"Red Dahlias" by Quinn Anderson (Sherlock)
This is a Sherlock vampire AU. Since this is actually an alternate universe where vampires play an important political/social role, you don't really need to know anything about canon to understand it but some background might be interesting/helpful.
The basic premise of the BBC series is this: Sherlock is a private detective, John is an army doctor recently returned from Afghanistan. They meet through a mutual acquaintes (Mike Stamford) because they're both looking for a flatmate in London. They start solving cases together and tons of queerbaiting ensues. The limp that is mentioned in the fanfic is canonical but it is actually Sherlock's brother Mycroft that first points out to John that he nevers limps when he is in danger / high on adrenaline.
The fanfic contains a decent amount of explicit sex, so be prepared. You can skip it and still get plenty out of the fanfic but I do think the discussions around vampirism and sex are also interesting. Depending on how you read the situation and pairing, consent could be considered dubious in the beginning, so be aware of that as well.