I could improve the electrical conductivity of polymers not metals but I hope it helps you. I worked in some kinds of conducting polymers and by adding the Ag nanoparticles ( I mean synthesis of nanocomposite) I could increase the electrical conductivity of the final polymers.
In mainstream science - nothing.
Pure metals have theoretically maximal possible electrical conductivity, determined by the amount of overlap of wavefunctions of their delocalized electrons.
Only alternatives are superconductors.
But i remember some controversal experiments about sodium-ammonia alloys at -90C temperature. These behaved nearly as superconductors (current in loop presisted for few hours). But they was not superconductors - temperature was too high and optical properties were seemingly metallic.
The problem was the extreme chemical reactivity, thermal instability and brittleness of these alloys. Experiment was nearly impossible to reproduce, and material absolutely impossible to use in any practical application.
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