Condensed Matter Seminar: Luka Trifunovic, Free University of Berlin - “Reflection symmetric second-order topological insulators and superconductors”

Second-order topological insulators are crystalline insulators with a
gapped bulk and gapped crystalline boundaries, but topologically protected
gapless states at the intersection of two boundaries. Without further
spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes
allow for the existence of such second-order topological insulators in two
and three dimensions. We show that reflection symmetry can be employed to
systematically generate examples of second-order topological insulators
and superconductors, although the topologically protected states at
corners (in two dimensions) or at crystal edges (in three dimensions)
continue to exist if reflection symmetry is broken. A three-dimensional
second-order topological insulator with broken time-reversal symmetry
shows a Hall conductance quantized in units of e^2/h.