When I encounter annoying behavior in the workplace, I try to ask myself "Is the behavior adding value to the organization or me?" If the answer is "yes" then I try to focus on that and maybe learn something.
From what the OP has said, the jerk's behavior is not adding value at all, but rather destroying value in terms of team cohesiveness and efficacy. You might, as DarkCygnus has suggested, raise the issue with management again, but focus on the negative effects on productivity the jerk has. Be prepared for management to either (A) still not care or (B) tell everyone who has an issue with the jerk to look for work elsewhere. You will have a better chance of getting management to listen if you offer a solution like
Please tell the jerk that even though he's very productive he has
to interact professionally with the rest of the team or he will be
Finally, in my experience (~30 years in Silicon Valley), when someone goes out of their way to criticize, then refuses to offer an improved solution, they are being a douchebag just for the sake of hurting others. This is completely unprofessional behavior and should be called out immediately and publicly as such, along the lines of
The fact that you refuse to offer a suggestion for improvement
indicates strongly that you can't offer an improvement and are nothing
but a (jerk|douchebag|asshole|choose a pejorative to fit your company
culture) who doesn't care about making a better product or
organization. Why don't you try helping for a change? And criticism
without suggestion for improvement is not help... it's just being a
(jerk|douchebag|asshole|choose a pejorative to fit your company
culture), which is what you are.
Others may suggest that name calling is just as unprofessional, but I would argue that it's done with the intent of improving the office environment/culture for the majority and thus of value.
I have done this before and have not been fired for it, yet. Also, it has made a positive difference in terms of the offender at least holding back on the vitriol if not being more helpful.