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Here, we present the measurements of $R_H$ in a series of $Ti_xSi_{100-x}$ amorphous reaching the critical concentration, $x_c\approx9-9.5$. For $x\geq17$, the Hall coefficient displays the behavior predicted by the perturbation theory, $R_H^{-1}\left(T\right)=R_H^{-1}\left(0\right)+bT^{1/2}$, which extends up to the temperature 150 K. The temperature dependence gets stronger in alloys with lower $x$; $R_H\left(0\right)$ diverges at $x_c$ displaying critical behavior. We used the combined conductivity and Hall coefficient data for alloys with high Ti content to test the theories of quantum corrections to conductivity. We found that the correction due to weak localization is dominated by the electron-phonon scattering with the rate varying with temperature as $\tau_{ep}^{-1}=A_{ep}T^2$. The extracted parameter $A_{ep}$ is in good agreement with the theory that considers the incomplete drag of impurities by lattice vibrations. The spin-orbit scattering time extracted from the weak localization correction was found to be two orders of magnitude larger than the time given by the standard estimate $\tau_{so}\approx\tau\left(\hbar c/e^2Z\right)^4$. The theory of the EEI quantum correction was tested using the Hall coefficient and specific heat data for Ti-Si and $\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ amorphous alloys, which allowed us to estimate all microscopic parameters needed by the theory. We found that, within the accuracy of our measurements, the EEI theory works exactly for alloys that follow the free electron model [$\left(Ag_{0.5}Cu_{0.5}\right)_{100-x}Ge_x$ with $x\le50$.] The deviation from the theory observed in all Ti-Si alloys and in Ag-Cu-Ge alloys with $x\geq60$ can be qualitatively explained by weakening of the electron screening in the systems., Comment: 11 pages, 4 figures, 5 tables

In this paper, we report the measurements of specific heat of an amorphous $Ti_{9.5}Si_{90.5}$ alloy located very close to the critical point of the metal-insulator transition. In the presence of a magnetic field, the specific heat is dominated by the Schottky anomaly caused by magnetic moments associated with the dangling bonds in the matrix of amorphous Si. Subtraction of this contribution exposes the behavior of the electronic specific heat coefficient $\gamma$. The coefficient 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 K, the coefficient $\gamma$ shows an anomalous downturn, which can be approximated by the dependence $\gamma\left(T\right)=\gamma_0ln{(T/T_0)}$, with $T_0\approx0.2$ 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., Comment: 9 pages, 5 figures

By means of muon spin rotation and relaxation ($\mu^+$SR) techniques, we have investigated the magnetism of quasi one-dimensional (1D) cobalt oxides $AE_{n+2}$Co$_{n+1}$O$_{3n+3}$ ($AE$=Ca, Sr and Ba, $n$=1, 2, 3, 5 and $\infty$), in which the 1D CoO$_3$ chain is surrounded by six equally spaced chains forming a triangular lattice in the $ab$-plane, using polycrystalline samples, from room temperature down to 1.8 K. For the compounds with $n$=1 - 5, transverse field $\mu^+$SR experiments showed the existence of a magnetic transition below $\sim$100 K. The onset temperature of the transition ($T_{\rm c}^{\rm on}$) was found to decrease with $n$; from 100 K for $n$=1 to 60 K for $n$=5. A damped muon spin oscillation was observed only in the sample with $n$=1 (Ca$_3$Co$_2$O$_6$), whereas only a fast relaxation obtained even at 1.8 K in the other three samples. In combination with the results of susceptibility measurements, this indicates that a two-dimensional short-range antiferromagnetic (AF) order appears below $T_{\rm c}^{\rm on}$ for all compounds with $n$=1 - 5; but quasi-static long-range AF order formed only in Ca$_3$Co$_2$O$_6$, below 25 K. For BaCoO$_3$ ($n$=$\infty$), as $T$ decreased from 300 K, 1D ferromagnetic (F) order appeared below 53 K, and a sharp 2D AF transition occurred at 15 K., Comment: 12 pages, 14 figures, and 2 tables