5. Leading order

1
Non-equilibrium tunnelling and field
emission from Luttinger liquids
Thomas Schmidt, Andrei Komnik
Physikalisches Institut, Universität Freiburg,
E-Mail tschmidt_at_uni-freiburg.de
1. System
4. Luttinger liquids
Host 1-D wire (interacting)
Detector
Luttinger liquid Hamiltonian
with bosonized fermion operators
V
2. What are we looking for?
Energy resolved current j(w), Full current
g Interaction parameter ( 0 lt g lt 1 )
3. How do we model the system?
4. Approach
Field emission Tunnelling into vacuum
Pertubation theory in tunnelling, Calculation in
Keldysh-space of the single-electron Greens
Function
Detector (non-interacting)
tunnelling term
Host (Luttinger liquid)
5. Leading order (primary processes)
7. Tertiary processes (double hot hole scattering)
We need the 6-point correlation function
Simple tunnelling
b
g
Host
Detector
Near the Fermi-Edge No contribution above wEF.
?
a
d
16 possible combinations of Keldysh indices
a,b,g,d
6. Secondary processes (single hot hole
scattering)
Below Fermi level We need the 4-point
correlation function
Principal result thus far Only 3 diagrams
contribute for wgt0
8. Work in progress

• Non-zero j(w) above Fermi level
• Divergent for weak interaction!
• Analyse next order

Detailed calculation of these 3 contributions.