[Paper Review] Triple-Well Charge Density Wave Transition Driven by Cooperation between Peierls-like Effect and Antiferromagnetic Order in FeGe

Binhua Zhang, Junyi Ji+2 more|arXiv (Cornell University)|Jul 20, 2023

Topological Materials and PhenomenaPhysics and Astronomy3 citations

TL;DR

This study reveals that the triple-well charge density wave (CDW) transition in FeGe is driven by a cooperative mechanism between a Peierls-like effect and antiferromagnetic order, where a downward shift of Ge 1 p_z bands by over 0.5 eV and Fermi energy pinning stabilize the CDW phase, while magnetic order weakens Fe-Ge hybridization and lowers Ge-band energy, resolving the long-standing puzzle of CDW stability without phonon instabilities in the pristine phase.

ABSTRACT

Kagome materials provide a promising platform to explore intriguing correlated phenomena including magnetism, charge density wave (CDW), and nontrivial band topology. Recently, a CDW order was observed in antiferromagnetic kagome metal FeGe, sparking enormous research interests in intertwining physics of CDW and magnetism. Two of the core questions are (i) what are the driving forces of the CDW transition in FeGe and (ii) whether magnetism play a critical role in the transition. Such questions are critical as conventional mechanisms of van Hove singularities and Fermi surface nesting fail to explain the stable pristine phase, as well as the role of magnetism. Here, supported by density functional theory and tight-binding models, we unravel the triple-well CDW energy landscape of FeGe, indicating that both the pristine and CDW phases are locally stable. We point out that an entire downward shift of Ge band, instead of the previously proposed Fe bands, competes with the lattice distortion energy, driving the triple-well CDW transition. It is indeed a cooperation between the Peierls-like effect and the Fermi energy pinning phenomenon, which is distinct from the conventional Peierls effect that drives a double-well transition. Moreover, we demonstrate that the antiferromagnetic order also plays a critical role in driving the CDW transition, through weakening the Fe-Ge hybridization by exchange splitting and lowering the position of Ge-bands with respect to the Fermi energy. Our work thus not only deepens the understanding of the CDW mechanism in FeGe, but also indicates an intertwined connection between the emergent magnetism and CDW in kagome materials.

Motivation & Objective

• To resolve the mechanism behind the stable, multistable CDW phase in FeGe, which lacks phonon instabilities in the pristine phase.
• To determine whether conventional CDW mechanisms—such as Fermi surface nesting or van Hove singularities—can explain the observed CDW transition.
• To investigate the role of antiferromagnetic order in driving or stabilizing the CDW phase in this kagome metal.
• To uncover the microscopic origin of the triple-well energy landscape in the CDW transition, distinct from conventional double-well Peierls transitions.

Proposed method

• First-principles density functional theory (DFT) calculations were used to compute the electronic structure and energy landscape of the pristine and CDW phases in FeGe.
• Tight-binding (TB) models were constructed to simulate the electronic band structure, with on-site energies and hopping integrals derived from DFT, enabling analysis of band splitting under lattice distortion.
• The four-state energy mapping method was applied to extract magnetic exchange interactions from DFT total energies, using a √3 × √3 × 1 supercell and 4×4×10 k-mesh.
• Monte Carlo simulations with 30×30×1 supercells and 100,000 MC steps per site were performed to validate the magnetic order and its influence on the CDW transition.
• The role of spin-orbit coupling was included in single-ion anisotropy calculations to ensure accurate magnetic modeling.
• The analysis focused on the Ge 1 p_z orbital band, tracking its energy shift and occupation during dimerization, to identify the Peierls-like effect and Fermi energy pinning.

Experimental results

Research questions

• RQ1 What drives the triple-well CDW energy landscape in FeGe, given the absence of phonon instabilities in the pristine phase?
• RQ2 How does the Peierls-like effect differ in this system from conventional Peierls transitions, and what role does the Ge 1 p_z band play?
• RQ3 To what extent does antiferromagnetic order contribute to the CDW transition through electronic structure modulation?
• RQ4 Why do conventional CDW mechanisms—Fermi surface nesting and van Hove singularities—fail to explain the CDW in FeGe?

Key findings

• The CDW transition in FeGe exhibits a triple-well energy landscape, with both the pristine and CDW phases being locally stable, explaining the absence of phonon instabilities in the high-temperature phase.
• The primary driving force is a Peierls-like effect involving a downward shift of the Ge 1 p_z band by more than 0.5 eV during Ge 1 dimerization, which lowers the system's total energy.
• Fermi energy pinning due to hybridization with other atoms leads to full occupation of the Ge 1 p_z band, further stabilizing the CDW phase.
• Antiferromagnetic order plays a critical role by reducing Fe-Ge hybridization through exchange splitting and lowering the energy of Ge bands relative to the Fermi level.
• The cooperation between the Peierls-like effect and magnetic order creates a unique triple-well transition distinct from conventional double-well Peierls transitions.
• Theoretical modeling confirms that the CDW phase is stabilized not by Fe-derived van Hove singularities or nesting, but by the interplay of Ge band shifts and magnetic order.