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A longstanding open problem in condensed matter physics is whether or not astrongly disordered interacting insulator can be mapped to a system ofeffectively non-interacting localized excitations. We investigate this issue onthe insulating side of the 3D metal-insulator transition (MIT) in phosphorusdoped silicon using the new technique of terahertz two dimensional coherentspectroscopy. Despite the intrinsically disordered nature of these materials,we observe coherent excitations and strong photon echoes that provide us with apowerful method for the study of their decay processes. We extract the firstmeasurements of energy relaxation ($T_1$) and decoherence ($T_2$) times closeto the MIT in this classic system. We observe that (i) both relaxation ratesare linear in excitation frequency with a slope close to unity, (ii) the energyrelaxation timescale $T_1$ counterintuitively increases with increasingtemperature and (iii) the coherence relaxation timescale $T_2$ has littletemperature dependence between 5 K and 25 K, but counterintuitively increasesas the material is doped towards the MIT. We argue that these features implythat (a) the system behaves as a well isolated electronic system on thetimescales of interest, and (b) relaxation is controlled by electron-electroninteractions. We discuss the potential relaxation channels that may explain thebehavior. Our observations constitute a qualitatively new phenomenology, drivenby the interplay of strong disorder and strong electron-electron interactions,which we dub the marginal Fermi glass.

Observation of a marginal Fermi glass using THz 2D coherent spectroscopy