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Wigner molecules in carbon-nanotube quantum dots

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. 2008. McEuen group, Nature 2008. gate-defined quantum dots.

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Wigner molecules in carbon-nanotube quantum dots

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

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

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

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

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

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

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

  8. 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)

  9. envelope function approximation Luttinger and Kohn 1955, Ando 2005 compute the wavefunction as a superposition of Slater determinants Rontani et al., J. Chem. Phys. 124, 124102 (2006) Hamiltonian single-particle term: mass + isospin + 1D harmonic confinement + B + spin-orbit coupling many-body term: Ohno potential, inter- and intra-valley channels (including short range terms) compute m(N), n(x), g(x),… exact diagonalisation ground & excited states

  10. experimental evidence split 4-fold degenerate spin-orbitals

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

  12. theory vs experiment PRB 80, 041404(R) (2009) McEuen group 2008 theory dielectric constant fitting parameter B (T)

  13. strongly correlated wave functions A & B states: strongly correlated same orbital wave functions differ in isospin only isospin = valley population A. Secchi and M.R., PRB 80, 041404(R) (2009)

  14. DSO interaction strength DSO spectrum affected by interaction N = 2 N = 1 A. Secchi & M.R., PRB 80, 041404(R) (2009)

  15. Bockrath group, Nature Phys. 2008 chemical potential m(N) 5h 3h 1h 8 0 B (T) crystallization criterion A. Secchi & M.R., PRB 82, 035417 (2010)

  16. crystallization criterion A. Secchi & M.R., PRB 82, 035417 (2010) A. Secchi & M.R., PRB 82, 035417 (2010) a b a = WM b = particle-in-a-box

  17. conclusions nanotube quantum dots strongly correlated Wigner molecules form in realistic samples outlook (II) www.nano.cnr.it www.nanoscience.unimore.it/max.html quantum devices (localization + spin-orbit coupling + electric control) scanning tunneling spectroscopy graphene quantum dots few-body physics of cold Fermi atoms M. Rontani et al., PRL 102, 060401 (2009)

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