1. Boundary Conformal Field Theory & Nano-structures
The Kondo problem
Boundary critical phenomena & boundary conformal field theory
Cr trimers on a Au surface: a non-Fermi liquid fixed point
with: Andreas Ludwig & Kevin Ingersent

2. The Kondo Problem
J renormalizes to  at low energies

3. -electrons on sites 2, 3, … are free
-residual local interactions, not
involving impurity are simply expressed
in terms of free electron operators and
are irrelevant
-a Fermi Liquid Fixed Point

4. Continuum formulation:

5. Boundary Critical Phenomena & Boundary CFT
Very generally, 1D Hamiltonians which
are massless/critical in the bulk with
interactions at the boundary renormalize
to conformally invariant boundary
conditions

6. (J. Cardy)
bulk exponent  r
exponent, ’ depends
on universality class
Of boundary
Boundary layer – non-universal

7. for non-Fermi liquid boundary conditions,
boundary exponents bulk exponents
trivial free fermion bulk exponents
turn into non-trivial boundary exponents
due to impurity interactions

8. Cr Trimers on Au (111) Surface: a non-Fermi liquid fixed point
Cr (S=5/2)
Cr atoms can be manipulated
and tunnelling current measured using
a Scanning Tunnelling Microscope
T Jamneala et al. PRL 87, (2001)

9. STM tip

10. 2 doublet (s=1/2) groundstates
with opposite helicity:
|>exp[i2/3]|> under: SiSi+1
represent by s=1/2 spin operators Saimp
and p=1/2 pseudospin operators aimp
3 channels of conduction electrons
couple to the trimer
these can be written in a basis of
Pseudo-spin eigenstates, p=-1,0,1

11. only essential relevant Kondo interaction:
(pseudo-spin label)
we have found exact conformally
invariant boundary condition by our
usual tricks:
conformal embedding
fusion