  Chain-like structured superconductive materials (such as A_2Cr_3As_3, with A
= K, Rb, Cs) exhibit the multiband electronic structure of single-particle
states, where coexisting quasi-one-dimensional (Q1D) and conventional
higher-dimensional energy bands take part in the creation of the aggregate
superconducting condensate. When the chemical potential approaches the edge of
a Q1D band in a single-band superconductor, the corresponding mean-field
critical temperature increases significantly but the superconductivity is
quenched by fluctuations. However, recent investigation has revealed that when
a Q1D band is coupled to a higher dimensional one by the interband Cooper-pair
transfer, the thermal superconductive fluctuations can be suppressed so that
the resulting critical temperature can be close to its mean-field value. In the
present work, we calculate the mean-field T_c0 and fluctuation-shifted T_c
critical temperatures for a two-band superconductor where a Q1D band coexists
with a higher-dimensional band, and investigate how the thermal fluctuations
are sensitive to the system parameters. We find that T_c is close to T_c0 in a
wide range of microscopic parameters, and even the dimensionality of the
higher-dimensional band does not play an essential role. Thus, the screening
mechanism for suppressing fluctuations via the pair-exchange coupling between
the bands is indeed relevant for a large class of Q1D multiband superconducting
materials, encouraging further experiments aimed at reaching larger critical
temperatures in such multiband superconductors.
