We consider the superconducting properties of Lieb lattice, which produces a flat-band energy spectrum in the normal state under the strong electron–electron correlation. Firstly, we show the hole-doping dependent superconducting order amplitude with various electron–electron interaction strengths in the zero-temperature limit. Secondly, we obtain the superfluid weight and Berezinskii–Kosterlitz–Thouless (BKT) transition temperature with a lightly doping level. The large ratio between the gap-opening temperature and BKT transition temperature shows similar behavior to the pseudogap state in high-T _c superconductors. The BKT transition temperature versus doping level exhibits a dome-like shape in resemblance to the superconducting dome observed in the high-T _c superconductors. However, unlike the exponential dependence of T _c on the electron–electron interaction strength in the conventional high-T _c superconductors, the BKT transition temperature for a flat band system depends linearly on the electron–electron interaction strength. We also show the doping-dependent superconductivity on a lattice with the staggered hoping parameter in the end. Our predictions are amenable to verification in the ultracold atoms experiment and promote the understanding of the anomalous behavior of the superfluid weight in the high-T _c superconductors.

我们考虑 Lieb 晶格的超导特性，它在强电子 - 电子关联下在正常状态下产生平带能谱。首先，我们展示了在零温度极限下具有各种电子 - 电子相互作用强度的空穴掺杂相关超导阶幅。其次，我们获得了轻掺杂水平的超流体重量和 Berezinskii-Kosterlitz-Thouless (BKT) 转变温度。间隙开口的温度和BKT转变温度示出了类似的行为之间的赝状态在高的大速比Ť _Ç超导体。BKT 转变温度与掺杂水平的关系表现出类似于在高T _{c 中}观察到的超导圆顶的圆顶形状超导体。然而，与传统高T _c超导体中T _c对电子 - 电子相互作用强度的指数依赖性不同，平带系统的 BKT 转变温度线性取决于电子 - 电子相互作用强度。我们还展示了最终具有交错希望参数的晶格上的掺杂相关超导性。我们的预测是经得起检验的超冷原子实验和推广超流的重量在高的异常行为的理解牛逼_Ç超导体。