2CHANNEL Kondo Scaling in Metal Nanoconstrictions: a Conformal Field Theory Calculation of Scaling Function.
Abstract
This thesis is concerned with experiments done by D. C. Ralph and R. A. Buhrman (RB92,Ralph93) at Cornell University on zerobias anomalies in conductance signals through metal nanoconstrictions. They have suggested that their data is in accord with the assumption that conduction electrons interact with twolevel tunneling systems in the constriction region according to the nonmagnetic 2 channel Kondo model. We quantitatively analyze their data within the theoretical framework of the 2channel Kondo model, in the regime of very low temperatures (T) and voltages (V). This regime is governed by the strongcoupling T = V = 0 fixed point of the 2channel Kondo model, at which the exact conformal field theory solution of Affleck and Ludwig (AL93) applies. Near the strongcoupling 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 onedimensional 2channel Kondo model. The bulk of this thesis is concerned with analytically calculating Gamma(x), which is a "fingerprint" of the 2channel Kondo problem, in order to compare it to experiment. Conceptually new is our treatment of nonequilibrium effects: we show that Hershfield's formulation of nonequilibrium 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 2channel 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT........63D
 Keywords:

 Physics: Condensed Matter