Unconventional large magnetoresistance in Cu$_{2-}_{x}$Te

Copper-based chalcogenides have been shown to have interesting physical properties which make them promising for thermoelectric, solar energy, and magnetic sensor devices. Here we report magnetotransport measurements on Cu$_{2-}_{x}$Te, for several polycrystalline samples with $x$ in the range 0.13 to 0.22. The results demonstrate that the magnetoresistance becomes linear above a relatively low applied field. The magnitude of the linear magnetoresistance reaches 250{\%} at 2 K in a 9 T field, comparable to the effect observed in Ag$_{2}$Se and Ag$_{2}$Te. We discuss the results in terms of recent evidence for topological band inversion in Cu$_{2}$Te, and the possibility of high mobility surface states. Evidence from NMR and transport vs. composition indicates the normal carriers to occupy simple hole pockets, precluding compensation effects. Furthermore, the magnitude of maximum magnetoresistance scales as the mobility, as does the crossover field, while the magnetoresistance amplitudes drop to lower values as the vacancy density ($x)$ increases. The results are discussed in terms of a Parish-Littlewood model and high mobility carriers.