Field-induced polarization of Dirac valleys in bismuth

Abstract

The electronic structure of certain crystal lattices can contain multiple degenerate ’valleys’ for their charge carriers to occupy. This valley degree of freedom could be useful in the development of electronic devices. The principal challenge in the development of ’valleytronics’ is to lift the valley degeneracy of charge carriers in a controlled way. Here we show that in semi-metallic bismuth the flow of Dirac fermions along the trigonal axis is extremely sensitive to the orientation of in-plane magnetic field. Thus, a rotatable magnetic field can be used as a valley valve to tune the contribution of each valley to the total conductivity. At high temperature and low magnetic field, bismuth’s three valleys are interchangeable and the three-fold symmetry of its lattice is maintained. As the temperature is decreased or the magnetic field increased, this symmetry is spontaneously lost. This loss may be an experimental manifestation of the recently proposed valley-nematic Fermi liquid state. Multiple valleys in the electronic structure of certain crystal lattices could enable the development of so-called valleytronic devices. But to do so, the degeneracy of these valleys must be lifted. Measurements of the anisotropic magnetoelectric response of bismuth suggest that its three-fold valley degeneracy breaks spontaneously at low temperatures and high fields.