Coulomb Interactions and Nanoscale Electronic Inhomogeneities in Manganites

We study electronic inhomogeneities in manganites using simulations on a microscopic model with Coulomb interactions amongst two electronic fluids—one localized (polaronic), the other extended—and dopant ions. The long range Coulomb interactions frustrate phase separation induced by the large on site repulsion between the fluids. A single phase ensues which is inhomogeneous at a nanoscale, but homogeneous on mesoscales, with many features that agree with experiments. This, we argue, is the origin of nanoscale inhomogeneities in manganites, rather than phase competition or disorder effects.

Figure 1

Real space electronic distribution obtained from simulations on a ${16}^3$ cube. Magenta (darkest) denotes hole clumps with occupied $b$ electrons, white (lightest) denotes hole clumps with no $b$ electrons, cyan (2nd lightest) denote singleton holes, and light blue (2nd darkest) represents regions with $\ell$ polarons. Left: Isolated clumps with occupied $b$ electrons ($b$-electron puddles). Right: Larger doping; percolating clumps. Inset: “macroscopic phase separation” absence of long range Coulomb interaction ($V_0=0.0$).

Figure 2

Critical doping levels $x_{c1}$ and $x_{c2}$. $x_{c1}$ separates the lightest region, where no $b$ states are occupied, from the intermediate shade region, which has $b$ states occupied in puddles. The darkest shaded region, with $x>x_{c2}$, has some occupied $b$ states that percolate through the ${10}^3$ box. Results shown are averages over 100 realizations of the $Ak$ ions. The solid line corresponds to the DMFT result [8] for $x_{c1}$.

Figure 3

DOS of $\ell$ polarons and $b$ electrons (average over 100 random initial conditions, size: ${10}^3$). The occupied states are shaded. The chemical potential $\mu$ and the $b$ band center $E_b$ are marked. Results shown are averages over 100 realizations of the $Ak$ ions. Inset: soft Coulomb gap of the polarons.