Topological Criticality on Brink of the Mott Transition in High-T_cSuperconductors

Abstract

The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-T c cuprates. The theory includes the effects of the relevant energy scales with the emphasis on the Coulomb interaction U governed by the electromagnetic U(1) compact group. The results are obtained for the layered t−t −t ⊥ −U −J system of strongly correlated electrons relevant for cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara "imaginary time", labelled by a topological winding numbers, governed by gauge flux changes by an integer multiple of 2π, are essential configurations of the phase field dual to the charge. The impact of these topological excitations is calculated for the phase diagram, which displays the "hidden" quantum critical point on verge of the Mott transition that is given by a divergence of the charge compressibility.