[Paper Review] Charge-density waves in kagome-lattice extended Hubbard models at the van Hove filling

Francesco Ferrari, Federico Becca+1 more|arXiv (Cornell University)|Apr 21, 2022

Advanced Condensed Matter PhysicsPhysics and Astronomy65 references49 citations

TL;DR

This study investigates charge-density wave (CDW) instabilities in the extended Hubbard model on the kagome lattice at van Hove filling (5/6) using variational Jastrow-Slater wave functions. It finds that nearest-neighbor repulsion (V) induces CDWs with strong charge disproportionation incompatible with experimental 2×2 CDW patterns in AV3Sb5, while electron-phonon coupling via the Su-Schrieffer-Heeger model stabilizes a tri-hexagonal distortion matching experimental observations, suggesting lattice degrees of freedom as key to CDW formation.

ABSTRACT

The Hubbard model on the kagome lattice is presently often considered as a minimal model to describe the rich low-temperature behavior of AV$_{3}$Sb$_{5}$ compounds (with A=K, Rb, Cs), including charge-density waves (CDWs), superconductivity, and possibly broken time-reversal symmetry. Here, we investigate, via variational Jastrow-Slater wave functions, the properties of its ground state when both onsite $U$ and nearest-neighbor $V$ Coulomb repulsions are considered at the van Hove filling. Our calculations reveal the presence of different interaction-driven CDWs and, contrary to previous renormalization-group studies, the absence of ferromagnetism and charge- or spin-bond order. No signatures of chiral phases are detected. Remarkably, the CDWs triggered by the nearest-neighbor repulsion possess charge disproportionations that are not compatible with the ones observed in AV$_{3}$Sb$_{5}$. As an alternative mechanism to stabilize charge-bond order, we consider the electron-phonon interaction, modeled by coupling the hopping amplitudes to quantum phonons, as in the Su-Schrieffer-Heeger model. Our results show the instability towards a tri-hexagonal distortion with $2 imes 2$ periodicity, in a closer agreement with experimental findings.

Motivation & Objective

• To determine the role of electronic correlations (U and V) in driving charge-ordering instabilities at van Hove filling (5/6) in the kagome Hubbard model.
• To assess whether the extended Hubbard model alone can stabilize the experimentally observed 2×2 CDW with C6 symmetry in AV3Sb5.
• To investigate the stability of chiral, ferromagnetic, and bond-order phases predicted by previous renormalization-group studies.
• To evaluate the role of electron-phonon coupling in stabilizing CDW patterns consistent with experimental observations in AV3Sb5.
• To resolve discrepancies between functional renormalization group predictions and variational Monte Carlo results regarding the nature of the ground state.

Proposed method

• Employing variational Jastrow-Slater wave functions to approximate the ground state, combining uncorrelated Slater determinants with a Jastrow factor for long-range correlations.
• Using stochastic variational Monte Carlo to compute observables such as charge density, spin structure factors, and density-density correlation functions.
• Performing energy minimization over Jastrow parameters and spin-dependent hopping terms to assess the stability of various broken-symmetry phases.
• Introducing electron-phonon coupling via the Su-Schrieffer-Heeger model, where hopping amplitudes are modulated by quantum phonons to simulate lattice distortions.
• Analyzing the long-wavelength behavior of the density-density structure factor to distinguish metallic from insulating phases.
• Testing for chiral and spin-bond order by introducing complex and spin-asymmetric hopping terms in the auxiliary Hamiltonian H0 and monitoring their optimization flow.

Experimental results

Research questions

• RQ1 Can the extended Hubbard model on the kagome lattice at 5/6 filling stabilize a 2×2 CDW with C6 symmetry, as observed in AV3Sb5?
• RQ2 Do electronic repulsions (U and V) alone lead to charge-bond order or chiral phases, as suggested by functional renormalization group studies?
• RQ3 Why do previous renormalization-group studies predict ferromagnetism and bond order, while this variational Monte Carlo study finds no such instabilities?
• RQ4 Can electron-phonon coupling via the Su-Schrieffer-Heeger mechanism stabilize a tri-hexagonal lattice distortion with 2×2 periodicity matching experimental CDW patterns in AV3Sb5?
• RQ5 What is the role of lattice distortions in stabilizing the experimentally observed CDW, as opposed to purely electronic instabilities?

Key findings

• The purely electronic model with U and V does not stabilize a C6-symmetric 2×2 CDW; instead, V-induced CDWs exhibit strong charge disproportionation on neighboring sites, incompatible with experimental observations.
• No evidence for ferromagnetism, charge-bond order, or spin-bond order is found in correlated Jastrow-Slater wave functions, contradicting previous functional renormalization group predictions.
• The inclusion of electron-phonon coupling via the Su-Schrieffer-Heeger model leads to a lattice distortion with short bonds along disconnected hexagons, stabilizing a tri-hexagonal 2×2 CDW pattern.
• The electron-phonon mechanism produces a charge reorganization that closely matches the star-of-David and tri-hexagonal patterns observed in AV3Sb5 compounds.
• Complex hopping terms required for chiral CDW order vanish during energy minimization, indicating no time-reversal symmetry breaking in the electronic model.
• The long-wavelength behavior of the density-density structure factor confirms a charge gap in the 2×2 CDW phase, while metallic phases show a linear decay of |q|²/N(q) as |q|→0.