Molecular electronics IV

• Advertisment• Back to CB or no CB

– single dot versus metallic dot• Coherent scattering on a vibration• Kondo and vibration

Niels Bohr Summer Institute 2005Niels Bohr Institute and Nano-Science Center

Transport in mesoscopic and single-molecule systems

In the series of Niels Bohr Summer Institutes a workshop on transport phenomena in nanostructures is held in Copenhagen, Denmark, in August 2005.

The fields of mesoscopic physics and single-molecular systems face common challenges in understanding the interplay of transport and correlation and interference phenomena. Therefore these two branches of nanoscience can benefit from joining their efforts and one of the main objectives of this meeting is to mediate such fruitful interaction. In order to achieve this goal, The Niels Bohr Summer Institute invites a number of distinguished researchers to participate in the workshop and the meeting is open to all interested researchers upon application.

The workshop will have introductory level lectures and excersises for Ph.D. students in the summer school and a symposium in the second week.

15-19 August Summer School22-26 August Symposium

www.nbi.ku.dk/nbsi2005

Coulomb blockade or no Coulomb blockade

Few level dot: large spacing between level

U

But also

If different story!Correlation part of separation of charge states

U Spacing ∆

“Usual” story for metallic island

R

CCondition for Coulomb blockade

What is R?Current of one and many levels

or

“Metallic” quantum dotN+1 electron state:

U

One electron occupying one N-electron state

Question: what is the probability that one N+1 electron state is occupied ??

UVg

Condition for CB in “metallic dot”

( with many levels all coupled weakly to the leads )

But:

If more than one level is fully transmitting is again a different story:

QDLeftlead

Rightlead

The open channelscreens away the chargingenergy associated with tunnelingthrough the other levels

Conclusions:

A “large” conductace or current does not by itself mean absence of CBfor a single level system, only Γ À U does

For large molecule (many levels) absence of CB means R À h/e2

Broadening of steps

Two possible mechanisms:

1. The molecular motion is damped -> finite lifetime of phonons

2. Strong tunnel coupling between molecular levelsand electronic stats of the leads -> finite lifetime of electronic state

Numbers for C60

x

Van der Waals interactionsOscillator frequency: 5 meV = 1 THz Oscillator length: 0.2 pmPosition dependence of tunneling: exp(-x κ) ~ 1, κ =1/(2 nm) (Φgold= 5eV)

Tunneling rates: Γ = Ι/e = 0.1 nA/e = 10 GHz << oscillator frequency

Sequential tunneling regime: ħ Γ = 60 mΚ << TNon-equilibrium phonons ?

oscillator frequency = 100 tunneling frequencyNot if Q-factor is less than 100

Experiments in opposite limitCNT

H2

- STM measurements on H2- Metallic wires- Molecules with strong chemical bonds to lead- Suspended nanotubes with good electrical contact

Coherent transport through resonant level with coupling to vibration

01

432

5

all information contained in spectral function

Example Hamiltonian- spinless electron

Different methods used

• Self-consistent Born approximation(works for small g)

• Truncated equation of motion

• Effective action

• Mean-field methods

• NRG

• ...

Exact solution for one electron SINGLE ELECTRON APPROXIMATION: NO FERMI SEA!

Glazman-Shehkter 1988 & Wingreen et al. 1989

-10 -5 5 10 15 20

0.5

1

1.5

2

-10 -5 5 10 15 20 25

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Sum of Lorentzians

Lorentzian

01

432

Sum of Lorentzians:

Resonant level - revisited

Lorentzian

“Two contributions”

Decaying out:

Decaying in:

THIS CANCELLATION WILL NOT OCCUR FOR WHEN COUPLING TO VIBRATION,HENCE THE BROADENING WILL BE SMALLER THAN Γ DUE THE PAULI PRINCIPLE

Reduction of widthdI

/dV

Width:

SPA

Tunnel broadening of sidebands

Coherent “Single electron” transport through a single level can survive coupling to phonons!

What about many-body effect such as the Kondo effect ??

Kondo effect in single-molecule transistor

Ground-state of V2+:S=1/2

With spin: Kondo effect and vibrations

Questions:Is the Kondo effect destroyed by coupling to phonons? (as with external ac field)If not, can one expect Kondo sidebands?(as with ac fields, see Kogan et al. Science 304, 1293 (04))

Answer: apparently yes

Yu et al. PRL, Dec 04

Effective Kondo model(Schüttler&Fedro, 1988)

Calculate current to 3rd order in J

NOTE:At the particle-symmetric point only even peaks are non-zero!(selection rule due parity)

(Paaske and KF, PRL in press)

Size of Kondo peak

T > TK

-2 2 4 6 8 10

10

20

30

40

50

Down by

T < TK

-2 2 4 6 8 10

10

20

30

40

50

For : J is unaffected byelectron-vibron coupling

Diamond plot with Kondo effect

Some theoretical problems

• How to describe coherence and correlation in molecular systems

• How does tunneling broadening play together with dissipative broadening?

• How is a supercurrent run through a molecule affected by the electron-vibron coupling? Sidebands on the Andreev states?

• What is the condition for a rectification?• What is the important of non-equilibrium

population of molecular states

Experimental problems

• How to make reproducible measurement or good statistics

• Ways to make sure that there is a molecule in the junction and not just a gold nano-particle

• Better control of the contacts, maybe by designing molecules with specific end groups

...

CONCLUSION

A lot of exciting things are going on the molecular electronics !

gate

Vbias

Vg