Origin of the Diagonal Double-Stripe Spin-Density-Wave and Potential Superconductivity in Bulk La$_3$Ni$_2$O$_{7}$ at Ambient Pressure

The discovery of high-temperature superconductivity (SC) with $T_c\approx 80$ K in the pressurized La$_3$Ni$_2$O$_{7}$ has aroused great interests. Currently, due to technical difficulties, most experiments on La$_3$Ni$_2$O$_{7}$ can only be performed at ambient pressure (AP). Particularly, various experiments have revealed the presence of spin-density wave (SDW) in the unidirectional diagonal double-stripe pattern with wave vector near $(\pi/2,\pi/2)$ in La$_3$Ni$_2$O$_{7}$ at AP. In this work, we employ first-principle calculations followed by the random phase approximation (RPA)-based study to clarify the origin of this special SDW pattern and the potential SC in La$_3$Ni$_2$O$_{7}$ at AP. Starting from our density-functional-theory band structure, we construct an eight-band bilayer tight-binding model using the Ni-$3d_{z^2}$ and $3d_{x^2-y^2}$ orbitals, which is equipped with the standard multi-orbital Hubbard interaction. Our RPA calculation reveals an SDW order driven by Fermi-surface nesting with wave vector ${Q}\approx(0,\pm0.84\pi)$ in the folded Brillouin zone (BZ). From the view of the unfolded BZ, the wave vector turns to ${Q}_0\approx\pm(0.58\pi,0.58\pi)$, which is near the one detected by various experiments. Further more, this SDW exhibits an interlayer antiferromagnetic order with a unidirectional diagonal double-stripe pattern, consistent with recent soft X-ray scattering experiment. This result suggests that the origin of the SDW order in La$_3$Ni$_2$O$_{7}$ at AP can be well understood in the itinerant picture as driven by Fermi surfaces nesting. In the aspect of SC, our RPA study yields an approximate $s^\pm$-wave spin-singlet pairing with $T_c$ much lower than that under high pressure. Further more, the $T_c$ can be strongly enhanced through hole doping, leading to possible high-temperature SC at AP.