Anomalous flux state in higher-order topological superconductors

TL;DR

This paper explores the unique flux states in higher-order topological superconductors, revealing robust zero modes and supersymmetric properties linked to rotation symmetry and fermion parity, with implications for quantum magnetism.

Contribution

It demonstrates the existence of anomalous flux states and supersymmetries in HOTSCs, connecting these phenomena to quantum magnets and emergent Majorana modes.

Findings

Zero modes trapped at $\

in 2D HOTSCs

Flux lines in 3D HOTSCs carry anomalous helical modes,

Abstract

We investigate the anomalous flux state of interacting higher-order topological superconductors (HOTSC) protected by rotation symmetries. By introducing a $\pi$ superconducting flux in 2D HOTSC, we demonstrate the existence of a robust zero mode trapped at the flux center. Remarkably, the rotation symmetry and fermion parity display projective representation inside the $\pi$ flux with $N=2$ supersymmetry algebra. A similar gapless flux pattern also exists in 3D HOTSCs, the flux lines of which carry anomalous helical modes that cannot be realized on purely one-dimensional lattice models. Notably, these exotic phenomena can be manifested in a 2D frustrated quantum magnet whose low energy excitation characterizes emergent Majoranas with HOTSC band structure and the $Z_2$ flux exhibiting supersymmetries.