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