Murray, David Norris and Manoj Nirmal were the first graduate students to work with Moungi Bawendi at MIT. As part of his thesis work, Murray helped to develop synthetic methods for making quantum dots, including identifying a longer chain version of trioctylphosphine oxide as being cheaper and having additional benefits when used in synthesis. In 1993, Murray, Norris and Bawendi published a breakthrough paper describing the hot injection synthesis method for making quantum dots.  Both Murrays and Bawendis contributions to the synthesis and characterization of semiconductor quantum dots were recognized by the American Chemical Society with its 1997 Nobel Laureate Signature Award.
Their method was both adaptable and reproducible, making it possible to consistently synthesise monodisperse nanoparticles and develop large-scale applications using quantum dots. Bawendi received the 2023 Nobel Prize in Physics for the development of this method.
Much of Murray's has work focused on the synthesis and characterization of nanoscale materials, including nanoscale magnets, semiconductor nanocrystals, and nanocrystal superlattices. Murray was recognized at IBM as a Master Inventor and patent evaluator. He holds at least 26 nanascale patents.
Murray is concerned with the synthesis and self-assembly properties of nanocrystals and the potential to create new mesoscopic materials with interesting properties and potential applications in energy, environmental sustainability, health, and information processing.
Murray is the Founding Chair of the World Economic Forum’s Global Councils on Nanotechnology (2008-2009) and Global Council on Emerging Technologies (2009-2010).