Found a major flaw in paper from home university – to which I would like to return

Don't make it personal. Keep it about the science. You can inform them of the flaw and let them fix it or you could just publish a new paper with better results, pointing out the flaw if needed. That would depend on whether you want the new result under your name or are happy enough for it to be under theirs.

If you write, however, and get pushback, evaluate it fully and then publish or not as you choose. But I wouldn't get into an argumentative back and forth about it. And if you just decide to publish it, as a courtesy you can send them your paper when you submit it to a publisher: For Your Information...

The science is the important thing.

I'm no physicist, but speaking from common sense: Depending on how "ground-breaking" your discovery of their mistake is, here are the options I would consider:

• Silly mistake that could have been avoided by being careful or by knowing a bit more math: Write up a correction, contact the group and offer to co-author the correction with them, so that way everyone "saves face" and you are likely to remain friends and future colegas.

• Fundamental mistake that some of their team members may not pick up even after lengthy communication: proceed as above initially, knowing that you may end up publishing alone (if you're correct about the mistake and manage to convince a journal). Friendships may or may not be damaged.

• Earth-shattering stuff that requires a gestalt shift: write up, contact them for the sake of politeness and to give them a chance for a rebuttal, but publish alone. Science wins, but friendships not so much.

In all cases, remain super polite and respectful, obviously.

A diplomatic way to title your write-up: "Corrigendum" or even "Comment" rather than "Rebuttal."

The first thing to do is to typeset your work and check it - if possible ask someone else to look over it if only superficially to make sure there is no obvious oversight on your part. Typesetting is a form of deep proofreading so this will also force you re-evaluate your own work with the mindset of explaining to others what you have done.

The next thing is to contact one of the persons involved (presumably the senior author if possible) in the erroneous paper, asking for clarifications and supplying your notes as evidence that you cannot duplicate or disagree with the original result. Statements like I am quite puzzled as to how you got from here to here because... or Could you clarify why you make this approximation because it seems to me... are useful for softly directing attention to the contentious issues.

Presumably this would be enough to get some sort of discussion going. The key point is to allow plenty of time for the other group to assess your own work and compare it to theirs.

Finally, you can eventually write your own rebuttal, including in the conclusion or acknowledgments discussions with authors of said papers if such a back-and-forth took place.

I have been on the receiving end of such papers, i.e. some groups have published results challenging work done with collaborators, whereas in fact we had never made the claims under challenge. I have also received advanced copies of manuscript citing my papers and found the authors to have overlooked a crucial details. I much prefer the second scenario, irrespective of where an error was to be found.