Wigner crystal phases in confined carbon nanotubes

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 $J\sim 100\mathrm{K}$ 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 $4$, 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.

arXiv comment14 pages, 13 figures

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• Wigner Crystals in Two-Dimensional Transition-Metal Dichalcogenides: Spin Physics and Readout
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits
• The carbon nanotube gatemon qubit
• Drive Dependence of the Hall Angle for a Sliding Wigner Crystal in a Magnetic Field
• Energy spectrum and structure of one-dimensional few-electron Wigner crystals with and without coupling to light in cavity