Optical conductivity and the sum rule in the DDW state

TL;DR

This paper investigates the optical conductivity in the DDW state of high-T_c cuprates, showing that spectral weight redistribution minimally violates the optical sum rule due to inter-branch electronic excitations.

Contribution

It provides a detailed analysis of how the DDW state affects optical conductivity and the sum rule, highlighting the role of inter-branch excitations in spectral weight redistribution.

Findings

Finite-frequency response arises from inter-branch excitations.

Optical sum rule is only weakly violated in the DDW state.

Spectral weight redistribution does not significantly alter the total optical sum.

Abstract

The density-wave with d-wave order parameter (DDW) is possibly realized in the underdoped regime of high-T_c cuprates. The DDW state is characterized by two branches of low-lying electronic excitations, and the quantum mechanical current has in particular an inter-branch contribution. The latter component causes a finite-frequency response in the optical conductivity and a reduction of the Drude contribution. We show that this redistribution of the spectral weight leaves the optical sum mostly intact, so that the restricted optical sum rule is only weakly violated.