Detecting isotropic density and nematic fluctuations using ultrafast coherent phonon spectroscopy

TL;DR

This paper develops a theoretical framework for detecting charge density and nematic fluctuations in three-dimensional materials using ultrafast coherent phonon spectroscopy, highlighting differences in their coupling to light and proposing experimental applications.

Contribution

It introduces a novel theoretical approach to distinguish and analyze isotropic and nematic fluctuations via ultrafast spectroscopy, emphasizing the unique coupling mechanisms and potential for probing electronic properties.

Findings

Nematic fluctuations couple to light only at fourth order due to symmetry.

Plasmon oscillations are driven by electron-light interactions at lowest order.

Proposes experiments on FeSe to observe nematic fluctuation effects.

Abstract

We propose a theoretical framework for the detection of order parameter fluctuations in three dimensions using ultrafast coherent phonon spectroscopy. We focus our attention on long wavelength charge density fluctuations (plasmons), and charged nematic fluctuations where the direction of the propagation vector is fixed perpendicular to the plane of anisotropy. By treating phonons and light classically and decoupling interactions to integrate out the fermionic degrees of freedom, we arrive at an effective theory of order parameter fluctuations about the spatially uniform saddle-point solution. We find that, due to the $(k_x^2-k_y^2) (B_{1g})$ symmetry of the form factor appearing in the vertex, nematic fluctuations couple to light only at fourth order, unlike isotropic density fluctuations which couple at second order. Hence, to lowest order, the interaction between electrons and the electromagnetic field contributes a driving force for plasmon oscillations while it provides a frequency shift for nematic fluctuations. From the resulting coupled harmonic oscillator equations of motion, we argue that ultrafast coherent phonon spectroscopy could be a useful tool to extract and analyze various electronic properties of interest such as the frequency of the collective mode and the coupling between electrons and phonons. Specific experiments are proposed on the normal state of FeSe to observe the frequency shift predicted here resulting directly from orbital ordering (nematic) fluctuations. Our paper presents a new mechanism for generating coherent phonons from long-range interactions (coherent long-range interaction induced phonons) that does not require the existence of multiple bands to act as intermediary states for quasiparticles.