Topological skyrmion phases of matter

TL;DR

This paper introduces a new class of topological phases called skyrmion phases in superconductors, revealing novel phase transitions and boundary signatures, with implications for Majorana modes and quantum transport.

Contribution

It defines topological skyrmion phases in superconductors, demonstrates their realization in models, and uncovers new phase transition mechanisms and boundary signatures.

Findings

Realization of skyrmion phases in a tight-binding model for spin-triplet superconductivity.

Identification of two types of topological phase transitions, including one without energy gap closing.

Prediction of two bulk-boundary signatures, including quantized transport and Majorana modes.

Abstract

We introduce topological phases of matter defined by skyrmions in the ground state spin -- or pseudospin -- expectation value textures in the Brillouin zone, the chiral and helical topological skyrmion phases of matter. These phases are protected by a symmetry present in centrosymmetric superconductors. We consider a tight-binding model for spin-triplet superconductivity in transition metal oxides and find it realizes each of these topological skyrmion phases. The chiral phase is furthermore realized for a parameter set characterizing Sr$_2$RuO$_4$ with spin-triplet superconductivity. We also find two types of topological phase transitions by which the skyrmion number can change. The second type occurs without the closing of energy gaps in a system described by a quadratic Hamiltonian without breaking the protecting symmetries when atomic spin-orbit coupling is non-negligible and there is a suitable additional degree of freedom. This contradicts the ``flat band'' limit assumption important in use of entanglement spectrum and Wilson loops, and in construction of the ten-fold way classification scheme of topological phases of matter. We furthermore predict two kinds of bulk-boundary correspondence signatures -- one for measurements which execute a partial trace over degrees of freedom other than spin, which yields quantized transport signatures -- and a second resulting from skyrmions trapping defects with their own non-trivial topology that is discussed in a second work, which yields generalizations of unpaired Majorana zero-modes.