A. Ramšak 1,2 and T. Rejec 2 1 Faculty of Mathematics and Physics, University of Ljubljana 2 J. Stefan Institute, Ljubljana, Slovenia Conductance of nano-systems.

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Presentation transcript:

A. Ramšak 1,2 and T. Rejec 2 1 Faculty of Mathematics and Physics, University of Ljubljana 2 J. Stefan Institute, Ljubljana, Slovenia Conductance of nano-systems with interaction

Nature 417, (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: ΔI = GΔV +ΔV

Conductance: ΔI = GΔV +ΔV IF the system is the Fermi liquid 

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

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)

Step 3. Quasiparticles in a finite system N

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

ring system

Step 5. Non-interacting system  ground-state energy:

Examples 1 Noninteracting system

2 Anderson impurity model Wiegman, Tsvelick (1982)

3 Double quantum dot Oguri, PRB 56, (1997)

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) : 4 Aharonov-Bohm system (Kondo-Fano)

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, (2003) T. Rejec and A. Ramšak, PRB 68, (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

PRB 44, (1991) exp.: “0.7” and “0.3” 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, (2003) and refs. therein

Tomi Rejec

Narrow wires (10~20 nm) “V”-groove