Presentazione di PowerPoint

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Cold Melting of Solid Electron Phases in Quantum
Dots
M. Rontani, G. Goldoni INFM-S3, Modena, Italy
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Why quantum dots?
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Energy scales in artificial atoms
experimental control N, density, De
De / e2/(le)
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Tuning electron phases à la Wigner
H T V
kinetic energy
e-e interaction

low
density n high B
field
T quenched
rs l / aB
n 1 / pl2
2DEG
l lQD / aB
QD
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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)
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Configuration interaction
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
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Monitoring crystallization
example N 5
total density
l 2
conditional probability
l 10
l 2
l 10
Rontani et al., Computer Phys. Commun. 2005
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Classical geometrical phases
conditional probability

• crystallization around l 4 (agreement with
  QMC)
• N 6 ?

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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

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Fine structure of transition
l 3.5
l 2
l 6
N 6
conditional probability
fixed electron
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Normal modes at low density
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Monitoring crystallization
l 2
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Monitoring crystallization
l 2.5
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Monitoring crystallization
l 3
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Monitoring crystallization
l 3.5
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Monitoring crystallization
l 4
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Monitoring crystallization
l 5
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Monitoring crystallization
l 6
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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
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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)
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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