Majoranas in mixed-valence insulators

Abstract

A physical model for a mixed-valence impurity in metal must satisfy the Friedel screening theorem for both valences. Such a model is shown, following earlier work which showed low-energy singularities in it, to be supersymmetric, leading to a free Majorana and a phase-shifted Majorana excitation. The theory extended approximately to a lattice of mixed-valence ions at appropriate filling gives, without fine-tuning the parameters, a protected gapless Majorana fermion band across the chemical potential, besides the mixed-valence particle and hole bands separated by gaps. In this situation, the system is electrically neutral in linear response but has de Haas-van Alphen oscillations. This is used to explain the recently observed magneto-oscillations in mixed-valence insulators as well as their accompanying low-energy thermodynamic and relaxation rate anomalies. Some predictions to test the validity of the theoretical results are provided, the most striking of which are that there should be extensive ground-state entropy in such compounds and no Zeeman splitting of the magneto-oscillation frequencies.

Topics & Concepts