Transcript Presentazione di PowerPoint - Istituto Nazionale di Ottica

Wigner molecules
in carbon-nanotube quantum dots
Massimo Rontani and Andrea Secchi
S3, 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 nanotubes
5h
3h
1h
0
McEuen group, Nature 2008
chemical potential m(N)
chemical potential m(N)
Bockrath group, Nature Phys. 2008
3e
2e
1e
8
B (T)
B (T)
B (T)
m R
 g*

  2  

 2

m ( N )  E0  m B B
ultraclean semiconducting nanotubes
5h
3h
1h
0
McEuen group, Nature 2008
chemical potential m(N)
chemical potential m(N)
Bockrath group, Nature Phys. 2008
3e
2e
1e
8
B (T)
m R
 g*

m ( N )  E0  m B B   2  

 2

B (T)
B (T)
E0  E0 ( N )  E0 ( N  1)
independent from B
ultraclean semiconducting nanotubes
5h
3h
1h
0
McEuen group, Nature 2008
chemical potential m(N)
chemical potential m(N)
Bockrath group, Nature Phys. 2008
3e
2e
1e
8
B (T)
m R
 g*

m ( N )  E0  m B B   2  

 2

B (T)
B (T)
   ( N )   ( N  1)
spin added electron
ultraclean semiconducting nanotubes
5h
3h
1h
0
McEuen group, Nature 2008
chemical potential m(N)
chemical potential m(N)
Bockrath group, Nature Phys. 2008
3e
2e
1e
8
B (T)
m R
 g*

m ( N )  E0  m B B   2  

 2

B (T)
B (T)
   ( N )   ( N  1)
isospin added el.
(angular momentum)
ultraclean semiconducting nanotubes
5h
3h
McEuen group, Nature 2008
ground state
spin & isospin
polarized
1h
0
chemical potential m(N)
chemical potential m(N)
Bockrath group, Nature Phys. 2008
3e
2e
1e
8
B (T)
B (T)
B (T)
m R
 g*

  2  

 2

m ( N )  E0  m B B
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
envelope function approximation
n ( x, y, z; s)  Fn ( x) ( x, y, z)  (s)
Luttinger and Kohn 1955, Ando 2005
single-particle term: mass + isospin + 1D harmonic confinement + B + spin-orbit coupling
many-body term: Ohno potential, inter- and intra-valley channels (including short range terms)
(1)
( 2)
ˆ
ˆ
ˆ
H  H V
compute the wavefunction as a superposition of Slater determinants
| iN   cl† cm†  ' ' | 0
N   ciN iN

H  Hij
i
Rontani et al., J. Chem. Phys. 124, 124102 (2006)
compute m(N), n(x), g(x),…
exact diagonalisation
ground & excited states
experimental evidence
split 4-fold degenerate
spin-orbitals
non-interacting physics?
two-electron ground state:
one Slater determinant
no correlation
chemical potential
the simplest interpretation
theory vs experiment
PRB 80, 041404(R) (2009)
McEuen group 2008
theory
dielectric constant
fitting parameter
B (T)
strongly correlated wave functions
A & B states:
strongly correlated
same orbital wave
functions
differ in isospin only
isospin =
valley population
A. Secchi and M.R., PRB 80, 041404(R) (2009)
spectrum affected by interaction
SO
N=2
N=1
SO
interaction strength
A. Secchi & M.R., PRB 80, 041404(R) (2009)
crystallization criterion
Bockrath group, Nature Phys. 2008
chemical potential m(N)
A. Secchi & M.R., PRB 82, 035417 (2010)
5h
3h
1h
0
8
B (T)
crystallization criterion
A. Secchi & M.R., PRB 82, 035417 (2010)
A. Secchi & M.R., PRB 82, 035417 (2010)
a
b
a = WM
b = particle-in-a-box
conclusions
www.nano.cnr.it
Wigner molecules form in realistic samples
outlook (II)
quantum devices
(localization + spin-orbit coupling + electric control)
scanning tunneling spectroscopy
graphene quantum dots
few-body physics of cold Fermi atoms
M. Rontani et al., PRL 102, 060401 (2009)
www.nanoscience.unimore.it/max.html
nanotube quantum dots strongly correlated