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Coulomb versus spin-orbit interaction in carbon-nanotube quantum dots

Coulomb versus spin-orbit interaction in carbon-nanotube quantum dots. Andrea Secchi and Massimo Rontani. CNR-INFM Research Center S3 and University of Modena, Modena, Italy. exact diagonalization of few-electron Hamiltonian clarification of recent tunneling experiments.

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Coulomb versus spin-orbit interaction in carbon-nanotube quantum dots

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  1. Coulomb versus spin-orbit interaction in carbon-nanotube quantum dots Andrea Secchi and Massimo Rontani CNR-INFM Research Center S3 and University of Modena, Modena, Italy • exact diagonalization of few-electron Hamiltonian • clarification of recent tunneling experiments

  2. Carbon-nanotube quantum dots quasi-1D systems F. Kuemmeth et al., Nature 452, 448 (2008) double degeneracy

  3. Strong correlation or not in CN QDs?

  4. Strong correlation or not in CN QDs? Low temperature SETS experiment spin-orbit interaction splits 4-fold degenerate spin-orbitals spin isospin

  5. Strong correlation or not in CN QDs? the simplest interpretation two-electron ground state: one Slater determinant no correlation chemical potential

  6. CI model: 1D harmonic potential configuration-interaction (CI) calculation: two valleys QD: harmonic potential forward & backward Coulomb interactions spin-orbit coupling free parameter: e theory exp M. Rontani et al., JCP 124, 124102 (2006)

  7. Strongly correlated CI wave functions different harmonic oscillator quantum numbers A & B states: strongly correlated same orbital wave functions differ in isospin only isospin = valley population A. Secchi and M. Rontani, arXiv: 0903.5107

  8. A and B: correlated T3 = 0, 1 split by spin-orbit int. only T3 = 1 T3 = 0 T3 = -1/2 T3 = 1/2 Independent-particle feature explained exp theo N = 2 N = 1 B(T) A. Secchi and M. Rontani, arXiv: 0903.5107

  9. Non-universal tunneling spectrum exp N = 2 N = 1 A. Secchi and M. Rontani, arXiv: 0903.5107

  10. n(x) x CI two-electron energy spectrum ungerade gerade A. Secchi and M. Rontani, arXiv: 0903.5107

  11. Pair correlation functions g(X) = probability to find a couple of electrons at relative distance X

  12. Conclusions • spin-orbit and Coulomb interactions coexist • non-interacting features of tunneling spectra explained • we predict electrons to form a Wigner molecule andrea.secchi@unimore.it massimo.rontani@unimore.it www.s3.infm.it www.nanoscience.unimore.it/max.html

  13. Single-particle Hamiltonian Bloch states in K and K’ valleys envelope function spin-orbit interaction and magnetic field

  14. Effective 1D Coulomb interaction Ohno potential trace out x and z degrees of freedom forward backward

  15. Fully interacting Hamiltonian

  16. six-fold degenerate Spin-orbit coupling for two electrons

  17. isospin T = additional degree of freedom either (S = 0, T = 1) or (S = 1, T = 0) Tz = -1, 0, +1 Sz = -1, 0, +1 Wigner-Mattis theorem is not appliable in nanotubes nodeless in the ground state S = 0

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