Understanding the nature of collective charge dynamics in the Coulomb gap phase is essential for revealing the existence of many-body localization. However, the corresponding many-particle excitation spectra remain poorly understood. Here, we present a comprehensive investigation of \(^{27}\) Al and \(^{63}\) Cu nuclear magnetic/quadrupole resonance (NMR/NQR), along with specific heat ( \(C_p\) ) measurements, in the p-type semiconductor CuAlO \(_2\) . Our study unveils distinct changes in charge dynamics at two crossover temperature scales which separate three regimes associated with Anderson localization of charge carriers: thermally activated transport ( \(T>150\) K) \(\rightarrow\) Mott variable-range hopping (VRH) \(\rightarrow\) Efros–Shklovskii (ES) VRH with Coulomb gap formation ( \(T<50\) K). In the ES VRH regime, we observe a striking divergence in the zero-field \(^{63}\) Cu spin-lattice relaxation rate, \((T_1T)^{-1}\) , which is strongly suppressed by an applied magnetic field, indicative of quantum critical charge fluctuations. This is further supported by a distinct magnetic field-dependence of \(C_p/T\) deep within the Coulomb gap phase. Taken together, these results provide compelling evidence for the emergence of strong, gapless collective charge fluctuations within the Anderson insulating phase where single-particle excitations are gapped.
