General theory of the metal-insulator transition

Abstract

We present a general theory of the metal-insulator transition based on the formal introduction of an auxiliary irrotational gauge field and the subsequent behavior of the system in response to it. Correspondingly general scaling relations are derived which determine the point of transition at a critical value of the controlling density in terms of a series expansion with respect to a coupling constant. Functional integral techniques are also used to show the relation of this transition to a density-fluctuation instability. Finally, an interpretation is given of the transition in terms either of condensation of gauge bosons or, alternatively, in terms of the appearance of an additional geometric phase, an interpretation that is valid for quite general condensed-matter systems. © 1992 The American Physical Society.