Sharpened to a Single Atom

Weapons that have been sharpened to a single atom are a particular type of Absurdly Sharp Blade that are so sharp, their cutting edge can be measured in terms of atoms or molecules, often being just a single molecule wide. This usually gives the weapons Absurd Cutting Power, but generally requires the blade to be made out of some sort of Unobtanium to maintain that sharpness without dulling instantly (or just shattering into a million pieces) the first time it's used. For these reasons, the trope is most frequently encountered in Science Fiction settings.

A common term used for this is "monomolecular". Most often seen with knives or swords, but occurs from time to time with Razor Wire, too. This can be particularly troublesome, as monomolecular wire is usually functionally invisible, and walking into one can slice through vital bits without being immediately noticed.

A weapon is only an example of this trope when a specific (very small) width is given for the blade's edge; if no specific measurement is given, then it's just an Absurdly Sharp Blade.

Anime and Manga

 * Mamoru's katana from Until Death Do Us Part is a high tech monomolecular blade, able to break the bonds between molecules and cut anything (if the katana's angled properly). At one point he cuts a gun in half; when the pieces are pushed back together, it appears as if the gun was undamaged, because the cut is that sharp.
 * In Kiddy Grade, Sinistra and Dextera's ship can split into two, creating a 'monodimensional' blade between the halves.

Comics

 * Nemesis, a member (and former enemy) of Alpha Flight, uses a saber whose blade is only a single molecule wide.
 * In Kingdom Come Wonder Woman has a sword that is sharp enough to "carve the electrons off an atom". Leaving aside the ways that doesn't actually make sense, it suggests a blade with an edge thinner than an atom. Superman accidentally cuts himself on the blade.

Film

 * In Stargate Continuum, the blade held by Ba'al (later stolen by Qetesh) has an edge "only one atom thick", making it thin enough to cut Ba'al clean in half.
 * The assassin in Johnny Mnemonic has a monomolecular wire concealed in a prosthetic thumb tip.

Literature

 * The variable sword used in the Known Space stories of Larry Niven is a length of monomolecular wire held straight by a projected stasis field. There's a little red ball at the end of the wire so the wielder can tell where the otherwise invisible "blade" ends.
 * The Posleen in John Ringo's Posleen War Series have monomolecular blades that can carve up an Armored Combat Suit as easy as a Ginzu knife cuts through a tin can. And then they can slice a tomato so thin you can read a newspaper through it!
 * Brasyl, by Ian McDonald, one-ups monomolecular-edged knives with the Q-knives: they have an edge that can cut quantum strings. Y'know, the stuff that decides matter is matter. If a Q-knife ever breaks, the fragments sink towards the Earth's core.
 * In Snow Crash, by Neal Stephenson, Dmitri "Raven" Ravinoff uses knives made of knapped glass with monomolecular edges. They slash through Kevlar body armor, thick bamboo and people quite effortlessly, though they're.
 * The main character, as well as just about everyone, in Sergey Lukyanenko's A Lord From Planet Earth series wields a monoatomic sword called a planar sword. The main character, in fact, dual-wields them and carries them on his back. As expected, the swords can cut through any known material. In one-on-one combat with planar swords, one of the swords will invariably slice through the other. The trick is making sure you hit the opponent's sword at just the right angle with a thinner blade. The blade dulls with each strike and swing, requiring it to be periodically sharpened by a button on the hilt (a blade can only handle about 1500 sharpenings). Being a battle-hardened Earthling, the main character comes up with some nonstandard (and questionable) applications for the technology. He creates a throwing disc with monoatomic edges, which can literally take a person's head off. Later, he uses smaller hollow-point monoatomic discs that fire from a blowgun.
 * Flann O'Brien's The Third Policeman features a spear so sharp that if you were to prick yourself with it, your finger would begin to bleed about 2 inches before the point appeared to reach your finger. In fact, when your finger starts to bleed, the spear point had penetrated your skin 2 inches ago, but was so thin it slipped between the atoms of your finger without causing any damage.
 * In Man of the Ice Garden, Vuko Drakkainen, a visitor from future Earth to a primitive planet, uses a Nordland Aeronautics shinobi ken sword with monomolecular blade. He once made a swing at a "monster" and accidentally cut through the ceiling without even noticing until some of its parts fell down. He also accidently cut through the dog, which hit the ground twice.
 * In the Star Trek Novel Verse, the Tholians have blades with monomolecular edges. The swords become important to the plot in the novels The Sundered and Reap the Whirlwind.
 * In the Firebird Trilogy, the edges of crystaces' blades are precisely one atom thick.
 * The Dark Side of the Sun by Terry Pratchett features a monomolecular blade (which shatters when swung against a villain gifted with luck manipulation).
 * They came up again in his Discworld series - both Death's scythe and sword have edges one molecule thick.
 * Star Wars Expanded Universe
 * In the short story "Side Trip", Jodo Kast, who is actually Thrawn in disguise, gives one to.
 * Blades like this make an appearance in the novel Specter of the Past by Timothy Zahn, in the form of the Xana "molecular stiletto." Depicted somewhat realistically, in that it's described as being capable of cutting through almost anything, but is extremely delicate, with even the carefully executed cutting of a hard surface (such as a lock) being as likely as not to ruin the blade.
 * In the Sten novels, Sten has a small knife in his forearm (within a surgical compartment) that can cut through virtually anything. It's five molecules wide at its tip.
 * Matthew Mantrell wields one in at least the first book of A Wizard in Rhyme.
 * In The City Who Fought by Anne McCaffrey and S.M. Stirling, Joat lays a trap using monomolecular wire. The effects are messy.

Live Action TV

 * Andromeda once depicted a "monomolecular lash", basically a whip that can cut through anything and has to emit a glow in order for anyone to see it. Since it cuts through its wielder as easily as anything else, it's exceedingly difficult to master without killing yourself with it and expert users of it are very rare, mostly making it Awesome but Impractical.

Tabletop Games

 * Most combat blades in Warhammer 40000 have an edge one molecule thick. This includes combat knives, swords, some types of ammunition, etc. Such blades are quite commonplace in their armies.
 * They're no more effective at punching through armour for it, however, unless you're playing Dark Heresy.
 * The Eldar Harlequin units have a weapon called The Harlequin's Kiss, which is a molecule thick whip yards long, delivered in a neat bundled package with a punch, at which point it unfurls, and then snaps back into the delivery device. They deploy this weapon by shoving the neat bundled package right into your mouth (with the open end down your throat), thus the name.
 * Fading Suns has wireblades -- monomolecular swords that will cut through anything with ease. In game mechanics, this means they ignore any armor the opponent is wearing.
 * Shadowrun had monomolecular axes that possessed a monofilament edge capable of cutting through virtually anything. It tends to lose its edge quickly though. In later editions, other bladed weapons could be outfitted with a monofilament edge. There's also a monofilament whip, noted by 'in character' reviews to be as big a threat to the user as to a potential enemy.
 * GURPS Ultratech has a number of (increasingly super-science) ways of working this into the game mechanics. Superfine blades divide damage resistance by two. Monowire blades divide damage resistance by ten. Nanothorn blades divide damage resistance by ten and shreds the bonds that hold the atoms in molecules together.
 * Monofilament Swords are a common bladed weapon in Eclipse Phase, made with self-sharpening smart materials. They easily have some of the highest penetration and damage of any melee weapon in the game.

Video Games

 * The manual for Starcraft hints that Ultralisk blades are monomolecular. That they bother to point this out is quite strange, as the Ultralisk does a ridiculously low (for its size and implied danger) 20 damage, requiring two hits to kill the weakest game unit. The Torrasque does a far more respectable 50 damage, which is a one-hit-kill against most infantry units.
 * In the Buck Rogers games, mono(molecular) knives and swords are described in this way. In true RPG fashion, they are superior to most of the 25th-century guns available.
 * In One Must Fall 2097, the manual describes Thorn's spikes and Katana's blades as using "monofilament technology".
 * Cerberus Phantoms (ninja mooks) in Mass Effect 3 carry monomolecular swords.
 * The Dragon Tooth Blade from Deus Ex is said to be made of self-organizing nanites which keep the blade always molecularily sharp.

Western Animation

 * In Batman Beyond, Assassin Curare uses a monomolecular sword that effortlessly cuts through anything standing in the way of her swings.

Real Life

 * Contemporary nanotechnology is actually capable of creating blades like this, but, with a few exceptions (see below, mostly), not sustaining them. Regular blades go dull; an edge that can be measured in atoms becomes an ordinary knife very quickly if those atoms do not have very strong atomic and intermolecular bonds.
 * Knapped obsidian blades are a small and measurable number of molecules in thickness. And while diamond is the harder material, obsidian can be made sharper. The greatest of care should be used in handling obsidian knives and arrow points etc because they can remain truly Absurdly Sharp even centuries after being made and will cut you badly with even the slightest touch. The drawback of course is that being basically an exotic form of glass, they wear out quickly in use.
 * Obsidian blades are still used in eye surgery when a clean cut is needed.
 * Anthropologists and paleontologists have "tested" the technology available to Stone Age humans by using hand-knapped obsidian blades to butcher an elephant's carcass.
 * Obsidian can be made up to 100 times sharper than steel (the cutting edge can be reduced to 3 nanometers thick). According to The Other Wiki, "even the sharpest metal knife has a jagged, irregular blade when viewed under a strong enough microscope; when examined even under an electron microscope an obsidian blade is still smooth and even." For surgical application, the blades are so sharp that in certain circumstances, no anesthetic is necessary to make the cut.
 * Single-layer graphene is probably the sharpest blade that can be made with conventional matter. It's a single atom thick, and since the atom is carbon (atomic number 6, very low on the periodic table), it's thinner than you can get pretty much any substance without distributed electron orbitals to stiffen it, and it's essentially the strongest material known that operates on that scale. Per unit area, it's stronger than diamond, though diamond is superior at greater thicknesses, due to graphene's weak inter-layer binding.
 * Carbon nanotubes are basically graphene sheets rolled up into a tube, so by definition are a single molecule thick.
 * To prepare a slide for an electron microscope, a diamond or broken glass blade is used to get a less-than-paper-thin slice. Once properly sharpened, it's about a hundred atoms wide, and it will slide through your hand as easily as through the air. Glass blades are sharper (and cheaper) but wear out after a few dozen slides; diamond blades last almost forever.
 * A Scanning Tunneling Microscope has a sensor which is a needle coming to a tip which consists of a single carefully placed atom.
 * That's a bit of oversimplification. The working part of this sensor (which is called just the tip — gotta love the simplicity) is indeed a single atom, but the slope of the tip doesn't extend all the way to it. Instead it terminates in a relatively large dome-shaped end with the radius of ~10 nm (or, in layman's terms, about 100-200 atoms wide). On the other hand, 100 atoms, while not one, still are absurdly sharp. Even if the slightest sideways force bends the tip end, if you apply it head on you can easily pierce your finger through.