STOCKHOLM — David J. Thouless of University of Washington, F. Duncan M. Haldane of Princeton University and J. Michael Kosterlitz of Brown University were awarded the 2016 Nobel Prize in physics on Monday for theoretical discoveries of topological phase transitions and topological phases of matter.

The three are credited with discovering “exotic” phases of matter used to design new materials for electronics.

Last year’s Nobel Prize in physics was shared by Takaaki Kajita of the University of Tokyo and Arthur B. McDonald of Queen’s University in Canada. Kajita and McDonald were honored for their work on neutrinos, some of the subatomic particles that make up our universe. The two men contributed to research showing that neutrinos, once thought to be massless, indeed have mass.

The award, which was established by Swedish inventor Alfred Nobel in 1895, comes with a prize worth 8 million Swedish krona, or about $937,000.

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