Wigner crystal phases in confined carbon nanotubes

TL;DR

This paper provides a comprehensive theoretical study of Wigner crystal phases in confined semiconducting carbon nanotubes, revealing an SU(4) symmetric exchange interaction and explaining experimental phase boundaries.

Contribution

It introduces a detailed semi-microscopic model showing SU(4) symmetry in exchange interactions and analyzes magnetic structures, connecting theory with experimental observations.

Findings

Exchange interaction reaches up to 100 K in small nanotubes.

Theoretical phase boundaries match experimental results.

Spin-orbit coupling modifies but does not drastically change phase boundaries.

Abstract

We present a detailed theoretical analysis of the Wigner crystal states in confined semiconducting carbon nanotubes. We show by robust scaling arguments as well as by detailed semi-microscopic calculations that the effective exchange interaction has an SU(4) symmetry, and can reach values even as large as $J\sim 100 {\rm \,K}$ in weakly screened, small diameter nanotubes, close to the Wigner crystal - electron liquid crossover. Modeling the nanotube carefully and analyzing the magnetic structure of the inhomogeneous electron crystal, we recover the experimentally observed 'phase boundaries' of Deshpande and Bockrath [V. V. Deshpande and M. Bockrath, Nature Physics $\mathbf 4$, 314 (2008)]. Spin-orbit coupling only slightly modifies these phase boundaries, but breaks the spin symmetry down to SU(2)$\times$SU(2), and in Wigner molecules it gives rise to interesting excitation spectra, reflecting the underlying SU(4) as well as the residual SU(2)$\times$SU(2) symmetries.