g-Tensors and Band Structure Evolution of BiSb Alloys under Magnetic Field*

Bi and Sb alloys exhibit novel physical phenomena depending on the antimony concentration, such as semimetal-semiconductor transitions, giant spin Hall conductivities, and topologically protected phases including Weyl semimetal phases. Although the band structures of Bi and Sb are well studied in terms of k.p or tight-binding Hamiltonians, it is still a challenge to predict the behavior of the band edges as a function of the alloy concentration. Simple linear virtual crystal approximations lack the correct symmetries of the electron and hole pockets; on the other hand, alternative VCA approaches are insufficient to describe band crossings at different Sb concentrations. In this work, we introduce a new VCA parametrization describing the symmetries and crossing of the band edges using a 16 band tight-binding Hamiltonian. Then, from that Hamiltonian, we derive and calculate g-tensors of the electrons and holes and show that the large spin-orbit couplings of Bi and Sb result in giant effective g-factors whose axes of symmetry differ from the crystallographic axes. We also show that the band gap between symmetric and antisymmetric bands at the L point can be closed by a moderate magnetic field due to large g-factors. The closing of this gap produces a Weyl state.