Optical study of the metal-insulator transition in Bi$_{1-x}$Sb$_{x}$ alloys

Bi$_{1-x}$Sb$_{x}$ exhibits rich physics related to fact that it is an exactly charge compensated plasma of electrons and holes. The electronic structure is controlled by a massive hole band and a 3 dimensional Dirac cone with a gap. The latter gap can be tuned through zero by controlling the Sb concentration, which also results in a relative shift of the bands. Samples can be prepared which are either semi-metallic, semiconducting, or insulating in the bulk with a topological conducting phase at the surface. ~ Detailed optical studies have been realized by means of infrared reflectivity on four different Bi$_{1-x}$Sb$_{x}$ alloys doped at 1{\%}, 6.5{\%}, 7{\%} and 10{\%}. This systematic study demonstrates that chemical pressure tuning induces a zero-temperature metal-insulator transition and reveals a spontaneous phase separation for the 6.5{\%} doped sample.