exact results for Kitaev models which are based on reflection positivity, which is not fulfilled by the pentaheptite lattice. We further elaborate on potential realizations of our chiral spin liquid proposal in strained α-RuCl3.

Topological Kondo insulators are a rare example of an interaction-enabled topological phase of matter in three-dimensional crystals -making them an intriguing but also hard case for theoretical studies. Here, we aim to advance their theoretical understanding by solving the paradigmatic two-band model for topological Kondoinsulators using a fully spin-rotation invariant slave-boson treatment. Within a mean-field approximation, we map out the magnetic phase diagram and characterize both antiferromagnetic and paramagnetic phases by their topological properties. Among others, we identify an antiferromagnetic insulator that shows, for suitable crystal terminations, topologically protected hinge modes. Furthermore, Gaussian fluctuations of the slave boson fields around their mean-field value are included in order to establish the stability of the mean-field solution through computation of the full dynamical susceptibility. arXiv:1911.11217v1 [cond-mat.str-el]