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.

14 pages, 13 figures

References in corpus (16)

• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Coupling of Spin and Orbital Motion of Electrons in Carbon Nanotubes
• Orbital Kondo effect in carbon nanotubes
• Static dielectric properties of carbon nanotubes from first principles
• Nonequilibrium Singlet-Triplet Kondo Effect in Carbon Nanotubes
• Spin-orbit interaction and anomalous spin relaxation in carbon nanotube quantum dots
• Wigner crystal physics in quantum wires
• Dependence of exciton transition energy of single-walled carbon nanotubes on surrounding dielectric materials
• Incipient Formation of an Electron Lattice in a Weakly-Confined Quantum Wire
• Coulomb versus spin-orbit interaction in few-electron carbon-nanotube quantum dots
• AFM probe for the signatures of Wigner correlations in the conductance of a one-dimensional quantum dot
• Few-electron physics in a nanotube quantum dot with spin-orbit coupling
• Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement
• Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models
• The Magnetic Ordering of the 3d Wigner Crystal
• Wigner localization in a graphene quantum dot with a mass gap

Cited by in corpus (3)

• 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
• Energy spectrum and structure of one-dimensional few-electron Wigner crystals with and without coupling to light in cavity