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In ferromagnetic superconductors, like URhGe, superconductivity co-existswith magnetism near zero field, but then re-appears again in a finite fieldrange, where the system also displays mass enhancement in the normal state. Wepresent theoretical understanding of this non-monotonic behavior. We explorethe multi-band nature of URhGe and associate re-entrant superconductivity andmass enhancement with the finite field Lifshitz transition in one of the bands.We found good agreement between our theory and a number of experimental resultsfor URhGe, such as weakly first order reentrant transition, the dependence ofsuperconducting $T_c$ on a magnetic field, and the field dependence of theeffective mass, the specific heat and the resistivity in the normal state. Ourtheory can be applied to other ferromagnetic multi-band superconductors.

Effects of Lifshitz transitions in ferromagnetic superconductors: the case of URhGe