Monowire

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Monowire weapons (also called monofilament or mono-molecular, depending on the setting) are a common class of soft sci-fi close-combat weapons. The idea is that, since blades cut better when their edge is thinner, blades one atom thick are the ultimate in slicing tools (short of energy weapons like lightsabers). Expect one-stroke battles where the two combatants rush past each other, sheathe their mono-swords, and one of them splits in half. Ever heard of a parry, moron? Despite what dumber-than-hell Hollywood portrays, edge on edge sword-play is pretty rare as it damages both blades.

Settings with weapons of this type may or may not explain how blades one atom molecule thick manage to hold together for any reasonable length of time. The answer usually involves hand-waving about a stabilizing force field or something (an exotic or otherwise non-natural molecular bonding is the most probable). Alternatively, they may explicitly declare that such weapons are extremely delicate, requiring frequent replacement of the blade. Realistically though if the blade could be even sharpened to that degree, that particular hurdle would be self resolved (anything hard enough to be sharpened to a mono-molecular level is not going to chip easily), skirted (like if the edge was tempered in such a way to resharpen itself via flaking) or outright null (only a mono-molecular blade would be able to concentrate enough kinetic force to deform another----see parrying).

Warhammer 40,000

The Eldar and Dark Eldar of Warhammer 40,000 use guns that shoot monowire nets that slice up infantry. Astartes combat blades and the teeth of chainswords are supposed mono-molecular as well.