LiOsO$_3$ has been recently identified as the first unambiguous ferroelectric metal, experimentally realizing a prediction from 1965 by Anderson and Blount. In this work, we investigate the metallic state in LiOsO$_3$ by means of infrared spectroscopy supplemented by Density Functional Theory and Dynamical Mean Field Theory calculations. Our measurements and theoretical calculations clearly show that LiOsO$_3$ is a very bad metal with a small quasiparticle weight, close to a Mott-Hubbard localization transition. The agreement between experiments and theory allows us to ascribe all the relevant features in the optical conductivity to strong electron-electron correlations within the $t_{2g}$ manifold of the osmium atoms.
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