Post on 17-Jan-2016
Wigner moleculesin carbon-nanotube quantum dots
Massimo Rontani and Andrea SecchiS3, Istituto di Nanoscienze – CNR, Modena, Italy
ultraclean semiconducting nanotubes
Bockrath group, Nature Phys. 2008 McEuen group, Nature 2008
gate-defined quantum dots
shallow confinement potentials (approx. parabolic)
ultraclean semiconducting nanotubesMcEuen group, Nature 2008
chem
ical p
ote
nti
al (
N)Bockrath group, Nature Phys. 2008
chem
ical p
ote
nti
al (
N)
0 8B (T)
1h
3h
5h
B (T)B (T)
1e
2e
3e
20 2
*)(
mRg
BEN B
ultraclean semiconducting nanotubesBockrath group, Nature Phys. 2008 McEuen group, Nature 2008
chem
ical p
ote
nti
al (
N)
chem
ical p
ote
nti
al (
N)
0 8B (T)
1h
3h
5h
B (T)B (T)
1e
2e
3e
20 2
*)(
mRg
BEN B
)1()( 000 NENEE
independent from B
ultraclean semiconducting nanotubesBockrath group, Nature Phys. 2008 McEuen group, Nature 2008
chem
ical p
ote
nti
al (
N)
chem
ical p
ote
nti
al (
N)
0 8B (T)
1h
3h
5h
B (T)B (T)
1e
2e
3e
20 2
*)(
mRg
BEN B
)1()( NN spin added electron
ultraclean semiconducting nanotubesBockrath group, Nature Phys. 2008 McEuen group, Nature 2008
chem
ical p
ote
nti
al (
N)
chem
ical p
ote
nti
al (
N)
0 8B (T)
1h
3h
5h
B (T)B (T)
1e
2e
3e
20 2
*)(
mRg
BEN B
)1()( NN isospin added el.(angular momentum)
ultraclean semiconducting nanotubesBockrath group, Nature Phys. 2008 McEuen group, Nature 2008
chem
ical p
ote
nti
al (
N)
chem
ical p
ote
nti
al (
N)
0 8B (T)
1h
3h
5h
B (T)B (T)
1e
2e
3e
20 2
*)(
mRg
BEN B
ground statespin & isospinpolarized
Wigner molecule?
single-particle + spin-orbit
motivation
Coulomb interaction vs single-particle physics
role of interaction?
exps at Harvard and Delft on coherent spin manipulation
outlook (I)
similar issues for graphene quantum dots
similar theoretical approach (see next slide)
Hamiltonian
exact diagonalisation ground & excited states
many-body term: Ohno potential, inter- and intra-valley channels (including short range terms)many-body term: Ohno potential, inter- and intra-valley channels (including short range terms)
compute the wavefunction as a superposition of Slater compute the wavefunction as a superposition of Slater
determinantsdeterminants ij
i
Ni
NiN HHc 0|| †
''† ml
Ni cc
Rontani et al., J. Chem. Phys. 124, 124102 (2006)
single-particle term: mass + isospin + 1D harmonic confinement + single-particle term: mass + isospin + 1D harmonic confinement + BB + spin-orbit coupling + spin-orbit coupling
compute compute ((NN), ), nn((xx), ), gg((xx),… ),…
envelope function envelope function approximationapproximationLuttinger and Kohn 1955, Ando 2005
)(),,()();,,( szyxxFszyx nn
)2()1( ˆˆˆ VHH
experimental evidence
split 4-fold degenerate spin-orbitals
non-interacting physics?
two-electron ground state:
one Slater determinant
no correlation chem
ical
pote
nti
al
the simplest interpretation
theory vs experiment
theoryPRB 80, 041404(R) (2009) McEuen group 2008
B (T)
dielectric constant
fitting parameter
strongly correlated wave functions
A & B states:
strongly correlated
same orbital wave functions
differ in isospin only
A. Secchi and M.R., PRB 80, 041404(R) (2009)
isospin = valley population
spectrum affected by interaction
N = 2
N = 1
A. Secchi & M.R., PRB 80, 041404(R) (2009)
interaction strength
SO
SO
crystallization criterionA. Secchi & M.R., PRB 82, 035417 (2010) Bockrath group, Nature Phys. 2008
chem
ical p
ote
nti
al (
N)
0 8B (T)
1h
3h
5h
crystallization criterionA. Secchi & M.R., PRB 82, 035417 (2010) A. Secchi & M.R., PRB 82, 035417 (2010)
a = WMb = particle-in-a-box
a
b
conclusions
Wigner molecules form in realistic samples
outlook (II)quantum devices (localization + spin-orbit coupling + electric control)
scanning tunneling spectroscopy
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w.n
an
oscie
nce
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imore
.it/max.h
tml
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w.n
an
o.c
nr.
it
nanotube quantum dots strongly correlated
graphene quantum dots
few-body physics of cold Fermi atomsM. Rontani et al., PRL 102, 060401 (2009)