Correlated insulating states in carbon nanotubes controlled by magnetic field

TL;DR

This paper explores how magnetic fields influence insulating states in nearly metallic zigzag carbon nanotubes, revealing multiple competing phases and symmetry-breaking phenomena driven by electron interactions and spin-orbit effects.

Contribution

It introduces a bosonic low-energy effective theory to map the phase diagram of insulating states near the magnetic flux-induced gap closing in carbon nanotubes.

Findings

Multiple insulating phases identified near the gap closing point.

Spontaneous mirror symmetry breaking leads to charge and spin currents.

Persistent energy gap observed despite single-particle predictions.

Abstract

We investigate competing insulating phases in nearly metallic zigzag carbon nanotubes, under conditions where an applied magnetic flux approximately closes the single particle gap in one valley. Recent experiments have shown that an energy gap persists throughout magnetic field sweeps where the single-particle picture predicts that the gap should close and reopen. Using a bosonic low-energy effective theory to describe the interplay between electron-electron interactions, spin-orbit coupling, and magnetic field, we obtain a phase diagram consisting of several competing insulating phases that can form in the vicinity of the single-particle gap closing point. We characterize these phases in terms of spin-resolved charge polarization densities, each of which can independently take one of two possible values consistent with the mirror symmetry of the system, or can take an intermediate value through a spontaneous mirror symmetry breaking transition. In the mirror symmetry breaking phase, adiabatic changes of the orbital magnetic flux drive charge and spin currents along the nanotube. We discuss the relevance of these results to recent and future experiments.