  Quantum electronic matter has long been understood in terms of two limiting
behaviors of electrons: one of delocalized metallic states, and the other of
localized magnetic states. Understanding the strange metallic behavior which
develops at the brink of localization demands new probes of the underlying
electronic charge dynamics. Using a state-of-the-art technique,
synchrotron-radiation-based Mossbauer spectroscopy, we have studied the
longitudinal charge fluctuations of the strange metal phase of beta-YbAlB4 as a
function of temperature and pressure. We find that the usual single absorption
peak in the Fermi-liquid regime splits into two peaks upon entering the
critical regime. This spectrum is naturally interpreted as a single nuclear
transition, modulated by nearby electronic valence fluctuations whose long
time-scales are further enhanced, due to the formation of charged polarons. Our
results represent a direct observation of critical charge fluctuations as a new
signature of strange metals.
