Reentrant superconductivity in UTe$_2$

Abstract: The reentrant superconductivity is the peculiar phenomenon observed in paramagnetic metal UTe$_2$ in magnetic field parallel to the hard magnetisation axis. It is difficult to explain it in terms of field dependent intensity of magnetic fluctuations like it is done for explanation of the formally similar phenomena in the ferromagnetic uranium superconductors URhGe, UCoGe. Extremely large initial slope of the upper critical field temperature dependence suggests that the phenomenon has the quasi-two-dimensional nature. Indeed, according to the recent band structure calculations by Yuanji Xu et al, Phys.Rev. Lett. {\bf 123}, 217002 (2019) the Fermi surface of UTe$_2$ consists of two types slightly corrugated cylinders.The theory of reentrant superconductivity in UTe$_2$ based on its quasi-two-dimensional structure is presented here.