Strain-engineered Majorana Zero Energy Modes and ϕ0 Josephson State in Black Phosphorus

Abstract

We develop a theory for strain control of Majorana zero energy modes and 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 super-harmonics into the supercurrent phase relation in addition to a ϕ0 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.

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• Analytical criteria for magnetization reversal in ${\phi }_0$ Josephson junction
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