Effective theory of fluctuating orbital currents in high-$T_c$ cuprate superconductors

We derive an effective dissipative quantum field theory for fluctuating orbital currents in clean $\mathrm{Cu}{\mathrm{O}}_2$ sheets of high-$T_c$ cuprates based on a three-band model. The Coulomb repulsion term between Cu and O sites is decoupled in terms of current operators representing horizontal and vertical parts of circulating currents within each $\mathrm{Cu}{\mathrm{O}}_2$ unit cell of the lattice. The model has ordering of currents at finite temperatures. The dissipative kernel in the model is of the form $\mid \omega \mid ∕\mid \mathbf{q}\mid$, indicating Landau damping. Applications of the effective theory to other models are also discussed.

Figure 1

(Color online) The circulating current phase ${\Theta }_{\mathrm{II}}$ (Ref. 1). Cu sites are gray circles and O sites are red. The unit cell is shown by the dashed square. A staggered magnetic moment pattern within each unit cell that repeats from unit cell to unit cell (the curl of the blue directed circles) is indicated.