Critical behavior of the specific heat in Ti-Si amorphous alloys at the metal-insulator transition: possible observation of many body localization

We report the measurements of specific heat of an amorphous Ti-Si alloy located very close to the critical point of the metal-insulator transition. The electronic specific heat coefficient gamma was is temperature-independent above 2 K and is, in order of magnitude, close to the value expected in the absence of electron-electron interactions. In the temperature range 0.4-1.5 the coefficient shows an anomalous downturn, which can be approximated by the logarithmic dependence and approximated to become zero at 0.2 K. In a companion paper, we found that the Hall coefficient in Ti-Si alloys is affected by the electron-electron interaction up to much higher temperature of 150 K and also varies critically across the metal-insulator transition. We compare our results with theoretical predictions for three models, which can potentially explain the anomalous behavior of the specific heat: generalized non-linear sigma model, Coulomb glass, and many-body localization.