Field-induced polarisation of Dirac valleys in bismuth

Electrons are offered a valley degree of freedom in presence of particular lattice structures. Manipulating valley degeneracy is the subject matter of an emerging field of investigation, mostly focused on charge transport in graphene. In bulk bismuth, electrons are known to present a threefold valley degeneracy and a Dirac dispersion in each valley. Here we show that because of their huge in-plane mass anisotropy, a flow of Dirac electrons 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. According to our measurements, charge conductivity by carriers of a single valley can exceed four-fifth of the total conductivity in a wide range of temperature and magnetic field. At high temperature and low magnetic field, the three valleys are interchangeable and the three-fold symmetry of the underlying lattice is respected. As the temperature lowers and/or the magnetic field increases, this symmetry is spontaneously lost. The latter may be an experimental manifestation of the recently proposed valley-nematic Fermi liquid state.Comment: 14 pages + 5 pages of supplementary information; a slightly modified version will appear as an article in Nature physic