CM Seminar - Topological Skyrmion phases of matter

Abstract

We introduce topological phases of matter defined by non-trivial homotopy groups into the literature, the chiral and helical topological Skyrmion insulators. These phases generalize and extend the concepts of the Chern insulator and quantum spin Hall insulator, respectively.

Hamiltonians characterizing chiral and helical topological Skyrmion insulator phases, which also possess particle-hole symmetry, may be re-interpreted as Bogoliubov de Gennes Hamiltonians describing counterpart chiral and helical topological Skyrmion superconductor phases of matter, and we find that both superconducting phases are realized in tight-binding models for spin-triplet superconductivity in transition metal oxide compounds, with symmetry requirements for realizing these phases widespread. The chiral topological Skyrmion superconductor phase is furthermore realized for a parameter set characterizing Sr2RuO4 with spin-triplet superconductivity. As well, one kind of topological phase transition by which the relevant topological invariant, the Skyrmion number, can change occurs without the closing of energy gaps in a system described by a quadratic Hamiltonian, which has important consequences very broadly for study of topological phases of matter.