"Still" , "Yet" and "Already" are words which often cause trouble for students of English. So let's try and distinguish clearly between them.
Still - continuing action
Yet - non-commenced or non-terminated action
Already - terminated action or an acquired state
We use still not yet or already to refer to the continuation of a situation:
I still meet my friends from my schooldays now and then. (I continue to meet my friends)
Not: I already meet my friends or I yet meet my friends
Negatives with yet mean that something has not happened up to now:
I haven’t spoken to Henry about the car yet.
Negatives with still suggest that the situation should have changed, but it has not:
I still haven’t found my passport. I know it’s here somewhere. (I’ve been looking for it for a long time. I should have found it by now)
Negatives with already are far less common than negatives with yet andstill. They usually refer to things which should have happened before they did happen:
I was surprised that they hadn’t already told me the news.