He has published over two hundred refereed papers and reviews in the fields of quantum transport, nanoelectronics, solid-state quantum computing, cold atoms, quantum noise, growth and pattern formation (full publication list).

Levitov is a pioneer in the theory of quasicrystals—orderly materials with non-crystallographic symmetries, discovered in 1985. He co-authored a theory explaining the structural properties of quasicrystals by introducing the concept of a structure projected from a high-dimensional periodic structure. In the ’90s, Levitov pioneered the theory of quantum noise in coherent electron transport. He formulated the counting statistics approach, which evolved into a new tool in the field of quantum transport. In 1993 he developed the concept of coherent current pulses allowing the transmission of electrical signals in a noise-free fashion. These pulses, observed in 2013 and dubbed ‘levitons,’ have become the basis of electron optics.