Disorder-Driven Metal-Insulator Transitions in Deformable Lattices

We show that, in the presence of a deformable lattice potential, the nature of the disorder-driven metal-insulator transition is fundamentally changed with respect to the noninteracting (Anderson) scenario. For strong disorder, even a modest electron-phonon interaction is found to dramatically renormalize the random potential, opening a mobility gap at the Fermi energy. This process, which reflects disorder-enhanced polaron formation, is here given a microscopic basis by treating the lattice deformations and Anderson localization effects on the same footing. We identify an intermediate “bad insulator” transport regime which displays resistivity values exceeding the Mott-Ioffe-Regel limit and with a negative temperature coefficient, as often observed in strongly disordered metals. Our calculations reveal that this behavior originates from significant temperature-induced rearrangements of electronic states due to enhanced interaction effects close to the disorder-driven metal-insulator transition.

Figure 1

Phase diagram.—Metal-insulator transition (MIT) at $T=0$ calculated for quantum phonons in the adiabatic regime (${\omega }_0=0.05$). The shaded area corresponds to the “bad insulator” behavior seen in transport (see text). The dashed line is a sketch of the expected behavior approaching the clean limit. The inset shows the effect of increasing phonon quantum fluctuations.

Figure 2

Spectral features and order parameter.—Panels (a)–(d), average (bold line) and typical DOS (shaded) across the MIT at $T=0$ for classical phonons. (a),(b) at $W=0.1$, for $\lambda =0.5$, 0.64; (c),(d) at $\lambda =0.05$, for $W=1.1$, 1.2; the dotted line is the TDOS at $\lambda =0$, shown for comparison; the DOS in the second row have been scaled down by an arbitrary factor for clarity. (e) Order parameter vs disorder amplitude $W$. From right to left, $\lambda =0$, 0.05, 0.1, 0.2, 0.3, 0.4. The crosses mark the polaron transition. The inset shows the quantum case for $\lambda =0.3$ and ${\omega }_0=0.2$.

Figure 3

Self-consistent fields and effective disorder.—(a) Lattice displacement $X_0$ as a function of $\epsilon$ and (b) effective disorder distribution: below ($W=1.0$, dashed), at ($W=1.15$, dotted) and beyond the polaronic transition ($W=1.2$, bold), for $\lambda =0.05$ and $T=0$. Thin lines in (a) and (b) are the NCA results for quantum phonons at $W=1.2$ and ${\omega }_0=0.2$ [the value of ${\omega }_0$ is marked by arrows in (b)].

Figure 4

Conductivity and Mott limit.—(a) $\sigma (T)$ in the weak-coupling regime, $\lambda =0.05$, expressed in units of ${\sigma }_M$ (see text); from top to bottom, $W=0.0$, 0.125, 0.25, 0.5; 0.8, 1.05, 1.16, 1.3, 1.5. For $W=W_c=1.16$ (bold) we also show the power-law extrapolation to $T=0$ (dotted). The shaded area is the experimental range $100–250\mu \mathrm{\Omega }\mathrm{cm}$ where the TCR is seen to vanish in most single-band materials [36, 37]. (b)–(d) Scattering time and order parameter for representative parameters in the metallic phase ($W=0.125$), at the Mott-Ioffe-Regel limit ($W=W^{*}=0.8$) and at the MIT ($W=W_c$). Both quantities are expressed in units of $1/D$.