Critical Behavior at the Mott-Anderson Transition: A Typical-Medium Theory Perspective

We present a detailed analysis of the critical behavior close to the Mott-Anderson transition. Our findings are based on a combination of numerical and analytical results obtained within the framework of typical-medium theory—the simplest extension of dynamical mean field theory capable of incorporating Anderson localization effects. By making use of previous scaling studies of Anderson impurity models close to the metal-insulator transition, we solve this problem analytically and reveal the dependence of the critical behavior on the particle-hole symmetry. Our main result is that, for sufficiently strong disorder, the Mott-Anderson transition is characterized by a precisely defined two-fluid behavior, in which only a fraction of the electrons undergo a “site selective” Mott localization; the rest become Anderson-localized quasiparticles.

Figure 1

(a) $T=0$ phase diagram for the disordered half-filled Hubbard model, obtained from the numerical SB4 solution of TMT-DMFT method. Panels (b) and (c) show the evolution of the quasiparticle weight $Z({\epsilon }_i)$ in the critical region. Behavior at (b) the Mott-Anderson transition ($W>U$) is illustrated by increasing disorder $W=2.5$, 2.6, 2.7, 2.8, 2.83 (from the black curve to the brown one), for fixed $U=1.25$; and at (c) the Mott-like transition ($W<U$) by increasing the interaction $U=1.5$, 1.6, 1.7, 1.8, and 1.86, at fixed $W=1.0$.

Figure 2

Frequency dependence of ${\rho }_{\mathrm{typ}}$ (full line) and ${\rho }_{\mathrm{av}}$ (dashed line) in the critical region. Results in top panels illustrate the approach to the Mott-Anderson transition ($W>U$) at $U=1.25$; the bottom panels correspond to the Mott-like transition ($W<U$) at $W=1.0$.

Figure 3

Typical and average values of $\rho (0)$ as the metal-insulator transition is approached for (a) $U=1.25$ and (b) $W=1.0$. The insets show $\rho (0)$ as a function of $\epsilon$ for (a) $W=2.5$, 2.6, 2.7, and 2.83 [from the black curve to the blue (or gray) one] and (b) $U=1.5$, 1.6, 1.7, and 1.86.

Figure 4

Frequency dependence of the typical DOS very close to the metal-insulator transition for (a) the Mott-Anderson transition ($W>U$) at $U=1.25$ and (b) the Mott-like transition $W<U$) at $W=1.0$. The insets show how, in both cases, the ${\rho }_{\mathrm{typ}}(\omega )$ bandwidth $t\to 0$ at the transitions.