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In the pursuit of higher critical temperature of superconductivity,quasi-flat electronic bands and van Hove singularities in two dimensions (2D)have emerged as a potential approach to enhance Cooper pairing on the basis ofmean-field expectations. However, these special electronic features suppressthe superfluid stiffness and, hence, the Berezinskii-Kosterlitz-Thouless (BKT)transition in 2D superconducting systems, leading to the emergence of asignificant pseudogap regime due to superconducting fluctuations. In thestrong-coupling regime, one finds that superfluid stiffness is inverselyproportional to the superconducting gap, which is the predominant factorcontributing to the strong suppression of superfluid stiffness. Here we revealthat the aforementioned limitation is avoided in a 2D superconductingelectronic system with a quasi-flat electronic band with a strong pairingstrength coupled to a deep band with weak electronic pairing strength. Owing tothe multiband effects, we demonstrate a screening-like mechanism thatcircumvents the suppression of the superfluid stiffness. We report the optimalconditions for achieving a large enhancement of the BKT transition temperatureand a substantial shrinking of the pseudogap regime by tuning the intrabandcouplings and the pair-exchange coupling between the two band-condensates.

High-$T_c$ Berezinskii-Kosterlitz-Thouless transition in 2D  superconducting systems with coupled deep and quasi-flat electronic bands  with van Hove singularities