Should I give professor gift at the beginning of my PhD?
I would prefer not get a gift from someone that is dependent on me. I don't want to end up in a situation of perceived (by the person receiving the gift, giving the gift, or by an outsider) bribery. I realize that in many cases it is an innocent show of appreciation, but just saying (or writing) "thank you" will achieve the same goal without the risk of it being perceived the wrong way.
No way! It puts them in an uncomfortable position, even if they do not (and were not tempted to) accept it. They have the choice of (possibly) upsetting you, considering this a potential influencing attempt, even if not ultimately completed, in some places having to report it.
In our place, we have to report all gifts or gift attempts, and hand them to the institution if they exceed a certain (very small) value. In other words, it creates extra work and we don't even get to enjoy it.
Thank the professors that decided to take you on by doing a good job.
(Answer from Germany)
Don't do this. Even small personal gifts in this situation are unusual here and may indeed create a "fishy" taste.
German professors are public officials and public servants (so also other employees at university) are subject to strict anti-corruption rules.
If you get an employment contract as PhD student, you'll also have to sign these rules among tons of other paperwork.
As soon as there is a relation to their office (e.g. the professor being one of your examiners for some exam such as your PhD defense), any kind of gift is a big no-no.
And not only before the marks are given, this is still true afterwards (even after prof retires!).
This makes a gift at the beginning of your PhD at the very least awkward. Not as bad as directly before the defense, but still...For other occasions, where the general opinion is that they are harmless small gifts are OK (e.g. in Hessen < 20 €, but e.g. Berlin < 5 or 10 €).
Think along the lines of being allowed to have some of the coffee, cookies or sandwiches another institute/company paid for during the project meeting. Or someone offering a ride to the train station. Or pens, paper and/or a coffee mug at a trade fair.If it is or looks more valuable, the receiver has to announce this gift to their boss or to anti-corruption administration who then decide what to do with it.
This of course creates burocratic hassle, so isn't appreciated. But this is how a professor can solve the conflict and save the face of a foreign student who's from a country where it is customary to give (even a valuable) gift to the professor which is clearly outside all accepable limits in Germany - but it would also hurt the student to refuse that gift.
Still, I'm happy you asked and thus can avoid putting the professor in such an awkward situation.The workgroup collecting money for a birthday gift of the professor is OK, as that's considered a private gift in no way related to their job.
What to do instead
In contrast, it is not only perfectly fine and polite but in some places even weakly expected that you bring e.g. some sweets from your home country for the whole group (if feasible). Or bake a cake, bring some ice cream or the like.
(Same btw. for your birthday)It is also fine if, after you successfully defended your PhD, you throw a party for your group and also include your professor in the invitations.