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Interplay between Rashba spin orbit interaction (SOI) and superconductivitycan give rise to many interesting effects where an in-plane magnetic field isessential. For instance, for a 2D system with strong Rashba SOI proximitycoupled to a s-wave superconductor, the in-plane magnetic field can drive thesystem into a gapless superconducting state while it can also induce a miragegap at finite energies for an Ising superconductor while keeping the main gapat Fermi level intact. We show that when a s-wave superconductor proximitizedto an altermagnet in the absence of SOI and in-plane magnetic field, thegapless superconducting state with mirage gap can emerge showing d-wavesignature, due to the anisotropic spin splitting of the altermagnet. When theRashba SOI is added, the system can turn into a gapped superconductor w ithmirage gap. Pairing mechanism and transport properties of mirage gap areinvestigated. Our result suggests that altermagnet is an ideal platform forstudying gapless superconducting state and mirage gap.

Gapless superconducting state and mirage gap in altermagnets