Temperature and doping dependent flat-band superconductivity on the Lieb-lattice*

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.