Topological Dirac Insulators

DIPC Seminars

Dr. Benjamin Wieder, Princeton University
Donostia International Physics Center
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Topological Dirac Insulators Over the past few years, the set of topological insulating phases has been expanded to include insulators with topological gapless surface features protected by surface crystal symmetries; new phases include mirror topological crystalline insulators and nonsymmorphic topological hourglass insulators. In fact, it can be shown that the complete set of time-reversal-symmetric 3D topological insulators with gapless surface modes can be obtained by group theoretic considerations of the 17 surface, or "wallpaper", groups. We find that the two wallpaper groups with multiple glide lines, pgg and p4g, allow for a new topological insulating phase, one whose surface spectrum consists of only a single, fourfold-degenerate, true Dirac fermion. Like the surface state of a conventional topological insulator, the surface Dirac fermion in this "topological Dirac insulator'' provides a theoretical exception to a fermion doubling theorem. Unlike the surface state of a conventional topological insulator, it can be gapped into topologically distinct surface regions while keeping time-reversal symmetry, allowing for networks of topological surface quantum spin Hall domain walls. We present topological invariants for these double-glide system by expanding on previous classifications of non-abelian Wilson loop connectivities. We conclude by presenting materials candidates for this topological Dirac insulating phase and for related hourglass insulating phases.