Strong magnetic field induces superconductivity in Weyl semi - metal

Microscopic theory of the normal-to-superconductor coexistence line of a 2D two-band Weyl superconductor subjected to magnetic field is constructed. It is shown that a Weyl semi-metal that is nonsuperconducting or having a small critical temperature $T_{c}$ at zero field, might become a superconductor at higher temperature when the magnetic field is tuned to a series of quantized values $H_{n}$. The pairing occurs on Landau levels. It is argued that the phenomenon is much easier detectable in Weyl semi - metals than in parabolic band metals since the quantum limit already has been approaches in several Weyl materials.. An experimental signature of the superconductivity on Landau levels is the reduction of magnetoresistivity. This has already been observed in $Cd_{3}As_{2}$ and several other compounds. The novel kind of quantum oscillations of magnetoresistance detected in $ZrTe_{5}$ is discussed along these lines.