Strain-engineered Majorana zero energy modes and φ₀ Josephson state in black phosphorus

We develop a theory for strain control of Majorana zero energy modes andJosephson effect in black phosphorus (BP) devices proximity coupled to asuperconductor. Employing realistic values for the band parameters subject tostrain, we show that the strain closes the intrinsic band gap of BP, howeverthe proximity effect from the superconductor reopens it and creates Dirac andWeyl nodes. Our results illustrate that Majorana zero energy flat bands connectthe nodes within the band-inverted regime in which their associated density ofstates is localized at the edges of the device. In a ferromagnetically mediatedJosephson configuration, the exchange field induces super-harmonics into thesupercurrent phase relation in addition to a φ₀ phase shift, correspondingto a spontaneous supercurrent, and strain offers an efficient tool to controlthese phenomena. We analyze the experimental implications of our findings, andshow that they can pave the way for creating a rich platform for studyingtwo-dimensional Dirac and Weyl superconductivity.