Figure 5: Topological phase transitions of an inversion breaking Weyl semimetal.

(a) A Weyl semimetal can be understood as an intermediate phase between a trivial insulator and a topological insulator as a function of a tuning parameter m. The grey circles represent the band touchings at the critical point, each of which is composed of two degenerate Weyl nodes. The black and white circles are the Weyl nodes with positive and negative chiral charges. The blue lines are the topological surface states. (b) The calculated Fermi surface of TaAs near the point. (c) In the Weyl semimetal TaAs, electrons exhibit an unusual path in real and momentum (z−k_x−k_y) space under an external magnetic field along the z direction. The orange arrows show the real-space motion of the electrons between the top and the bottom surfaces. The blue and red arrows show the electron’s momentum space trajectories tracing out the constant energy contour of the Fermi arcs on the surfaces. (d) In the topological insulator Bi₂Se₃, an electron tracing out a surface state constant energy contour will not encounter a bulk state and the wavefunction will always remain localized on the same surface. (e) An image of TaAs single crystals we have grown.