  Conventional two-dimensional superconductivity is destroyed when the critical
in-plane magnetic field exceeds the so-called Pauli limit. Some monolayer
transition-metal dichalcogenides lack inversion symmetry and the strong
spin-orbit coupling leads to a valley-dependent Zeeman-like spin splitting. The
resulting spin-valley locking lifts the valley degeneracy and results in a
strong enhancement of the in-plane critical magnetic field. In these systems,
it was predicted that the density of states in an in-plane field exhibits
distinct mirage gaps at finite energies of about the spin-orbit coupling
strength, which arise from a coupling of the electron and hole bands at energy
larger than the superconducting gap. In this study, we investigate the impact
of a triplet pairing channel on the spectral properties, primarily the mirage
gap and the superconducting gap, in the clean limit. Notably, in the presence
of the triplet pairing channel, the mirage-gap width is reduced for the low
magnetic fields. Furthermore, when the temperature is lower than the triplet
critical temperature, the mirage gaps survive even in the strong-field limit
due to the finite singlet and triplet order parameters. Our work provides
insights into controlling and understanding the properties of spin-triplet
Cooper pairs.
