Introducing High-Frequency Phonons to Cuprates with Light Elements*

Cuprate metal oxides host unconventional high-temperature superconductivity, whose microscopic mechanism is still under debate and investigation. Despite this lack of clarity, a great deal of research has been done on modifying the superconductivity which has provided information and constraints on the superconducting mechanisms.  Separately, within the BCS framework and its refinement by Eliashberg, high-frequency phonons, which can be introduced by light elements such as hydrogen and lithium, can give rise to relatively high-temperature superconductivity but go together with a sign-preserving s-wave gap that is not compatible with the observed d-wave superconductivity. Interestingly, recent studies have shown that electron-phonon coupling with vertex corrections can lead to sign-changing superconducting gap symmetry [Schrodi, PRB, 2021]. Inspired in part by these ideas, we aim to see how incorporation of light elements in cuprates may change the phonon modes and their effects on electronic structure. In our first principles theoretical density functional theory work, we choose Bi₂Sr₂CaCu₂O₈ (BSCCO, Bi-2212) as a prototype and study its structural, electronic, and phononic response to lithium and hydrogen doping.