Controllable anisotropic Andreev reflection in gapless few-layer phosphorene

Abstract

Andreev reflection at a normal/superconductor interface is studied in a system in which the normal region consists of a few-layer black phosphorus (BP) under an electric field applied perpendicularly to the material’s plane. The application of a strong electric field induces a phase transition, closing the BP gap and forming Dirac cones that preserve the unbiased material’s inherent anisotropic dispersion. This platform allows us to explore the effect of electric-field-tunable anisotropy on the Andreev reflection of massless Dirac quasiparticles, using a wave-packet time-evolution method. Our results show that the anisotropy of a BP electronic structure plays a central role in Andreev reflection, which results in a voltage–transmission relation that, in contrast to the case of isotropic materials, strongly depends on the wave vector angle and weakly depends on the Fermi level away from the superconducting gap, (i.e., for retro-reflection processes).