I guess the same material which they can build dyson shpere - will do, wink wink
- man really, dyson swarm, not sphere, why do you tow that old mistake from 70's which wasn't even original design.
And dyson swarm is quite efficient in therms of mass energy extraction, not necessarly the best out there, a good fusion reactor can be better, but it is okay.
Shellwords are a waste, however, they may look nice on paper, but too much dead mass in reality, which does nothing but gravity.
Ring world is more or less okay however, but not necessarly of that size.
Just rough estimation, as order of things, but a ring made of 50GPa carbon nanotubes(not a 100 for different reasons, including safety margin) will break once rotated in the way to have 1g at its surface, at a diameter of that ring being about 3200km, which is far cry from 2.5 million you requesting.
There is a way to fix that, which brings the structure in category of active supporting ones, having rotating internal structure and stationary external structure which the rotating one is pressing to with a help of some sliding interface.
This way limits defined by material strength may be significantly extended, and shifted to limits of such sliding interface, and mass of the shell and its strength ofcourse.
Scaling up that 3200km ring to a 2.5million km one, will require putting 1000 times more material to outer shell that one in rotating one.
- for fun, an iron ring, 1GPa one as will be 20km ring and to scale it same way will require to put 125'000 times more material to outer shell than internal shell. And mass of it will be a mass of earth for each about 1000km of width at least(with 3m deep soil, 8t per m2 mass of internal shell)
But the whole thing(if scaled to 2.5kk km) will require some nanomachines son stuff, for purposes of keeping it repaired top notch state it requires to be for its operation, so as for purposes of that sliding interface to have proper properties and specs, so as to balance all the stuf for stability, so as to keep it spinning, so as for noise reduction etc.
That nano-stuf does not have to be actual nano, or nano in all 3d dimensions, like a typical gray goo is imagined, it can be micro 2d structure stuff, meaning a smallest unit is microns sizes in 2 dimensions, with some nanostructure internal stuff, like made of carbon nanotubes internaly, typical molecules and stuff and have macroscopic length like cm's or meters. Such 2d micromachines still is a magic by our modern standarts, but it a lesser blackbox or a handwavium than a gray goo, and what can be useful in reality, imho.
So if you smear that ringword bearing with some micromachines, then variety of materials which can be used is quite wide, high strength sure are preffered, but at least you are not limited by some indistructable adamantium stuff.
Such 2d micromachines can't be considered as a handwavium (which your typical gray goo still can be one, even with high tech) in a high tech setting, as we do have examples of micron size machines which are cells and bacterias, they are just made out of poor materials, which flaw a carbon nanotubes can fix to a great degree.
So I would put 2.5kk km ringworld in a viable category, it just not necessarly such a mass efficient one in the first place, so as considering plenthy of carbon required then it makes sense to make it a smaller ring and maybe extend it to be a torus (if you like to have no edge of the world, continiuous internal surface) with a diameter of what is rotating to be around few thousand km's max but diameter of the torus itself can be those millions km's you require. So internal volume will be a closed system, not like ringworld stuff half open, and ligthing problem has to be solved in a different way.
you can actually have a ringworld as grand-pa requested, meaning scaling it down is not necessarly makes it simplier, that iron scaled up bearing ring with 125000 mass on its stationary shell, if wrapped around sun at 1 a.u. will have reduced proportion of external mass, like just 2000 times more mass in external shell than in the internal rotating thing, due the gravity of the sun, which is about 5 mm/s2 at that orbit if I recall correctly. So building one around actual star may be in some sense simplier as material choices, but it will require plenty of those material, which sort of a problem here. Also it requires more from sliding interface, more speed difference, however less compression requirements, which may extend it variety of those interface solutions, but micromachines will still do, speed difference it their lesser concern.
Ah, yeah, materials in general. Advanced does not mean magic, so creating materials from nothing, and(or) transporting them in a solar system in reasonable time requires great deal of energy, if we talk on scsle of planet masses. Moving those masses in a single star system also requires plenty of energy, but considerably less of it.
So as element composition, considering that the guys like to use available materials sparingly, they will have to stick to the elements present in the system.(lets ignore converting all the hydrogen to heavy elements)
So even if they can make gold to become an unobtanium of strength of adamantium, is does not mean they have enough of that element in the system.
If they can bend space and time and convert all the matter in a system in to some specific element they sure they may do that, but can't tell about those guys that much, so the guys I was talking about aren't that space time benging level, but if they were then why bother to ask, rigth?, lol