Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors

Abstract

We construct microscopic Hamiltonians for symmetry-preserving topologically ordered states on the surface of topological crystalline superconductors, protected by a ${\mathbb{Z}}_2$ reflection symmetry. Starting from $\nu$ Majorana cones on the surface, we show that the semion-fermion topological order emerges for $\nu =2$, and more generally, $\mathrm{SO}(\nu {)}_{\nu }$ topological order for all $\nu \ge 2$ and $\mathrm{Sp}(n{)}_n$ for $\nu =2n$.

references updated; published version

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Cited by in corpus (8)

• Anomalies and Symmetry Fractionalization
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• From coupled wires to coupled layers: Model with three-dimensional fractional excitations
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Boundary topological orders of (4+1)d fermionic ${\mathbb{Z}}_{2N}^{\mathrm{F}}$ SPT states
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly