sorry for my being 8 year old, but, does this better current capacity mean it can go faster? and the less heat problems mean it can do so without being cooled riduculously? (i.e. faster consumer products??)
Computing with graphene is still sci-fi territory, making a semiconductor only allows you to make transistors, not to necessarily make billions of transistors at nano-scales.
On the larger physical scale, transistors are used for stuff like mosfets and switching power supplies.
You might have noticed the new generation of Gallium Nitride (another semiconductor) USB chargers. They improve over silicon in every important dimension, I think, with a higher breakdown voltage, lower on resistance, higher electron mobility (which is what limits the speed it can cycle).
The gallium nitride chargers (when well engineered) waste less power, meaning they don't get as hot, and can be built much smaller for a given output.
I am not an engineer or a materials scientist, but I think graphene is better in thermal conductivity and electron mobility than GaN, but a semiconductor would probably have a smaller bandgap, because graphene naturally doesn't have much of one at all, meaning it'd have a smaller operating range in temperature and voltage.
A major problem with current ICs, which gets much worse in 3D (stacked etc) designs, is keeping the transistors cool.
The transistor has a maximum operating junction temperature[1] which is limited by material and process.
Higher density chips make it difficult to extract the generated heat, in order to keep those junctions cool.
The heat is generated when the transistors switch from either on to off or vice versa, due to all normal conductors having some resistance, and switching a transistor involves sending or draining a small amount of current to its control element called the gate. Thus switching faster means more heat. More transistors in the same area all switching means more heat.
So either by making it easier to wick away the heat, or by tolerating higher junction temperatures, a different material to silicon might allow for higher density or faster switching before heat becomes an issue.
Of course there are other obstacles to increasing density and frequency, so just because a material has better thermal properties doesn't imply it'll allow for higher density or frequency.