Boundary Conformal Field Theory Nano-structures：边界的共形场理论和纳米结构.ppt

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 Boundary Critical Phenomena Boundary CFT Cr Trimers on Au (111) Surface:a non-Fermi liquid fixed point * * 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: Very generally, 1D Hamiltonians which are massless/critical in the bulk with interactions at the boundary renormalize to conformally invariant boundary conditions Boundary layer – non-universal r exponent, ?’ depends on universality class Of boundary bulk exponent ? (J. Cardy) 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 atoms can be manipulated and tunnelling current measured using a Scanning Tunnelling Microscope T Jamneala et al. PRL 87, 256804 (2001) Au Cr (S=5/2)