Observation of Magnetic Pseudogap Behavior in Phosphorus-Doped Silicon

The recent discovery of a Kondo condensate in phosphorus-doped silicon (Si:P) presents its significant potential for achieving novel many-body quantum states. Si:P exhibits Kondo condensation, characterized by an energy gap in the electronic density of states, while the precise nature of its magnetic state has yet to be determined. Here, we utilize electron and muon spin resonance (ESR and µSR) techniques, optical spectroscopy, and specific heat measurements to unravel the magnetic ground state and spin dynamics of Si:P. Both optical and ESR spectroscopy reveal the onset of spin correlations below 150 K. Furthermore, the muon spin relaxation rate exhibits a power-law increase, λ_ZF∼T^-0.26(5), below T_KC ≈ 0.2 K, indicating the emergence of critical spin fluctuations within the Kondo condensate state. Strikingly, the concomitant occurrence of a Bardeen-Cooper-Schrieffer-like charge gap and power-law magnetic fluctuations closely parallels the pseudogap phases observed in doped Mott insulators. These findings evince that the critical spin fluctuations of the Kondo condensate state act as a driving force for pseudogap formation within inhomogeneous Kondo clouds.