Conductance of nanosystems with interaction

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Conductance of nanosystems with interaction
Anton Ramak and Toma Rejec Faculty of
Mathematics and Physics, University of Ljubljana,
Slovenia Joef Stefan Institute, Ljubljana,
Slovenia QinetiQ, Great Malvern, UK
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Strong correlations in nanosystems
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Open system
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Open system Ring
with auxiliary flux
Time-reversal symmetry f0 0
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Fermi liquid universality of the
ground-state energy
Number of electrons odd
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Linear conductance from the ground-state energy
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Linear conductance from the ground-state energy
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Linear conductance from the ground-state energy
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Example I Non-interacting double-barrier system
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Example II Kondo effect in a quantum dot
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Example III Aharonov Bohm ring
Broken time-reversal symmetry
Compared with W. Hoffstetter et al., Phys. Rev.
Lett. 87, 156803 (2001)
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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. Ramak, Phys. Rev. B 68, 033306
(2003) 68 035342 (2003)
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Formulae are exact IF the system is Fermi liquid

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

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Conductance formalisms
U 0
non-equilibrium transport T ? 0, V ? 0
Landauer Büttiker formula
In Fermi liquid systems
Fisher Lee relation
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Proof of the method
Step 1. Conductance of a Fermi liquid system at
T0
Kubo
T0
define (n.i. Fisher-Lee)
Landauer
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Step 2. Quasiparticle hamiltonian (Landau Fermi
liquid)
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Step 3. Quasiparticles in a finite system
N
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Step 4. Validity of the conductance formulas