Study X "at depth"?
I think you might have (con)fused "in depth" and "at length" with one another.
The Cambridge Dictionary define in-depth as:
done carefully and in great detail
For example:
You might have studied American modernism in-depth.
The idiom at length is defined by The Free Dictionary as:
in great detail
For example:
I studied American modernism in college, so I can speak about it at length.
You definitely study something "in depth". I wonder if you are thinking of the expression "at length"? "I studied the author in depth and then we discussed him at length".