Vorpal

The inexistent holy sword Vorpal(存在しない聖剣ヴォーパル; Sonzaishinai seiken vu~ōparu) is a Holy Sword with an interesting twist: it isn't in fact a sword, but instead a concept created by a nameless warrior(?) which it came to be by sheer force of thought. Currently, it is in the possession of Sakura Nagamura in DxD: Haremonogatari.

Summary
It turns out, Vorpal is not in fact a holy sword forged by the God of the Bible, but instead a concept created by a nameless warrior(?) who turned it into reality by sheer force of thought.

A long time ago, a nameless warrior said to his village that he slaughtered a dragon by the name of Jabberwocky and that he saved the village from a disaster. Without any proofs, he was ridiculed by his peers, and almost shunned out by the elders, only by a nail escaping. On the second day, the same nameless warrior appeared by the village saying that he brought Vorpal as a proof of his feet, but only him can see it, displaying nothing but apparently air on his hands. This time, the nameless warrior was indeed shunned away in a small cell around the village, only to be found dead inside of it, with his throat cut despite the lack of cutting objects inside his confinament.

The sword(?) would be forgotten for many ages, only to be found by another being whose existence is firmly linked by the thoughts of others: a Tulpa. It was later given to Ryuusei Amano as a token of friendship between the two, but the latter refused it, instead saying for Sakura to store it inside of herself for later use.

Appearance
Vorpal has no shape or form, being also weightless and invisible for the naked eye. Ryuusei describes it saying he can't feel anything while wielding it, and that the grip feels almost like nothing on his hands.

Abilities
Vorpal is an holy sword that only exists on the thoughts of others. Being able to slay devils and dark creatures like any holy sword, Vorpal can only manifest itself when the target believes in the existence of it, even for a small second or within the small doubt. As such, Vorpal is unable to cause collateral damage to the enviroument or the clothes of others, since they're not living beings, and as such can't be sentient to doubt about the sword's existence. However, this is also the main weakness of the sword, as anyone who doesn't believe in its existence will not be affected by it. This goes for any wielder as well, as Vorpal will cease its existence altogether.

Since the thought of the sword is what gives its shape, Vorpal has the ability to be teleported back to the user's hand by thought, saving the latter's the trouble to retrieve it.

Trivia

 * The image used for it comes from the Invisible Air ability from the FATE/ series.
 * Vorpal is named after a poem of the same name by Lewis Carrol.
 * According to Sakura, she can only sense Vorpal and tells its a Holy Sword, as anything else is a mystery for her.
 * It is unknown if Vorpal has any other additional abilities.