Robert-Jan Slager

The space group classification of topological band-insulators

Topological insulators are now shown to be protected not only by time-reversal symmetry, but also by crystal lattice symmetry. By accounting for the crystalline symmetries, additional topological insulators can be predicted.

Universal probes of two-dimensional topological insulators: dislocation and π flux.

We show that the π flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that π flux hosts a Kramers pair of zero modes in the topological Γ (Berry phase Skyrmion at the zero momentum) and M (Berry phase Skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a π flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.

Interplay between electronic topology and crystal symmetry : Dislocation-line modes in topological band insulators

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this

Impurity-bound states and Green's function zeros as local signatures of topology

\mathbf{K}\text{\ensuremath{-}}\mathbf{b}\text{\ensuremath{-}}\mathbf{t}

Self-organized pseudo-graphene on grain boundaries in topological band insulators

rule, the lattice topology, represented by dislocation lines oriented in direction

Zero-energy states bound to a magnetic π-flux vortex in a two-dimensional topological insulator

\mathbf{t}

Classification of point-group-symmetric orientational ordering tensors

with Burgers vector

Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematic liquid crystals

\mathbf{b}

Classification of nematic order in 2 + 1 dimensions: Dislocation melting and

, combines with the electronic-band topology, characterized by the band-inversion momentum

O(2)/Z_N

{\mathbf{K}}_{\mathrm{inv}}