Conductance of nanosystems with interaction

Anton Ramšak and Tomaž Rejec

Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Jožef Stefan Institute, Ljubljana, Slovenia QinetiQ, Great Malvern, UK

Strong correlations in nanosystems

V J

Open system

Open system Ring with auxiliary flux

N

1 Time-reversal symmetry: f 0 = 0

Fermi liquid

 universality of the ground-state energy

E g

 / 0 Number of electrons odd

Linear conductance from the ground-state energy

E

( f f 0 )

T

 0

Linear conductance from the ground-state energy

E

( f f 0 )

T

 0

Linear conductance from the ground-state energy

E

( f f 0 )

T

 0

Example I: Non-interacting double-barrier system

Example II : Kondo effect in a quantum dot

Example III : Aharonov – Bohm ring Broken time-reversal symmetry Compared with W. Hoffstetter

et al.,

Phys. Rev. Lett.

87

, 156803 (2001)

Summary • The ground state energy of the ring system with flux has a universal form if ‘open’ system is a Fermi liquid at

T

= 0 .

E

( f ) • Linear conductance can then be extracted from the ground-state energy: T. Rejec and A. Ramšak, Phys. Rev. B

68

, 033306 (2003);

68

035342 (2003)

Formulae are exact

IF

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

Conductance formalisms U = 0 U ≠ 0 non-equilibrium transport: T ≠ 0, V ≠ 0 Landauer – Büttiker formula Meir – Wingreen formula linear response regime: T ≠ 0, V ~ 0 Kubo formula zero-temperature linear response: T = 0, V ~ 0 In Fermi liquid systems Fisher – Lee relation …

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.

Validity of the conductance formulas