Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases

Abstract

In this paper we consider a layered heterostructure of an Abelian topologically ordered state (TO), such as a fractional Chern insulator/quantum Hall state with an s-wave superconductor in order to explore the existence of non-Abelian defects. In order to uncover such defects we must augment the original TO by a ${\mathbb{Z}}_2$ gauge theory sector coming from the s-wave SC. We first determine the extended TO for a wide variety of fractional quantum Hall or fractional Chern insulator heterostructures. We prove the existence of a general anyon permutation symmetry (AS) that exists in any fermionic Abelian TO state in contact with an s-wave superconductor. Physically this permutation corresponds to adding a fermion to an odd flux vortices (in units of $h/2e$) as they travel around the associated topological (twist) defect. As such, we call it a fermion parity flip AS. We consider twist defects which mutate anyons according to the fermion parity flip symmetry and show that they can be realized at domain walls between distinct gapped edges or interfaces of the TO superconducting state. We analyze the properties of such defects and show that fermion parity flip twist defects are always associated with Majorana zero modes. Our formalism also reproduces known results such as Majorana/parafermionic bound states at superconducting domain walls of topological/Fractional Chern insulators when twist defects are constructed based on charge conjugation symmetry. Finally, we briefly describe more exotic twist liquid phases obtained by gauging the AS where the twist defects become deconfined anyonic excitations.

14+8 pages. 6 figures

References in corpus (22)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional topological superconductors with fractionalized Majorana fermions
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Topological invariants for gauge theories and symmetry-protected topological phases
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Bridging Fermionic and Bosonic Short Range Entangled States
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors

Cited by in corpus (6)

• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• From orbifolding conformal field theories to gauging topological phases
• Families of Gapped Interfaces Between Fractional Quantum Hall States
• 3-Fermion topological quantum computation
• A coupled wire description of surface $ADE$ topological orders
• Twofold twist defect chains at criticality