Negative differential conductance with symmetric set-updoa17296/fisica/Curriculum/Talks/...Single...
Transcript of Negative differential conductance with symmetric set-updoa17296/fisica/Curriculum/Talks/...Single...
Frühjahrstagung Dresden 2011
Negative differential conductance with symmetric set-up ?
Andrea Donarini, Abdullah Yar, and Milena Grifoni
Institut für Theoretische Physik
Universität Regensburg
Single electron transistor
Small System size+ weak System‐Lead Tunnelling coupling
Strong e‐einteraction
on the System
Single electroncontrol
Vg
μS μDμN
μN‐1
μN+1
μN = E N ‐ E N‐1The chemical potential of the System with N particles
Vb
Source Drain
Gate
System
Vb
Vg
Single electron transistor
Small System size+ weak System‐Lead Tunnelling coupling
Strong e‐einteraction
on the System
Single electroncontrol
Vg
μS μDμN
μN‐1
μN+1
Vb
Source Drain
Gate
System
Vb
Vg
Vg
G
N‐1 N N+1
Single electron transistor
Small System size+ weak System‐Lead Tunnelling coupling
Strong e‐einteraction
on the System
Single electroncontrol
Vg
μS μDμN
μN‐1
μN+1
Vb
Source Drain
Gate
System
Vb
Vg
Vb
IdIdVb
Negative Differential Conductance
μS μDμN
μN‐1
μN+1
Vb
I
Negative differential conductance (NDC) is usually associatedwith a strong asymmetry in the coupling to the leads
dIdVb
NDC
The free energy formulation
Particle Number
Free
Ene
rgy
NN‐1 N+1
N‐1 N N+1Vg
Vb
AD, G Begemann, Milena GrifoniPRB, 82, 125451 (2010)
F = H – μ0N Free energy
Source transition
Drain transition
The free energy formulation
Particle Number
Free
Ene
rgy
NN‐1 N+1
N‐1 N N+1Vg
Vb
F = H – μ0N Free energy
Source transition
Drain transition
AD, G Begemann, Milena GrifoniPRB, 82, 125451 (2010)
NDC with symmetric set-upFree
Ene
rgy
N N+1
N N+1
Vg
Vb
A
B
The dynamics is evaluated with themaster equation: in the stationary limit
PN,0
A
B
PN+1,0 PN+1,1 Current
1/2 1/2 0
1/3 1/3 1/3
Γ01
Γ00
Γ00/2
1/3(Γ00 + Γ01)
NDC if IB < IA
Γ01 < Γ00/2
Role of the degeneraciesFree
Ene
rgy
N N+1
N N+1
Vg
Vb
A
BΓ01
Γ00
A
B
PN,0 PN+1,0 PN+1,1 Current
1/3 1/3 0
1/5 1/5 1/5
2Γ00/3
2/5(Γ00 + Γ01)
NDC if IB < IA
Γ01 < 2Γ00/3
The dynamics is evaluated with themaster equation: in the stationary limit
x 2
x 2
Role of the degeneraciesFree
Ene
rgy
N N+1
N N+1
Vg
Vb
A
BΓ01
Γ00
A
B
PN,0 PN+1,0 PN+1,1 Current
0 Γ00
(Γ00 + Γ01)
NDC if IB < IA
Γ01 < Γ00
The dynamics is evaluated with themaster equation: in the stationary limit
n x
x m
x m
n+m1
n+m1
n+2m
1
n+2m
1
n+2m
1n+mnm
n+2mnm n+m
m
An example: a suspended CNTFree
Ene
rgy
4N 4N+1
x 4
x 4
x 8
1 x
1 x
2 xћω
ћω
The transition rates are proportional to product of Frack‐Condon coefficients
∏=Γn
nij jiFC );,()( λ
A. Yar, AD, S. Koller, and M. Grifoni, arXiv:1101.3892 (2011)
An example: a suspended CNTFree
Ene
rgy
4N 4N+1
x 4
x 4
x 8
1 x
1 x
2 x
λ= 0.68 λ= 0.83 λ= 1.18
A. Yar, AD, S. Koller, and M. Grifoni, arXiv:1101.3892 (2011)
Conclusions
Transport through a single electron transistor is conveniently described bytransition between many‐body states in the free energy diagram
The negative differential conductance is the result of a redistribution of probabilities between fast and slow channels thus:
It is possible also in a completely symmetric set‐up .
It is related to the degeneracies of the many‐body
Suspended carbon nanotube quantum dots exhibits the NDC presentedhere due to the interplay between Franck‐Condon coefficients and spin/pseudospin degeneracies.
Thanks for your attention !
Particle Number
Free
Ene
rgy
NN‐1 N+1