Topologically protected Dirac cones in compressed bulk black phosphorus

Using the k.p theory and first-principles simulations, we predict that applying a moderate uniaxial or hydrostatic pressure (>0.6 GPa) on bulk or multilayer black phosphorus (BP) can diminish its bandgap and produce one-dimensional and even two-dimensional (2D) Dirac cones. Similar to topological insulators, these 2D Dirac cones result from two competing mechanisms: the unique linear band dispersion tends to open a gap via a "pseudo-spin-orbit" coupling, while the band symmetries preserve the material's gapless spectrum. In particular, these Dirac cones in BP are bulk states that do not require time-reversal symmetry, thus they can keep the high carrier mobility even in the presence of surface or magnetic perturbations. Finally, our predictions can be detected by the material's unusual Landau levels.