Wigner molecules in carbon-nanotube quantum dots Massimo Rontani and Andrea Secchi S3, Istituto di Nanoscienze – CNR, Modena, Italy.

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Presentation transcript:

Wigner molecules in carbon-nanotube quantum dots Massimo Rontani and Andrea Secchi S3, Istituto di Nanoscienze – CNR, Modena, Italy

ultraclean semiconducting nanotubes Bockrath group, Nature Phys. 2008McEuen group, Nature 2008 gate-defined quantum dots shallow confinement potentials (approx. parabolic)

ultraclean semiconducting nanotubes McEuen group, Nature 2008 chemical potential  (N) Bockrath group, Nature Phys chemical potential  (N) 0 8 B (T) 1h 3h 5h B (T) 1e 2e 3e

ultraclean semiconducting nanotubes Bockrath group, Nature Phys. 2008McEuen group, Nature 2008 chemical potential  (N) 0 8 B (T) 1h 3h 5h B (T) 1e 2e 3e independent from B

ultraclean semiconducting nanotubes Bockrath group, Nature Phys. 2008McEuen group, Nature 2008 chemical potential  (N) 0 8 B (T) 1h 3h 5h B (T) 1e 2e 3e spin added electron

ultraclean semiconducting nanotubes Bockrath group, Nature Phys. 2008McEuen group, Nature 2008 chemical potential  (N) 0 8 B (T) 1h 3h 5h B (T) 1e 2e 3e isospin added el. (angular momentum)

ultraclean semiconducting nanotubes Bockrath group, Nature Phys. 2008McEuen group, Nature 2008 chemical potential  (N) 0 8 B (T) 1h 3h 5h B (T) 1e 2e 3e ground state spin & isospin polarized Wigner molecule? single-particle + spin-orbit

motivation Coulomb interaction vs single-particle physics role of interaction? exps at Harvard and Delft on coherent spin manipulation outlook (I) similar issues for graphene quantum dots similar theoretical approach (see next slide)

Hamiltonian exact diagonalisation ground & excited states many-body term: Ohno potential, inter- and intra-valley channels (including short range terms) compute the wavefunction as a superposition of Slater determinants Rontani et al., J. Chem. Phys. 124, (2006) single-particle term: mass + isospin + 1D harmonic confinement + B + spin-orbit coupling compute  (N), n(x), g(x),… envelope function approximation Luttinger and Kohn 1955, Ando 2005

experimental evidence split 4-fold degenerate spin-orbitals

non-interacting physics? two-electron ground state: one Slater determinant no correlation chemical potential the simplest interpretation

theory vs experiment theory PRB 80, (R) (2009)McEuen group 2008 B (T) dielectric constant fitting parameter

strongly correlated wave functions A & B states: strongly correlated same orbital wave functions differ in isospin only A. Secchi and M.R., PRB 80, (R) (2009) isospin = valley population

spectrum affected by interaction N = 2 N = 1 A. Secchi & M.R., PRB 80, (R) (2009) interaction strength  SO

crystallization criterion A. Secchi & M.R., PRB 82, (2010) Bockrath group, Nature Phys chemical potential  (N) 0 8 B (T) 1h 3h 5h

crystallization criterion A. Secchi & M.R., PRB 82, (2010) a = WM b = particle-in-a-box a b

conclusions Wigner molecules form in realistic samples outlook (II) quantum devices (localization + spin-orbit coupling + electric control) scanning tunneling spectroscopy nanotube quantum dots strongly correlated graphene quantum dots few-body physics of cold Fermi atoms M. Rontani et al., PRL 102, (2009)