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Tetragonality induced superconductivity in anti-ThCr$_2$Si$_2$-type $RE_2$O$_2$Bi ($RE$ = rare earth) with Bi square net

We report a series of layered superconductors, anti-ThCr$_2$Si$_2$-type $RE_2$O$_2$Bi ($RE$ = rare earth), composed of electrically conductive Bi square nets and magnetic insulating $RE_2$O$_2$ layers. The superconductivity was induced by separating Bi square nets as a result of excess oxygen incorporation, irrespective of the presence of magnetic ordering in $RE_2$O$_2$ layers. Intriguingly, the transition temperature of all $RE_2$O$_2$Bi including nonmagnetic Y$_2$O$_2$Bi was approximately scaled by the unit cell tetragonality ($c$/$a$), implying a key role of relative separation of the Bi square nets to induce the superconductivity.