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

The Kondo Problem J renormalizes to  at low energies

-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

Continuum formulation:

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

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

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

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, 256804 (2001)

STM tip

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

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