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Cold Melting of Solid Electron Phases in Quantum Dots

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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?

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

Energy scales in artificial atoms

De / e2/(le)

experimental control: N, density,De

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

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)

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

Monitoring crystallization

example:

N = 5

total density

l = 2

conditional probability

l = 10

l = 2

l = 10

Rontani et al., Computer Phys. Commun. 2005

Classical geometrical phases

conditional probability

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

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

Fine structure of transition

l = 3.5

l = 2

l = 6

N = 6

conditional probability

= fixed electron

rotational bands

cf. Koskinen et al. PRB 2001

N = 6

(mod 5) - replicas

l = 8

“Normal modes” at low density

Monitoring crystallization

l = 2

Monitoring crystallization

l = 2.5

Monitoring crystallization

l = 3

Monitoring crystallization

l = 3.5

Monitoring crystallization

l = 4

Monitoring crystallization

l = 5

Monitoring crystallization

l = 6

Numerical results

top

view

top-dot electron

bottom-dot electron

phase I

phase II

phase III

Rontani et al., EPL 2002

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)

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