Wigner molecules in carbon-nanotube quantum dots

Abstract

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a `Wigner molecule'. Our exact diagonalisation calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy -indeed some of them have already been observed by Deshpande and Bockrath [Nature Phys. 4, 314 (2008)]. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions.

12 pages (6 color figures, 3 b/w figures, 3 tables). This paper has been extensively revised, including more theoretical material, the discussion of experiments by Deshpande and Bockrath (Nature Phys. 2008) and Kuemmeth et al. (Nature 2008), the location of their quantum-dot devices in the proposed theoretical phase diagram. To appear in Physical Review B

References in corpus (20)

• Valley filter and valley valve in graphene
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Coupling of Spin and Orbital Motion of Electrons in Carbon Nanotubes
• Universal theory of nonlinear Luttinger liquids
• Full configuration interaction approach to the few-electron problem in artificial atoms
• Electron-nuclear interaction in 13C nanotube double quantum dots
• Tunable few-electron double quantum dots and Klein tunnelling in ultra-clean carbon nanotubes
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Excitation spectrum of two correlated electrons in a lateral quantum dot with negligible Zeeman splitting
• A molecular state of correlated electrons in a quantum dot
• All-Optical Manipulation of Electron Spins in Carbon-Nanotube Quantum Dots
• Absence of Wigner Crystallization in Graphene
• Coulomb versus spin-orbit interaction in few-electron carbon-nanotube quantum dots
• Correlated electrons in optically-tunable quantum dots: Building an electron dimer molecule
• Few-electron physics in a nanotube quantum dot with spin-orbit coupling
• Intermediate Low Spin States in a Few-electron Quantum Dot in the $\nu \le 1$ Regime
• The low energy spectrum of finite size metallic SWNTs
• The spectrum of interacting metallic carbon nanotubes: Exchange effects and universality
• Deformed Wigner crystal in a one-dimensional quantum dot
• Exchange effects in spin polarized transport through carbon nanotube quantum dots

Cited by in corpus (24)

• Quantum transport in carbon nanotubes
• Imaging the Wigner Crystal of Electrons in One Dimension
• Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube
• Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes
• Spin-Orbit Effects in Carbon-Nanotube Double Quantum Dots
• Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization
• Three interacting atoms in a one-dimensional trap: A benchmark system for computational approaches
• Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions
• Inter-valley scattering induced by Coulomb interaction and disorder in carbon-nanotube quantum dots
• One-dimensional few-electron effective Wigner crystal in quantum and classical regimes
• Wigner crystal phases in confined carbon nanotubes
• Wigner localization in a graphene quantum dot with a mass gap
• Double Quantum Dots in Carbon Nanotubes
• Fermionic versus bosonic behavior of confined Wigner molecules
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits
• Shape-sensitive Pauli blockade in a bent carbon nanotube
• Wigner molecules in phosphorene quantum dots
• Current hot spot in the spin-valley blockade in carbon nanotubes
• Exchange and correlation effects in the transmission phase through a few-electron quantum dot
• Interaction-driven giant orbital magnetic moments in carbon nanotubes
• Collective ground states in small lattices of coupled quantum dots
• Inter- and intra-band Coulomb interactions between holes in silicon nanostructures
• Binding and spontaneous condensation of excitons in narrow-gap carbon nanotubes
• Anomalous screening in narrow-gap carbon nanotubes