Spin excitations in bilayer La${}_3$Ni${}_2$O${}_7$ superconductors with the interlayer pairing

Prompted by the recent discovery of high-temperature superconductivity in La${}_3$Ni${}_2$O${}_7$ under pressure, this study delves into a theoretical investigation of spin excitations within this intriguing material. Through self-consistent mean-field calculations, we propose that superconductivity in this compound is primarily driven by interlayer pairing mechanisms. This interlayer pairing results in an effective $s_{\pm }$ pairing gap, with the sign of the pairing gap varying across different Fermi pockets. In the superconducting state, our analysis reveals a striking absence of a spin resonance mode. Moreover, we reveal a spectrum of energy-dependent incommensurate spin excitations. The observed incommensurate structures are elegantly explained by the nesting effect of energy contours, providing a coherent and comprehensive account of experimental observations. The implications of these spin excitations in La${}_3$Ni${}_2$O${}_7$ are profound, offering critical insights into the superconducting mechanism at play. Our results not only contribute to the understanding of this novel superconductor but also pave the way for further research into the interplay between spin dynamics and unconventional superconductivity in layered materials.