Amplitude mode of the $d$-density wave state and its relevance to high-$T_c$ cuprates

TL;DR

This paper calculates the amplitude (Higgs-like) mode spectrum of the $d$-density wave state in high-$T_c$ cuprates, revealing potential peaks at different wave vectors and explaining multiple neutron peaks.

Contribution

It provides a theoretical analysis of the amplitude mode spectrum in the $d$-density wave state, highlighting non-universal features and multiple excitation peaks.

Findings

Amplitude mode can peak at both $q=(0,0)$ and $q=(,)$.

Spectrum depends on microscopic parameters, showing one or two peaks.

Explains how multiple neutron peaks can arise from a single order parameter.

Abstract

We calculate the spectrum of the amplitude mode, the analog of the Higgs mode in high energy physics, for the $d$-density wave (DDW) state proposed to describe the pseudogap phase of the high $T_c$ cuprates. Even though the state breaks translational symmetry by a lattice spacing and is described by a particle-hole singlet order parameter at the wave vector $q=Q=(\pi,\pi)$, remarkably, we find that the amplitude mode spectrum can have peaks at both $q=(0,0)$ and $q=Q=(\pi,\pi)$; we shall lattice spacing to unity. In general, the spectrum is non-universal, and, depending on the microscopic parameters, can have one or two peaks in the Brillouin zone, signifying existence of two kinds of magnetic excitations. Our theory sheds important light on how multiple inelastic neutron peaks at different wave vectors can, in principle, arise even with an order parameter that condenses at $Q=(\pi,\pi)$.