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

TL;DR

This paper investigates how interactions affect Majorana zero modes on the surface of a 3D topological insulator, revealing a new symmetry-breaking Majorana stripe order through quantum Monte Carlo simulations.

Contribution

It introduces a minimal lattice model for Majorana zero modes that maps to a sign-problem-free quantum spin model, demonstrating the emergence of Majorana stripe order due to interactions.

Findings

Interaction induces a Majorana stripe state breaking lattice symmetries

Model maps to a sign-problem-free quantum spin model

Interaction effects lead to symmetry-breaking phases rather than topological criticality

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.