Visibility of the Amplitude (Higgs) Mode in Condensed Matter

TL;DR

This paper investigates the visibility of the Higgs (amplitude) mode in condensed matter systems, showing that scalar susceptibility measurements can reveal the mode despite decay channels that obscure it in other susceptibilities.

Contribution

It demonstrates that the scalar susceptibility enhances the visibility of the amplitude mode, providing a new approach for experimental detection in various condensed matter systems.

Findings

Scalar susceptibility suppresses low-frequency divergence, exposing the Higgs mode.

Conductivity in the O(2) theory shows suppressed absorption below the Higgs mass.

Interlayer plasma frequency affects the detection threshold in layered superconductors.

Abstract

The amplitude mode is a ubiquitous collective excitation in condensed matter systems with broken continuous symmetry. It is expected in antiferromagnets, short coherence length superconductors, charge density waves, and lattice Bose condensates. Its detection is a valuable test of the corresponding field theory, and its mass gap measures the proximity to a quantum critical point. However, since the amplitude mode can decay into low-energy Goldstone modes, its experimental visibility has been questioned. Here we show that the visibility depends on the symmetry of the measured susceptibility. The longitudinal susceptibility diverges at low frequency as \chi_{\sigma\sigma} ~ i/\omega (d=2) or log(1/|\omega|) (d=3), which can completely obscure the amplitude peak. In contrast, the scalar susceptibility is suppressed by four extra powers of frequency, exposing the amplitude peak throughout the ordered phase. We discuss experimental setups for measuring the scalar susceptibility. The conductivity of the O(2) theory (relativistic superfluid) is a scalar response and therefore exhibits suppressed absorption below the Higgs mass threshold, \sigma ~ \omega^{2d+1}. In layered, short coherence length superconductors, (relevant e.g. to cuprates) this threshold is raised by the interlayer plasma frequency.