His research focusses on developing a theory of quantum mechanics called density functional theory.

Density functional theory is a way of solving the equations of quantum mechanics for the electrons in any substance. Because DFT equations can be solved relatively quickly on modern computers, DFT has become a very popular tool in many branches of science, especially chemistry and materials science. Last year, at least 30,000 scientific papers used DFT. For example, hydrogen sulphide was predicted by DFT calculations to have a high superconducting temperature under pressure, and a year later, it was tested and became the world-record holder, at 203K.

Prof Burke works on developing all aspects of DFT: formalism, extensions to new areas, new approximations, and simplifications. His work is heavily used in materials science, chemistry, matter under extreme conditions (such as planetary interiors or fusion reactors), magnetic materials, molecular electronics, and so on. He has given talks in theoretical chemistry, condensed matter physics, applied mathematics, computer science, and even organic chemistry. His graduate students and postdocs usually come from either the chemistry or physics departments, but his undergraduate researchers also come from math, computer science, and engineering.