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

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

3. Energy scales in artificial atoms experimental control: N, density,   / e 2 /(l  )

4. low density n high B field Tuning electron phases à la Wigner H = T + V kinetic energy e-e interaction T quenched r s = l / a B n = 1 /  l 2 = l QD / a B 2DEG: QD:

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

6. 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 Configuration interaction s p d

7. Monitoring crystallization example: N = 5 total density conditional probability    Rontani et al., Computer Phys. Commun. 2005

8. Classical geometrical phases crystallization around  (agreement with QMC) N = 6 ? conditional probability

9. No spin polarization! N = 6 single-particle basis: 36 orbitals maximum linear matrix size ≈ 1.1 10 6 for S = 1 about 600 hours of CPU time on IBM-SP4 with 40 CPUs, for each value of  and M

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

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

12. Monitoring crystallization = 2

13. Monitoring crystallization = 2.5

14. Monitoring crystallization = 3

15. Monitoring crystallization = 3.5

16. Monitoring crystallization = 4

17. Monitoring crystallization = 5

18. Monitoring crystallization = 6

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

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

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