The insulating state of matter: a geometrical theory
Dipartimento di Fisica, Università di Trieste, Strada Costiera 11, 34151 Trieste, Italy
2 DEMOCRITOS National Simulation Center, Istituto Officina dei Materiali (CNR), Trieste, Italy
Corresponding author: a email@example.com
Published online: 19 January 2011
In 1964 Kohn published the milestone paper “Theory of the insulating state”, according to which insulators and metals differ in their ground state. Even before the system is excited by any probe, a different organization of the electrons is present in the ground state and this is the key feature discriminating between insulators and metals. However, the theory of the insulating state remained somewhat incomplete until the late 1990s; this review addresses the recent developments. The many-body ground wavefunction of any insulator is characterized by means of geometrical concepts (Berry phase, connection, curvature, Chern number, quantum metric). Among them, it is the quantum metric which sharply characterizes the insulating state of matter. The theory deals on a common ground with several kinds of insulators: band insulators, Mott insulators, Anderson insulators, quantum Hall insulators, Chern and topological insulators.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011