  It is now well established, both theoretically and experimentally, that very
small changes in the size of isolated nanograins lead to substantial
nonmonotonic variations, and sometimes enhancement, of the mean-field
spectroscopic gap of conventional superconductors. A natural question to ask,
of broad relevance for the theory and applications of superconductivity, is
whether these size effects can also enhance the critical temperature of a bulk
granular material composed of such nanograins. Here we answer this question
affirmatively. We combine mean-field, semiclassical, and percolation techniques
to show that engineered nanoscale granularity in conventional superconductors
can enhance the critical temperature by up to a few times compared to the
nongranular bulk limit. This prediction is valid for three-dimensional and also
quasi-two-dimensional samples, provided the thickness is much larger than the
grain size. Our model takes into account an experimentally realistic
distribution of grain sizes in the array, charging effects, tunnelling by
quasiparticles, and limitations related to the proliferation of thermal
fluctuations for sufficiently small grains.
