Conductance of nano-systems with interaction

A. Ramšak

1,2

and T. Rejec

2 1 Faculty of Mathematics and Physics, University of Ljubljana 2 J. Stefan Institute, Ljubljana, Slovenia

Nature 417 , 725 - 729 (13 June 2002)

Kondo resonance in a single-molecule transistor

WENJIE LIANG*, MATTHEW P.

SHORES†, MARC BOCKRATH*, JEFFREY R. LONG† & HONGKUN PARK*

open system

Conductance: Δ

I

=

G

Δ

V

+Δ

V

Conductance: Δ

I

=

G

Δ

V

IF

the system is the Fermi liquid  +Δ

V

Gogolin (1994): persistent currents for non-interacting systems even odd

Conductance formulas: two-point energy: Favand and Milla (1998): for non-interacting systems,

g

<<1 Molina et al. (2003)

Conductance formulas: two-point energy: persistent current: Sushkov (2001) Meden and Schollwöck (2003)

Conductance formulas: two-point energy: persistent current: charge stiffness:

min max charge stiffness:

note: • Fermi liquid • linear conductance • zero temperature • non-interacting single-channel leads

Proof of the method

Step 1.

Conductance of a Fermi liquid system at

T

=0 Kubo

T

=0

define

(n.i.: Fisher-Lee) ‘Landauer’

Step 2.

Quasiparticle Hamiltonian (Landau Fermi liquid)

N

Step 3.

Quasiparticles in a finite system

Step 4.

Quasiparticle energies ‘single (quasi)particle energy’; also eigenenergy of 

Φ

dependence of is as in non-interacting systems

Step 5.

Non-interacting systems

open system

open system ring system

Step 5.

Non-interacting system  ground-state energy:

1

Noninteracting system

Examples

2

Anderson impurity model Wiegman, Tsvelick (1982)

3

Double quantum dot Oguri, PRB

56

, 13422 (1997)

4

Aharonov-Bohm system (Kondo-Fano) broken time reversal symmetry (e.g., due to external magnetic field) :

4

Aharonov-Bohm system (Kondo-Fano) broken time reversal symmetry (e.g., due to external magnetic field) :

Bułka, Stefanski, PRL (2001) Hofstetter, König, Schoeller, PRL (2001)

Summary:

1. IF the system is Fermi liquid … 2. Calculate the ground-state energy of the interacting (ring) system 3. Determine the conductance from the two (four)-point energy formula T. Rejec and A. Ramšak, PRB

68

, 033306 (2003) T. Rejec and A. Ramšak, PRB

68

, 035342 (2003)

‘0.7 anomaly’

1988

“0.7

structure”

Thomas

et al

. PRL

77

, 136 (1996):

Resonant scattering

Singlet transmission Triplet transmission

Results: “1/4” and “3/4” anomalies

exp.: “0.7” and “0.3”

PRB

44

, 13549 (1991) Phil. Mag.

77

, 1213 (1998)

V-groove

PRL 2002

Summary

   •  “0.7” anomaly is “

1/4

”+”

3/4

” anomaly anomalies also in

S

and  in magnetic field “1/2” extended Anderson model (Kondo) open problems: - Kondo physics?

- doping dependence?

- “

0.5

” anomaly  Rejec, Ramšak, Jefferson, PRB

67

, 075311 (2003) and refs. therein

Tomi Rejec

Narrow wires (10~20 nm)

“V”-groove