Special Condensed Matter Seminar, Chen Fang, “Topological Insulators and Semimetals with Point Group Symmetries”
In this talk we will first discuss topological band insulators with crystallographic point group symmetries (PGS), extending the regime of topological phases to include systems beyond those having time-reversal symmetry. In principle, any discrete symmetry gives rise to a topological classification of insulators indexed by quantum numbers characteristic to that symmetry. We will inspect three major topological indices of insulators with PGS: quantum Hall conductance, magnetoelectric response and, most importantly, the number of protected midgap states in the entanglement spectrum. We further show that the last index can be promptly calculated from the Bloch wavefunctions at high-symmetry points in the Brillouin zone (BZ). The role of PGS in 3D semimetals will next be discussed. With only translational symmetry, band crossing points in BZ in these 3D semimetals are generically Weyl nodes, featuring 3D linear band dispersion. But the addition of PGS can in general bring together Weyl nodes of same monopole charge to a high symmetry point and create a multi-Weyl node with higher order dispersion. Such effect is explicitly shown in 3D ferromagnet HgCr$_2$Se$_4$, a double-Weyl semimetal protected by $C_4$ symmetry.
Location: Jadwin 111
Date/Time: 03/13/12 at 2:45 pm - 03/13/12 at 4:00 pm
Category: Condensed Matter Seminar