DFT Seminar

[ferialdi at ts.infn.it]

Wednesday 6 May 2009 - 15.00 hrs.
Room 204 (DFT - LB 2nd floor)

Raffaele RESTA
(University of Trieste)

WHY ARE INSULATORS INSULATING AND METALS CONDUCTING?

Abstract
The qualitative difference between metals and insulators manifests itself
in the
response to a macroscopic electric field. In metals the electronic charge
flows
over macroscopic distances, while in insulators it appears "bound": the field
induces a finite dielectric polarization. The textbook explanation of this
qualitative difference, originally due to A.H. Wilson (1931), is based on
the
excitation spectra (presence or absence of an energy gap).

In 1964 W. Kohn published the paper "Theory of the insulating state",
based on
the revolutionary idea that insulators and metals differ in their
electronic
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, Kohn's theory
remained somewhat incomplete (and little cited) for many years.

Apparently unrelated work, published about 30 years later, has
revolutioned our
view of the dielectric polarization in condensed matter, leading to a genuine
change of paradigm. Since (as said above) insulators and metals polarize
in a qualitatively different way, it was later found that the modern
theory
of polarization has fundamental implications for the theory of the insulating
state. These implications have been investigated since 1999 and are still
an active subject of research.

Both the modern theory of polarization and the modern theory of the
insulating
state are based on geometrical properties of the electronic wavefunction
(Berry
phase, connection, curvature, quantum metric).