Postdoc interview follow-up: HR or PI and how should I approach the conversation?
You could contact both, actually, but differently. It is probably early for them to make a decision (scheduling meetings, perhaps), but not to early to follow up with the PI to give thanks for consideration and ask a bit more about the position and the work if you have any remaining question. You can also, safely, express your enthusiasm. 

But pressing them for an early decision is probably a mistake. 

HR, on the other hand could be asked about the typical length of time for decisions. I assume they are not as invested in the decision as the PI.