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 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 superharmonics in the supercurrent phase relation in addition to a ϕ 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.

Evolution of pair correlation symmetries and supercurrent reversal in tilted Weyl semimetals

“…As recently demonstrated, control of these parameters is possible by, for example, applying strain to the system. [9][10][11] To further shed light on the symmetry profiles of these superconducting correlations, in Figs. 1-3, we present a few representative profiles for the real and imaginary parts of the equal-Pspin and opposite-Pspin components as a function of the momenta k x and k y .…”

“…Such situations can be precisely determined by first-principles calculations; e.g., when the system experiences external strain or is subject to doping and intercalation. A practical example is when a black phosphorus mono- layer is under the application of an external strain, as was recently discussed [9][10][11] . The band-structure parameters were obtained using density-functional-theory computations, and symmetry calculations demonstrated that the momenta coefficients can change sign depending on the strength and direction of the applied in-plane strain.…”

“…We note that, in order to accommodate a wide range of parameters without missing the important physics, we make no assumptions and approximations regarding the strength of the parameters involved that would normally simplify the wavefunctions. For example, the quasiclassical approximation assumes that µ is largest energy in the system, which considerably simplifies the wavefunctions, but at the cost of losing important information for regimes where µ is small [7][8][9][10] . The resultant analytic expressions involving 1 × 8 spinors are therefore very cumbersome, and we omit the explicit expressions, presenting numerical results only when evaluating observable quantities.…”

“…4,5 This topological phase results in the band structure in the bulk of Weyl semimetals being gapless, although Fermi arc states connect pairs of Weyl points. [6][7][8][9][10][11] As has been widely discussed, the presence of gapless surface states opens up transport channels free from backscattering. For a conventional type-I WS, the Fermi surface is point-like, where electron and hole states occupy separate energy ranges above or below the Weyl point.…”

“…These intriguing phenomena have motivated a significant wave of interest to the Weyl metal systems both theoretically and experimentally. [7][8][9][10][11]26, When discussing the superconducting state of a Weyl semimetal, the symmetry of the electron-electron coupling potential, ∆, is an important property that gives insight into the nature of the pairing correlations. Moreover, when a relationship exists between the quasiparticle excitations in the Weyl phase and the pair correlations, a more complete understanding of the underlying electronic structure can be obtained.…”