Can the spin - orbit interaction break the channel degener - acy of the two - channel orbital Kondo problem ?

PACS. 72.15.Cz – Electrical and thermal conduction in amorphous and liquid metals and alloys. PACS. 72.10.Fk – Scattering by point defects, dislocations, surfaces, and other imperfections (including Kondo effect). PACS. 71.55.-i – Impurity and defect levels. Abstract. – Two-level systems (TLS) interacting with conduction electrons are possibly described by the two-channel Kondo Hamiltonian. In this case the channel degeneracy is due to the real spin of the electrons. The possibility of breaking that degeneracy has interest on his own. In fact, we show that the interaction of the conduction electrons with a spin-orbit scatterer nearby the TLS leads to the breaking of the channel degeneracy only in the case of electron-hole symmetry breaking. The generated channel symmetry breaking TLS-electron couplings are, however, too weak to result in any observable effects. Our analysis is also relevant for heavy fermion systems. In the general form of the orbital Kondo model a single particle is moving between two localized orbitals and is interacting with the conduction electrons in a metal. This orbital Kondo model has been justified by a detailed scaling analysis [1, 2, 3, 4], though it is presently unclear if the two-channel Kondo fixed point can be experimentally reached in the case of TLS's [5, 6, 7]. The particle can be an atom or a group of atoms. Similar orbital models emerge in the context of 4f heavy fermion impurities [2]. In these models the real electronic spin variable does not occur in the coupling constants, thus there is a spin degeneracy in the variables of the particles and all interaction terms are diagonal in the conduction electron spin. In realistic materials, however, spin-orbit interaction is always present, and it always induces cross-scattering between different spin orientations. It is, therefore, a fundamental question, whether spin-orbit interaction can break this channel symmetry and invalidate the 2CK description or not. In this paper we examine the possibility of breaking the channel degeneracy of the orbital Kondo problem due to the interaction of the conduction electrons with a spin-orbit scatterer nearby the TLS, using the renormalization group method in leading logarithmic order. It turns out, that in case of electron-hole symmetry the spin-orbit interaction has no effect on the two-channel Kondo behavior. In contrary, in case of electron-hole symmetry breaking, new, relevant channel symmetry breaking couplings are generated between the TLS and the c EDP Sciences