Electron Spin Resonance near the Metal Insulator Transition in Phosphorous doped Si

Phosphorus doped Si offers a platform to study the quantum phase transition from an Anderson localized insulating state to a metallic state from an impurity band. Localized electrons interact through dipolar and exchange interactions while their individual energies are disordered due to the random nature of the doping process. As a result, this system can be used to raise & answer fundamental questions about the nature of thermalization and decoherence in strongly-interacting disordered systems. 

Here, we utilize an ion-implanted layer of phosphorus donors in high-resistivity Si doped near the critical doping density. We fabricate coplanar microwave resonators out of NbTiN. The high-critical field of NbTiN enables electron spin resonance (ESR) measurements in static fields of about 200 mT at mK temperatures. We observe resonant dissipation from the impurity band as well as hyperfine-split localized electrons in a single sample. The impurity band ESR line is motionally narrowed from 25 mK to 1 K. Using Hahn echo techniques, we measure non-exponential energy and phase relaxation from the isolated donors. While these observations can be partly attributed to the inhomogeneities in doping density, a complete picture requires incorporating many-body dynamics of the interacting spins.