Not yet, but there are hints.
The usual buzz phrase is "mono filament." The idea is a cable made of a single strand of atoms, or possibly molecules. For example, it has been contemplated that "bucky balls" could be lined up and made into a tube of carbon atoms.
https://en.wikipedia.org/wiki/Carbon_nanotube
This would be a few 10's of Angstroms across. This is far narrower than the edge on a steel blade could be maintained. So it means the force required to pull it through a material being cut would be far smaller.
Now there are lots of problems. It isn't clear that such nanotubes can be made arbitrarily long. It isn't clear they will stay strong over that length. It isn't clear how to manipulated them. For example, it might be necessary to "braid" them in some fashion, possibly with a bonding agent. That would mean the cord was not as strong as first indicated, since braided cables are usually weaker, especially if they are made of short segments of fiber. And the bonding agent would be the limitation. And it would mean the cable was thicker. Thing of yarn as compared to a single thread of sheep's wool.
Also, cutting something with such a thread has some interesting features. Some materials will separate quite nicely if cut this way. But some materials, often metals, will close over the cut and re-join. It may leave a flaw that is weaker, but might not separate. So, in the scene you reference in "The Three Body Problem" there is a large steel structure affected. (Trying not to give too many spoilers.) This might not have gone the way depicted. The steel structure might have re-welded itself. That is, the cut might have been narrow enough, and dislocated the metal sufficiently little, that it closed over the hole. It might have left a weak point but not split the structure. This is due to the same process that happens in vacuum welding.
https://en.wikipedia.org/wiki/Vacuum_cementing
Because the hole is so small, very little air can get in. So the ultra clean surfaces left by the thread might just re-join. Especially if there was significant pressure pushing them together. As there was in the steel structure in "The Three Body Problem."