He appears to be a quantum physicist, if dialogue lines are an indication:
The best are actually found in the first episode:
Harrison Wells' work in quantum theory is light-years ahead of anything they're doing at CERN.
My name is Harrison Wells. Tonight, the future begins. The work my team and I will do here will change our understanding of physics.
But really, that's all we have to go on. The "Who is Harrison Wells?" episode is surprisingly unhelpful. We know he's a Doctor in some field of science. His degree or majors aren't mentioned (whereas Barry explicitly tells Dr. McGee of Mercury Labs that he majored in physics and chemistry).
No on-screen version of his diploma or credentials has appeared,
This is also the case for the Earth-2 Harrison. He's also a Doctor (although we don't know if that means Ph.D. on their Earth), and a "scientist".
It may be important to realize that no matter what degrees someone has earned, they could still be a scientist of any other field, depending on what else they choose to research and become experts in. Trying to pin him to one field may be functionally useless, because he's shown relevant expertise in a variety of fields. This is further shown by the fact that regardless of Wells' education, Eobard Thawne was able to convincingly assume that role.
There are quantum physicists, and chemistry/physics crossover scientists, but the capabilities of what these types of scientists can do in The Flash is purely fiction.