CeFe$_2$Al$_{10}$: a Correlated Metal with a Fermi Surface Exhibiting Nonmetallic Conduction

Metals can be defined as materials with a Fermi surface or as materials exhibiting metallic conduction (i.e., $\mathrm{d} ρ/ \mathrm{d}T > 0$). Usually, these definitions both hold at low temperatures, such as liquid-helium temperatures, as the Fermi energy is sufficiently larger than the thermal energy. However, they may not both hold in correlated electron systems where the Fermi energy is reduced by renormalization. In this paper, we demonstrate that although the resistivity of CeFe$_2$Al$_{10}$ increases with decreasing temperature below $\sim20$ K, CeFe$_2$Al$_{10}$ is a metal with a Fermi surface. This assertion is based on the observation of Shubnikov--de Haas oscillations and a Hall resistivity that changes sign with the magnetic field, which requires the coexistence of electron and hole carriers. Our analysis of Shubnikov--de Haas and magnetotransport data indicates that the Fermi energies are as small as $\sim$30 K and that, despite the increasing carrier mobility with decreasing temperature as in conventional metals, the loss of thermally excited carriers leads to nonmetallic conduction ($\mathrm{d} ρ/ \mathrm{d}T < 0$) below $\sim20$ K. Furthermore, we investigate how this anomalous metal transforms to a more conventional metal with metallic conduction by the application of high pressure and a high magnetic field. This study illustrates the subtle distinction between semimetals and semiconductors in correlated electron systems. This distinction is relevant to investigations of correlated topological insulators and semimetals.