Observation of gapless collective charge fluctuations in an Anderson insulating state

Abstract

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.