Tunable surface electron gas and effect of phonons in Sr$_2$CuO$_3$: A first-principles study

While the conducting CuO$_2$ planes in cuprate superconductors have been widely recognized as a crucial component in producing high superconducting $T_\text{c}$, recent experimental and theoretical studies on Ba$_{2-x}$Sr$_x$CuO$_{3+}$$_\delta$ have also drawn much attention to the importance of Cu-O chains in one-dimensional (1D) cuprates. To better understand the cuprates containing Cu-O chains, here we have studied the electronic, magnetic, and phonon properties of Sr$_2$CuO$_3$ bulk and films based on the spin-polarized density functional theory calculations. We first reproduced the typical Mott insulator feature of the cuprate parent compound for bulk Sr$_2$CuO$_3$, and then built a Sr$_2$CuO$_3$ thin film with Cu-O chains exposed on the surface to directly investigate their characteristics. Different from the insulating bulk phase, the Sr$_2$CuO$_3$ surface shows interesting metallic properties. Further electronic structure calculations reveal the existence of spin-polarized electron gas between surface Sr atoms that strongly depends on the interchain coupling of Cu spins. Moreover, the phonon modes that involve the vibrations of in-chain and out-of-chain O atoms can induce strong charge and spin fluctuations in the surface layer of Sr$_2$CuO$_3$ film, which suggests significant multiple degree-of-freedom couplings that may be important for the superconductivity in 1D cuprates. Our work provides a comprehensive viewpoint of the properties of Cu-O chains in Sr$_2$CuO$_3$, facilitating a complete understanding of 1D cuprate superconductors.