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The geometry of the insulating state of matter

Raffaele Resta
University of Trieste
Thursday, March 3, 2016 - 16:15 to 17:45

The insulating vs conducting behaviour of condensed matter is usually addressed in terms of excitation spectra. At variance with such wisdom, W. Kohn hinted in 1964 that the insulating state of matter should also reflect a peculiar organization of the electrons in their ground state. The modern “theory of the insulating state” started in 1999, and continue to these days; at the root of these developments is the modern theory of polarization, developed in the early 1990s, and based on geometrical concepts (Berry phase). Since insulators and metals polarize in a qualitatively different way, the theory of polarization has fundamental implications for the theory of the insulating state as well. A common geometrical “marker”, based on the quantum metric, caracterizes all insulators (band insulators, Anderson insulators, Mott insulators, quantum Hall insulators. . . ) and discriminates them from conductors. 

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