Direction dependent switching of carrier-type enabled by Fermi surface geometry

While charge carriers can typically be designated as either electron- or hole- type, depending on the sign of the Hall coefficient, some materials defy this straightforward classification. Here we find that LaRh$_6$Ge$_4$ goes beyond this dichotomy, where the Hall resistivity is electron-like for magnetic fields along the $c$-axis but hole-like in the basal plane. Together with first-principles calculations, we show that this direction-dependent switching of the carrier type arises within a single band, where the special geometry leads to charge carriers on the same Fermi surface orbiting as electrons along some directions, but holes along others. The relationship between the Fermi surface geometry and occurrence of a Hall sign reversal is further generalized by considering tight-binding model calculations, which show that this type of Fermi surface corresponds to a more robust means of realizing this phenomenon, suggesting an important route for tailoring direction dependent properties for advanced electronic device applications.