First-principles Study of Electronic Structures and Phonons in FeSe$_{1-x}$

We present first-principles density functional theory based calculations to assess the effects of Se vacancies (which are essential for the material to be superconducting) and strength of on-site correlation on (a) phonon frequencies, and (b) electronic density of states of the non-magnetic and different magnetic phases of $FeSe_{1-x}$. Our calculations show that energetically anti-ferromagnetic stripe ordering is favorable compared to the non-magnetic and other magnetic phases. We also find that the phonon frequencies are quite sensitive to the vacancies, magnetic ordering and on-site correlation parameter U, and interpret these results in terms of spin-spin and spin-phonon couplings. Our estimate of the spin-phonon coupling is comparable to the superconducting transition temperature of FeSe. The presence of Se vacancies in the system results in a large peak in the density of states near the Fermi level, which possibly enhances the superconducting transition temperature.