You say that making the character drunk wouldn't work because there'd be evidence, e.g. a hangover. But so what? If someone woke up with a hangover, he'd know he'd been drunk, maybe he'd realize that he didn't remember anything he did the night before, but it would be quite a leap from "I was so drunk I don't remember what I did last night" to "I must have murdered someone".
Ditto various other drugs.
The idea of a brilliant detective being a drunkard or a drug addict seems a little out of character to me, but you could always come up with a reason why this one time he did something out of character, like an extreme personal problem. Or someone deliberately drugged him. (Ooh, suddenly gave me an amusing idea: A woman wakes up to realize that someone has given her a date-rape drug. While she's trying to figure out just who did it and what he did to her, she finds out that while she was drugged, she murdered someone. Like, she's thinking she was the victim and then it turns out she was the criminal.)
People who have amnesia don't remember what they did. That's pretty much the definition of amnesia. You'd have to give some explanation for it -- you can't just say, "oh, by the way, he had amnesia".
If it's a science fiction story, you can always invent some machine that erases memories. Then you can introduce the machine early in the story and have it be a part of the plot way before you reveal that it was used on the detective.
To follow up on someone else's suggestion: Is it necessary to your story for the hero to have deliberately killed the person? If not, then it could be some sort of accident and he doesn't realize anyone was killed. Ranging from "I wonder what this switch does?" to "I thought I hit someone with my car in the dark but there's no sign of a body", like because the person was thrown somewhere that the hero can't see the body, or maybe he runs away and dies somewhere else.
BTW saying this or that scenario would leave evidence: That would be a good thing, so there is some foreshadowing. You don't want to get to the final scene in the story and then with absolutely no warning say, "And then he noticed that the glove found at the scene was a perfect match for the one glove in his own coat pocket. He suddenly realized that he himself was the murderer. The end." There have to be some clues building up to this point. An early scene where the detective has a period of time that he doesn't remember what he did, which is then explained away in some plausible manner, and then brought back at the end, if done properly could be a nice piece of foreshadowing.