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In contrast to the Berry connection, which is physical only after integrating around a closed path, the Berry curvature is a gauge-invariant local manifestation of the geometric properties of the wavefunctions in the parameter space, and has proven to be an essential physical ingredient for understanding a variety of electronic properties.
Behavior of the curvature function (Berry connection) for the Kitaev model (top panel) as a function of a parameter change in parameter space (bottom panel). The vertical red lines depict topological phase boundaries. Across the topological phase transitions, the Berry connection diverges and flips sign around the high-symmetry points k=0.
The phenomenon was independently discovered by S. Pancharatnam (1956), [2] in classical optics and by H. C. Longuet-Higgins (1958) [3] in molecular physics; it was generalized by Michael Berry in (1984). [4] It is also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase.
Sir Michael Victor Berry (born 14 March 1941) is a British theoretical physicist.He is the Melville Wills Professor of Physics (Emeritus) at the University of Bristol.. He is known for the Berry phase, a phenomenon observed in both quantum mechanics and classical optics, as well as Berry connection and curvature.
The Hannay angle is defined in the context of action-angle coordinates.In an initially time-invariant system, an action variable is a constant. After introducing a periodic perturbation (), the action variable becomes an adiabatic invariant, and the Hannay angle for its corresponding angle variable can be calculated according to the path integral that represents an evolution in which the ...
One comes from the axion coupling , a quantity that is determined from bulk considerations as we have seen, while the other is the Berry phase of the surface states at the Fermi level and therefore depends on the surface. In summary for a given surface termination the perpendicular component of the surface anomalous Hall conductivity to the ...
It is generally argued that the Aharonov–Bohm effect illustrates the physicality of electromagnetic potentials, Φ and A, in quantum mechanics.Classically it was possible to argue that only the electromagnetic fields are physical, while the electromagnetic potentials are purely mathematical constructs, that due to gauge freedom are not even unique for a given electromagnetic field.
Trigonal bipyramidal molecular shape ax = axial ligands (on unique axis) eq = equatorial ligand (in plane perpendicular to unique axis). The Berry mechanism, or Berry pseudorotation mechanism, is a type of vibration causing molecules of certain geometries to isomerize by exchanging the two axial ligands (see the figure) for two of the equatorial ones.