Vulcan can refer either to a single member of the alien race belonging to the Star Trek continuum, or to the home planet of said species.
The Vulcans are a humanoid race with pointed ears and eyebrows which slant down towards their noses, giving them a perpetually solemn and serious look. This is not misleading, as they are known for being stoic and logical. To have a Vulcan show emotion of any sort without justification (such as pon farr) is a charge.
Vulcans have eidetic memories, which means that their neuralyzed memories of Sues can be recalled with sufficient effort (or through triggering). However, their heavy mental discipline also implies that they can be persuaded to repress those memories again. They are also touch-telepaths, implying that they can ascertain the thoughts of another person through touch. Vulcan hands are extremely sensitive, and used to express gestures of intimacy.
Vulcans in Badfic
The Vulcans are also generally considered to be incredibly good looking, and are common Lust Objects for Star Trek. Spock may be considered one of the first Sue targets. In addition, many Sues claim to be Vulcan or half-Vulcan in order to share that with their Lust Object, and to gain Suvian good looks. However, they forget that being Vulcan means being logical. Many Sues therefore claim to be Vulcan but to embrace emotion instead of logic, not recognising that Vulcans raised on Vulcan that reject Surakian principles run along the range of the V'tosh ka'tur to the Romulans, and are generally frowned upon by the rest of Vulcan society.
Many Vulcans (especially Spock) forced into a relationship with a Mary Sue have been known to be territorial, possessive, manipulative, and over-emotional, with barely-there control on their emotions. Given that Vulcans have been trained extensively from childhood to erect mental shields and repress their memories, such a change in character is a chargeable offence and may even lead to character replacement.
A Vulcan that intrudes on another person's mindspace without permission is doing the Vulcan equivalent of mind-rape. It is also a chargeable offence.
Even in non-romance badfic, Vulcans can be written badly. Some badly-written OCs that don't have a love interest can still claim to be Vulcan or half-Vulcan for non-sexual reasons: they might want to have something in common with a Vulcan character they find cool (but not necessarily hot), they might want to be able to do things such as mind melds or nerve pinches, or they might simply think it's neat to be an alien. However, these OCs, and canon Vulcan characters, are not safe from authors making them act illogically and/or emotionally even if romance isn't involved, sometimes for comedy or because the author simply isn't good at figuring out how a Vulcan would respond to scenarios like those outside the plot.
Any fanfiction involving pon farr, romance or not, sometimes becomes a badfic by having a Vulcan act open about their pon farr, even though canonically, it's a very sensitive and private topic.