Majorana stripe order on the surface of a three-dimensional topological insulator

Abstract

The issue on the effect of interactions in topological states concerns not only interacting topological phases but also novel symmetry-breaking phases and phase transitions. Here we study the interaction effect on Majorana zero modes (MZMs) bound to a square vortex lattice in two-dimensional (2D) topological superconductors. Under the neutrality condition, where single-body hybridization between MZMs is prohibited by an emergent symmetry, a minimal square-lattice model for MZMs can be faithfully mapped to a quantum spin model, which has no sign problem in the world-line quantum Monte Carlo simulation. Guided by an insight from a further duality mapping, we demonstrate that the interaction induces a Majorana stripe state, a gapped state spontaneously breaking lattice translational and rotational symmetries, as opposed to the previously conjectured topological quantum criticality. Away from neutrality, a mean-field theory suggests a quantum critical point induced by hybridization.

4 pages, 5 figures + supplemental material

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Cited by in corpus (8)

• Interacting Majorana Fermions
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• Phase diagrams of Majorana-Hubbard ladders
• Supersymmetry in an interacting Majorana model on the kagome lattice
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Exact Ground States and Phase Diagram of the Quantum Compass Model under an in-plane Field
• Triangular lattice Majorana-Hubbard model: Mean field theory and DMRG on a width-4 torus
• Subsystem symmetries, critical Bose surface, and immobile excitations in an extended compass model