Microscopic origin of the nemato-elastic coupling and dynamics of hybridized collective nematic-phonon excitations

TL;DR

This paper develops a microscopic formalism to understand the hybridized collective modes formed by nematic electronic fluctuations and transverse acoustic phonons in metals, revealing complex dynamics near the nematic quantum critical point.

Contribution

It introduces a microscopic model for nemato-elastic coupling via impurities and analyzes the resulting hybrid nemato-elastic modes and their dynamics.

Findings

Emergence of hybrid nemato-elastic modes with mixed phononic and electronic characteristics

Identification of underdamped and overdamped modes depending on proximity to quantum criticality

Implications for nematic fluctuation-mediated superconductivity

Abstract

Electronically-driven nematic order breaks the rotational symmetry of a system, e.g., through a Pomeranchuk instability of the Fermi surface, with a concomitant distortion of the lattice. As a result, in a metal, the nematic collective mode interacts with two different sets of gapless excitations: the particle-hole excitations of the metal and the lattice fluctuations that become soft at the induced structural transition, namely, the transverse acoustic phonons. However, the \textit{dynamics} of these hybridized collective modes formed by the transverse acoustic phonons and the metallic electronic-nematic fluctuations has remained largely unexplored. Here we address this problem by developing a formalism in which the nemato-elastic coupling is obtained microscopically from the direct coupling between electrons and transverse acoustic phonons enabled by impurities present in the crystal. We then demonstrate the emergence of hybrid nemato-elastic modes that mix the characteristics of the transverse phonons and of the nematic fluctuations. Near the nematic quantum critical point in a metal, two massless modes emerge with intertwined dynamic behaviors, implying that neither mode dominates the response of the system. We systematically study the non-trivial dependence of these collective modes on the longitudinal and transverse momenta, revealing a rich landscape of underdamped and overdamped modes as the proximity to the quantum critical point and the strength of the electron-phonon coupling are changed. Since dynamics play an important role for determining superconducting instabilities, our results have implications for the study of pairing mediated by electronic nematic fluctuations.