Percolative Metal-Insulator Transition in LaMnO$_3$

We show that the pressure-induced metal-insulator transition (MIT) in LaMnO$_3$ is fundamentally different from the Mott-Hubbard transition and is percolative in nature, with the measured resistivity obeying the percolation scaling laws. Using the Gutzwiller method to treat correlation effects in a model Hamiltonian that includes both Coulomb and Jahn-Teller interactions, we show, One, that the MIT is driven by a competition between electronic correlation and the electron-lattice interaction, an issue that has been long debated, and Two, that with compressed volume, the system has a tendency towards phase separation into insulating and metallic regions, consisting, respectively, of Jahn-Teller distorted and undistorted octahedra. This tendency manifests itself in a mixed phase of intermixed insulating and metallic regions in the experiment. Conduction in the mixed phase occurs by percolation and the MIT occurs when the metallic volume fraction, steadily increasing with pressure, exceeds the percolation threshold $v_c \approx 0.29$. Measured high-pressure resistivity follows the percolation scaling laws quite well, establishing the percolative nature of conduction, and the temperature dependence follows the Efros-Shklovskii variable-range hopping behavior for granular materials.