Strong magnetic field induces superconductivity in a Weyl semimetal

Microscopic theory of the normal-to-superconductor coexistence line of a multiband Weyl superconductor subjected to magnetic field is constructed. It is shown that the Weyl semimetal that is nonsuperconducting or having a small critical temperature Tc at zero field might become a superconductor at higher temperatures when the magnetic field is tuned to a series of quantized values Hn. The pairing occurs on Landau levels. It is argued that the phenomenon is detectable much easier in Weyl semimetals than in parabolic band metals since the quantum limit already has been approached in several Weyl materials. The effect of Zeeman coupling leading to splitting of the reentrant superconducting regions on the magnetic phase diagram is considered. An experimental signature of the superconductivity on Landau levels is the reduction of magnetoresistivity. This has been observed already in Cd3As2 and several other compounds. The novel kind of quantum oscillations of magnetoresistance detected in ZrTe5 is discussed along these lines.