Fluctuating Stripes in Strongly Correlated Electron Systems and the Nematic-Smectic Quantum Phase Transition

TL;DR

This paper investigates the quantum phase transition between nematic and smectic metallic states in strongly correlated electrons, revealing non-Fermi liquid behavior near the critical point due to critical fluctuations.

Contribution

It introduces an order-parameter theory for the nematic-smectic transition, analyzing fluctuation effects, collective modes, and quasiparticle dynamics in both continuum and lattice systems.

Findings

Critical smectic fluctuations disrupt Fermi liquid behavior near the QCP.

Quasiparticles in the smectic phase behave as Fermi liquids.

Gauge coupling is irrelevant at the quantum critical point.

Abstract

We discuss the quantum phase transition between a quantum nematic metallic state to an electron metallic smectic state in terms of an order-parameter theory coupled to fermionic quasiparticles. Both commensurate and incommensurate smectic (or stripe) cases are studied. Close to the quantum critical point (QCP), the spectrum of fluctuations of the nematic phase has low-energy ``fluctuating stripes''. We study the quantum critical behavior and find evidence that, contrary to the classical case, the gauge-type of coupling between the nematic and smectic is irrelevant at this QCP. The collective modes of the electron smectic (or stripe) phase are also investigated. The effects of the low-energy bosonic modes on the fermionic quasiparticles are studied perturbatively, for both a model with full rotational symmetry and for a system with an underlying lattice, which has a discrete point group symmetry. We find that at the nematic-smectic critical point, due to the critical smectic fluctuations, the dynamics of the fermionic quasiparticles near several points on the Fermi surface, around which it is reconstructed, are not governed by a Landau Fermi liquid theory. On the other hand, the quasiparticles in the smectic phase exhibit Fermi liquid behavior. We also present a detailed analysis of the dynamical susceptibilities in the electron nematic phase close to this QCP (the fluctuating stripe regime) and in the electronic smectic phase.