Landau-Ginzburg theory of charge density wave formation accompanying lattice and electronic long-range ordering

TL;DR

This paper develops an analytical Landau-Ginzburg framework to describe charge density waves coupled with various long-range orders, providing insights into phase stability and spatial modulations in quantum materials.

Contribution

It introduces a novel biquadratic gradient coupling in the Landau-Ginzburg free energy, crucial for understanding spatially-modulated phases in charge-ordered and superconducting systems.

Findings

Derived thermodynamic conditions for phase stability.

Provided analytical expressions for phase energies and order parameters.

Explained the role of gradient couplings in spatial phase modulation.

Abstract

We propose an analytical Landau-Ginzburg theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include electronic wave function of superconducting Cooper pairs, structural distortions, electric polarization, and magnetization. We formulate the Landau-Ginzburg free energy density as power expansion with respect to the charge density and other long-range order parameters, as well as their spatial gradients, and biquadratic coupling terms. We introduced a biquadratic coupling between the charge density gradient and long-range order parameters, as well as nonlinear higher gradients of the long-range order parameters. The biquadratic gradient coupling is critical to the appearance of different spatially-modulated phases in charge-ordered ferroics and high-temperature superconductors. We derived the thermodynamic conditions for the stability of the spatially-modulated phases, which are the intertwined spatial waves of charge density and lattice/electronic long-range order. The analytical expressions for the energies of different phases, corresponding order parameters, charge density waves amplitudes and modulation periods, obtained in this work, can be employed to guide the comprehensive physical explanation, deconvolution and Bayesian analysis of experimental data on quantum materials ranging from charge-ordered ferroics to high-temperature superconductors.