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?.

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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

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


Cold melting of solid electron phases in quantum dots

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


Cold melting of solid electron phases in quantum dots

Energy scales in artificial atoms

De / e2/(le)

experimental control: N, density,De


Tuning electron phases la wigner

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


Cold melting of solid electron phases in quantum dots

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)


Cold melting of solid electron phases in quantum dots

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


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

example:

N = 5

total density

l = 2

conditional probability

l = 10

l = 2

l = 10

Rontani et al., Computer Phys. Commun. 2005


Cold melting of solid electron phases in quantum dots

Classical geometrical phases

conditional probability

  • crystallization around l = 4 (agreement with QMC)

  • N = 6 ?


Cold melting of solid electron phases in quantum dots

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


Cold melting of solid electron phases in quantum dots

Fine structure of transition

l = 3.5

l = 2

l = 6

N = 6

conditional probability

= fixed electron


Cold melting of solid electron phases in quantum dots

rotational bands

cf. Koskinen et al. PRB 2001

N = 6

(mod 5) - replicas

l = 8

“Normal modes” at low density


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

l = 2


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

l = 2.5


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

l = 3


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

l = 3.5


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

l = 4


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

l = 5


Cold melting of solid electron phases in quantum dots

Monitoring crystallization

l = 6


The six electron double dot system

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


Cold melting of solid electron phases in quantum dots

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)


Cold melting of solid electron phases in quantum dots

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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