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Unconventional Superconductivity in UTe2

The novel spin-triplet superconductor candidate UTe2 was discovered only recently at the end of 2018 and attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe2 is a heavy-fermion paramagnet, but right after the discovery of superconductivity it has been expected to be close to a ferromagnetic instability showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. The competition between different types of magnetic interactions and the duality between the local and itinerant character of the 5f Uranium electrons, as well as the shift of the U valence appear as key parameters in the rich phase diagrams discovered recently under extreme conditions like low temperature, high magnetic field, and pressure. We discuss macroscopic and microscopic experiments at low temperature to clarify the normal phase properties at ambient pressure. Special attention will be given to the occurrence of a metamagnetic transition at Hm = 35 T for a magnetic field applied along the hard magnetic axis b. Adding external pressure leads to strong changes in the magnetic and electronic properties with a direct feedback on superconductivity. Attention will be given on the possible evolution of the Fermi surface as a function of magnetic field and pressure. Superconductivity in UTe2 is extremely rich exhibiting various unconventional behaviors which will be highlighted. It shows an exceptionally huge superconducting upper critical field with a re-entrant behavior under magnetic field and the occurrence of multiple superconducting phases in the temperature field, pressure phase diagram. There is evidence for spin-triplet pairing. The different theoretical approaches will be described. Notably we discuss that UTe2 is a possible example for the realization of a fascinating topological superconductor.