Mott transition in granular aluminum

A Mott transition in granular Al films is observed by probing the increase of the spin-flip scattering rate of conduction electrons as the nanosize metallic grains are being progressively decoupled. The presence of free spins in granular Al films is directly demonstrated by $\mu \mathrm{SR}$ measurements. Analysis of the magnetoresistance in terms of an effective Fermi energy shows that it becomes of the order of the grains electrostatic charging energy at a room temperature resistivity ${\rho }_{300\mathrm{K}}\approx 50000\mu \Omega \mathrm{cm}$, at which a metal to insulator transition is known to exist. As this transition is approached the magnetoresistance exhibits a heavy-fermion-like behavior, consistent with an increased electron effective mass.

Figure 1

Temperature dependence of the muon spin relaxation rate of electronic origin $\lambda$ for a sample with ${\rho }_{300\text{K}}\approx 140\mu \Omega \mathrm{cm}$. $\lambda$ appears to saturate around a temperature where the resistivity starts to increase [6] (inset).

Figure 2

Critical temperature (blue squares) $T_c$ and effective Fermi energy (red dots) as a function of the room temperature resistivity. The dashed line is a guide to the eye, the dash dotted line follows $E_F^{*}\propto {\rho }^{-0.7}$ and the dash double dotted line is showing the limit of the electrostatic energy for a 2 nm grain. The arrow marker points to the critical resistivity $\rho \approx 50000\mu \Omega \mathrm{cm}$ at which a Mott transition should occur.

Figure 3

Magnetoresistance of a high resistivity film ($\rho \approx 13000\mu \Omega \mathrm{cm}$) at low temperatures. Below 20 K, the magnetoresistance is positive at low fields and negative at high fields. Down to 8 K the variation of the magnetoresistance changes sign at a fixed field, as is the case for a Kondo lattice.