Figure 1: Bismuth structure and its high-field magnetoresistance.

(a) Dirac-like dispersion of electrons near L-point and parabolic dispersion of holes near T-point of the Brillouin zone in bismuth. The horizontal axis is for the wave vector along the high symmetry points. (b) Dirac valleys are elongated ellipsoids at the boundaries of the Brillouin zone. φ is the angle between the magnetic field and one of the binary axes. The central grey circle is for the hole pocket while the electron pockets are in red, blue and green, which corresponds to the bands with same colours in c. (c) Lattice structure seen as two interpenetrating face-centred-cubic (FCC) sub-lattices. In real space, each valley is associated with easy flow of charge between neighbouring atoms, indicated by the rod colours. (d) Transverse magnetoresistance of a bismuth crystal up to 65 T at T=1.56 K for magnetic fields along the three equivalent binary (black) and bisectrix (red) crystalline axes labelled in e. Thicker lines correspond to larger φ. The large drop is a consequence of the total evacuation of one or two electron valleys as sketched in the inset. (e) Polar plot of angle φ dependence of magnetoresistance for different fields at T=1.56 K. Note the dramatic enhancement of angular oscillations at 55 T. The abbreviation bin. (bis.) denotes binary (bisectrix) axes. (f) Magnetoresistance up to 90.5 T in another bismuth single crystal at 1.4 K (magenta) and 9 K (blue) as the field is along binary and the current is along bisectrix. The system remains metallic in the whole field range.