2-CHANNEL Kondo Scaling in Metal Nanoconstrictions: a Conformal Field Theory Calculation of Scaling Function.

This thesis is concerned with experiments done by D. C. Ralph and R. A. Buhrman (RB92,Ralph93) at Cornell University on zero-bias anomalies in conductance signals through metal nanoconstrictions. They have suggested that their data is in accord with the assumption that conduction electrons interact with two-level tunneling systems in the constriction region according to the non-magnetic 2 -channel Kondo model. We quantitatively analyze their data within the theoretical framework of the 2-channel Kondo model, in the regime of very low temperatures (T) and voltages (V). This regime is governed by the strong-coupling T = V = 0 fixed point of the 2-channel Kondo model, at which the exact conformal field theory solution of Affleck and Ludwig (AL93) applies. Near the strong-coupling fixed point, the conductance G(V,T) is predicted (RLvDB94) to obey the following scaling relation: {G(V,T)-G(0,T)over T^ alpha}=B[Gamma(Ax)-1] . Here Gamma(x) is a universal scaling function, and the universal exponent alpha is predicted to have the value alpha= {1over2}. We show that the data of Ralph and Buhrman indeed obey the above scaling relation, with alpha=0.5+/- 0.05; this we take as strong evidence that their samples can plausibly be described by a simple one-dimensional 2-channel Kondo model. The bulk of this thesis is concerned with analytically calculating Gamma(x), which is a "fingerprint" of the 2-channel Kondo problem, in order to compare it to experiment. Conceptually new is our treatment of non-equilibrium effects: we show that Hershfield's formulation of non-equilibrium problems (Hers93) can be combined with Affleck and Ludwig's conformal field theory approach to deal with the V ne0 situation. When our results for Gamma(x) are combined with recent numerical (NCA) results (HKH94) for the same model, good quantitative agreement with the data is obtained, indicating that the 2-channel Kondo model is in accord with all experimental facts. However, the theoretical justification for the model employed here has recently been called into question (MF95,WAM95), indicating that more theoretical work is needed before the experiment can be regarded as completely understood. The thesis contains six lengthy appendices, intended as a pedagogical introduction to Affleck and Ludwig's conformal field theory solution of the Kondo problem.