Screening of pair fluctuations in superconductors with coupled shallow and deep bands: a route to higher temperature superconductivity

A combination of strong Cooper pairing and weak superconducting fluctuations is of crucial importance to achieve and stabilize high-Tc superconductivity. Here we demonstrate that a coexistence of a shallow carrier band with strong pairing and a deep band with weak pairing, together with Josephson-like pair transfer between the bands to couple the two condensates, realizes an optimal superconducting multicomponent system: it preserves the regime of strong pairing to generate large gaps and very high pairing temperatures but screens the detrimental superconducting fluctuations, thus suppressing the pseudogap in the normal state. Surprisingly, we find that the screening is very efficient even when the pair-transfer coupling is considerably small. Thus, a multi-band superconductor with a coherent mixture of condensates in the BCS regime (deep band) and in the BCS-BEC crossover regime (shallow band) exhibits a promising route to obtain higher superconducting critical temperatures.