• Semi Conductors Nano structures
• Theory and Applications of Terahertz Technology
• Quantum transport in general
• Localisation and metal-insulator transitions
• Properties of strongly interacting electron gases
• Bose-Einstein condensation in the solid state
• Hybrid magnetic-semiconductor structures
• Physics in medicine and biology

Sir Michael pioneered the study of low dimensional electron gas systems and the associated quantum effects, and his career has encompassed both academic and industrial sectors. Following a period of semiconductor research at the Caswell Research Laboratory of the Plessey Company he moved to the Cavendish Laboratory, Cambridge University, in 1973, where he remained until the end of 2008. Whilst there, he started a long collaboration with the late Sir Nevill Mott, (Nobel Laureate, 1977) using semiconductor devices to investigate fundamental physics. In  1982 he left Plessey to join the GEC Hirst Research Centre and set up joint Cavendish-GEC projects.

He founded the Semiconductor Physics Research Group at the Cavendish in 1985, and was appointed Professor of Physics there in 1987. In 1991, he was appointed Managing Director of the newly established Toshiba Cambridge Research Centre (now known as the Cambridge Research Laboratory (CRL) of Toshiba Research Europe) and since 2007 he has been a senior adviser to the company. In 2001, he cofounded TeraView - a company formed to commercialise the terahertz research work of CRL - and was appointed Scientific Director.

Sir Michael has been associated with many of the major themes of condensed matter physics; was one of the three authors of the first paper announcing the discovery of the quantum Hall effect and with his group he developed the techniques of electrostatically modifying a 2D electron gas to form 1D and 0D systems with many associated discoveries, such as quantisation of the conductance of ballistic 1D electrons.

Sir Michael was elected a Fellow of the Royal Society in 1983 and a Fellow of Trinity College in 1982. He has been awarded the Hughes Medal and the Royal Medal of The Royal Society and the first Mott Medal of the Institute of Physics, as well as the Guthrie (Gold) Medal and the Europhysics Prize of the European Physical Society. He received a knighthood in the 2006 New Year's Honours list for services to physics and has received honorary degrees and given named lectures including the Mountbatten Memorial Lecture of the IET and the Royal Society’s Bakerian Lecture.
 
Sir Michael was appointed to the Pender Professorship of Nanoelectronics from 1 January 2009 in the Department of Electronic and Electrical Engineering at University College London, as well as being a staff  member of the London Centre for Nanotechnology and holding an Honorary Professorship in the Department of Physics and Astronomy.