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Cold Melting of Solid Electron Phases in Quantum Dots

Cold Melting of Solid Electron Phases in Quantum Dots. Fermi liquid - like. Wigner molecule. correlation in quantum dots. configuration interaction. spin polarization. high density. low density. phase diagram. M. Rontani , G. Goldoni INFM-S3, Modena, Italy. Why quantum dots?.

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Cold Melting of Solid Electron Phases in Quantum Dots

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  1. Cold Melting of Solid Electron Phases in Quantum Dots Fermi liquid - like Wigner molecule correlation in quantum dots configuration interaction spin polarization high density low density phase diagram M. Rontani, G. Goldoni INFM-S3, Modena, Italy

  2. Why quantum dots? potential for new devices single-electron transistor, laser, single-photon emitter laboratory to explore fundamentals of few-body physics quantum control of charge and spin degrees of freedom easy access to different correlation regimes

  3. Energy scales in artificial atoms De / e2/(le) experimental control: N, density,De

  4. Tuning electron phases à la Wigner H = T + V kinetic energy e-e interaction low density nhigh B field Tquenched 2DEG: rs = l / aB n = 1 / pl2 QD: l = lQD / aB

  5. Open questions in correlated regimes 2D: spin-polarized phase? disorder favors crystal ferromagnet 0D: crystallization? spin polarization? melting? crystal liquid Tanatar and Ceperley 1989 controversy for N = 6 QMC: R. Egger et al., PRL 82, 3320 (1999) CI: S. M. Reimann et al., PRB 62, 8108 (2000)

  6. Configuration interaction d p s envelope function approximation, semiconductor effective parameters second quantization formalism 1) Compute H parameters from the chosen single-particle basis 2) Compute the wavefunction as a superposition of Slater determinants

  7. Monitoring crystallization example: N = 5 total density l = 2 conditional probability l = 10 l = 2 l = 10 Rontani et al., Computer Phys. Commun. 2005

  8. Classical geometrical phases conditional probability • crystallization around l = 4 (agreement with QMC) • N = 6 ?

  9. No spin polarization! N = 6 • single-particle basis: 36 orbitals • maximum linear matrix size ≈1.1 106 for S = 1 • about 600 hours of CPU time on IBM-SP4 with 40 CPUs, for each value of l and M

  10. Fine structure of transition l = 3.5 l = 2 l = 6 N = 6 conditional probability = fixed electron

  11. rotational bands cf. Koskinen et al. PRB 2001 N = 6 (mod 5) - replicas l = 8 “Normal modes” at low density

  12. Monitoring crystallization l = 2

  13. Monitoring crystallization l = 2.5

  14. Monitoring crystallization l = 3

  15. Monitoring crystallization l = 3.5

  16. Monitoring crystallization l = 4

  17. Monitoring crystallization l = 5

  18. Monitoring crystallization l = 6

  19. The six-electron double-dot system Numerical results top view top-dot electron bottom-dot electron phase I phase II phase III Rontani et al., EPL 2002

  20. Cold melting I and III classical configurations same dot different dots II novel quantum phase, liquid-like Rontani et al., EPL 2002 I III (rad)

  21. Conclusion phase diagram of low-density quantum dots spin-unpolarized N = 6 ground state classically metastable phase close to melting How to measure? inelastic light scattering [EPL 58, 555 (2002); cond-mat/0506143] tunneling spectroscopies [cond-mat/0408454] FIRB, COFIN-2003, MAE, INFM I.T. Calcolo Parallelo http://www.s3.infm.it

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