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In the nearest vicinity of the critical temperature, types I and II of conventional single-band superconductors interchange at the Ginzburg-Landau parameter κ = 1/ √ 2. At lower temperatures this point unfolds into a narrow but finite interval of κ's, shaping an inter-type (transitional) domain in the (κ, T )-plane. In the present work, based on the extended Ginzburg-Landau formalism, we show that the same picture of the two standard types with the transitional domain in between applies also to multi-band superconductors. However, the inter-type domain notably widens in the presence of multiple bands and can become extremely large when the system has a significant disparity between the band parameters. It is concluded that many multi-band superconductors, such as recently discovered borides and iron-based materials, can belong to the inter-type regime.

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A combination of strong Cooper pairing and weak superconducting fluctuations is crucial to achieve and stabilize high-Tc superconductivity. We demonstrate that a coexistence of a shallow carrier band with strong pairing and a deep band with weak pairing, together with the Josephson-like pair transfer between the bands to couple the two condensates, realizes an optimal multicomponent superconductivity regime: it preserves strong pairing to generate large gaps and a very high critical temperature but screens the detrimental superconducting fluctuations, thereby suppressing the pseudogap state. Surprisingly, we find that the screening is very efficient even when the inter-band coupling is very 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) offers a promising route to higher critical temperatures.PACS numbers: 74.20. De, 74.70.Ad Multi-band and multi-gap superconductors have demonstrated a potential to exhibit novel coherent quantum phenomena that can enhance the pairing energy and the critical temperature T c [1]. The well-known examples are magnesium diboride [2-4] and iron-based superconductors [5,6], where multiple Fermi surfaces can be effectively controlled by doping or by applying pressure [7,8]. Multi-band superconductivity can be also achieved in artificial inhomogeneous structures made of a single-band superconducting material -nanofilms, nanostripes or samples with spatially controlled impurity distributions [9][10][11][12].The phenomenon entangled with the multi-band superconductivity, important in this work, is the BCS-BEC crossover [13][14][15][16]. Proximity to this crossover in multiband materials with deep and shallow bands can give rise to a notable increase of superconducting gaps [17][18][19][20], which on the mean-field level leads to higher T c . The physical reason is the depletion of the Fermi motion in a shallow band, which yields short-sized pairs. In such materials the superconducting state is a coherent mixture of a BCS condensate in deep bands and BCS-BEC-crossover or even nearly BEC condensate in shallow bands. This takes place in, e.g., in MgB 2 [19], many of iron-based superconductors [8,[21][22][23][24] and in nanoscale samples [17,18].However, the largest enemy of the high-T c superconductivity in such materials is superconducting fluctuations. They are significant for the same reason which leads to a higher T c -the depletion of the carrier motion in a shallow band that is associated with a low super-conducting stiffness. The fluctuations give rise to the pseudogap state in the interval T c < T < T c0 , where the extracted from the mean-field calculations T c0 marks the appearance of incoherent and short lived Cooper pairs. The latter develop a coherent state below T cthe true critical temperature of the superconducting condensate [25,26]. For shallow bands T c ≪ T c0 and this eliminates all gains of the BCS-BEC crossover regime.In this Letter we consider the mechanis...

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