The insulating state of matter: a geometrical theory
By Raffaele Resta. 2010
323 citations recorded by the source corpus.
Abstract. 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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/06e5c7718e616d253d67da3e24f2c8170eaa45bd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Fractional quantum Hall physics in topological flat bands (2013, unknown): “As has been our theme overall, we will attempt only to give a flavor of this vast area, and identify a few interesting results that have emerged from such studies.”
- Topological photonics (2018, background): “The physics of an energy band is captured in part by its dispersion relation EnðkÞ, but also by the geometrical properties of how its eigenstates un;kðrÞ vary as a function of k (Karplus and Luttinger, 1954; Adams and Blount, 1959; Resta, 1994, 2011; Nagaosa et al., 2010).”
- Superconductivity, superfluidity and quantum geometry in twisted multilayer systems (2021, background): “This motion of the Wannier center as a function of the BZ momentum kx ∈ [0, 2π) is called the Wilson loop [11, 106] and is shown for TBG in Fig.”