Observation of a marginal Fermi glass

A long-standing open problem in condensed-matter physics is whether or not a strongly disordered interacting insulator can be mapped to a system of effectively non-interacting localized excitations. Using terahertz two-dimensional coherent spectroscopy, we investigate this issue in phosphorus-doped silicon, a classic example of a correlated disordered electron system in three dimensions. Despite the intrinsically disordered nature of these materials, we observe coherent excitations and strong photon echoes that provide us with a powerful method for the study of their decay processes. We extract the energy relaxation and decoherence rates close to the metal–insulator transition. We observe that both rates are linear in excitation frequency with a slope close to unity. The energy relaxation timescale counterintuitively increases with increasing temperature, and the coherence relaxation timescale has little temperature dependence below 25 K, but increases as the material is doped towards the metal–insulator transition. Here we argue that these features imply that the system behaves as a well-isolated electronic system on the timescales of interest, and relaxation is controlled by electron–electron interactions. Our observations constitute a distinct phenomenology, driven by the interplay of strong disorder and strong electron–electron interactions, which we dub the marginal Fermi glass.