Strain-engineered Majorana zero energy modes and ?0 Josephson state in black phosphorus

We develop a theory for strain control of Majorana zero energy modes and the Josephson effect in black phosphorus (BP) devices proximity coupled to a superconductor. Employing realistic values for the band parameters subject to strain, we show that the strain closes the intrinsic band gap of BP; however, the proximity effect from the superconductor reopens it and creates Dirac and Weyl nodes. Our results illustrate that Majorana zero energy flat bands connect the nodes within the band-inverted regime in which their associated density of states is localized at the edges of the device. In a ferromagnetically mediated Josephson configuration, the exchange field induces superharmomcs in the supercurrent phase relation in addition to a pi(0) phase shift, corresponding to a spontaneous supercurrent, and strain offers an efficient tool to control these phenomena. We analyze the experimental implications of our findings and show that they can pave the way for creating a rich platform for studying two-dimensional Dirac and Weyl superconductivity.