General theory of the metal-insulator transition

Arbitrary mixture of two charged interacting particles in a magnetic Aharonov–Bohm ring: persistent currents and Berry's phases

“…The idea on which the following calculation is based is actually a generalization of a largely unnoticed paper by Berry [19] (that referred to a single particle), where a geometric phase due to a slow overall rotation of the ring turns out to consist of 2 terms: the 1 st is the usual AB phase (the one that would result from adiabatic transport of a box with rigid walls [18]), and the 2 nd is directly related to the electric current. It is worth emphasizing here on the possible use of a geometric phase as a "theoretical detector" of conduction (in an interacting system, in the sense of [20]), and this should be contrasted to the theory of Macroscopic Polarization [21,22] where generalized Berry's phases also appear (but with adiabatic parameters defined in k-rather than in real space). Because our Hamiltonian consists of two additive terms (with one describing the CM and the other the internal motion) and these two terms commute, it turns out that, if we use adiabatic parameters that couple separately to the CM and the relative subsystem, the overall Berry's phase can be written as a sum of two separate parts, namely showing that now the CM-Berry's phase is only related to the probability current, while the relativeBerry's phase has one AB term, and one term related to the electric current only.…”

Symmetry and Higher Superconductivity in the Lower Elements

“…Precisely the same result obtains [12] for a charged two-component system (corresponding, for example, to (1)); the result is exact and, importantly, it hold independent of the symmetry of the states actually taken up, in particular for states displaying off-diagonal long-range-order. But among such phases might well be in insulating states, in which case J = 0, necessarily.…”

“…If so then so far as the energy is concerned, and for the limiting case of a system with the Kamerlingh-Onnes ring topology mentioned earlier, an insulating state will then not detect the presence of A, an important distinction first emphasized by Kohn [13]. As has been emphasized in Ref [12], a transition from insulating to metallic state can actually be viewed as the breaking of a global gauge symmetry (and the condensation of gauge bosons). Accordingly given the breaking of a gauge symmetry associated with formation of the superconducting state in the presence of a magnetic field, it may be interesting to seek a deeper connection between superconductivity and the metal-insulator transition [12].…”

“…As has been emphasized in Ref [12], a transition from insulating to metallic state can actually be viewed as the breaking of a global gauge symmetry (and the condensation of gauge bosons). Accordingly given the breaking of a gauge symmetry associated with formation of the superconducting state in the presence of a magnetic field, it may be interesting to seek a deeper connection between superconductivity and the metal-insulator transition [12]. This notion evidently gains more prominence when the same question is asked of Hamiltonian (3); in a one-electron approximation this eventually leads, as noted, to band-structure.…”

“…The first involves its role in detecting an insulator to metal transition. Thus when (4) is augmented to include the effects of A, it can be shown [12] that the consequent ground-state energy per electron (i.e < H > /N) satisfies…”