Analysis of Charge Order in the Kagome Metal $A$V$_3$Sb$_5$ ($A=$K,Rb,Cs)

Abstract: Motivated by the recent discovery of unconventional charge order, we develop a theory of electronically mediated charge density wave formation in the family of kagome metals $A$V$3$Sb$_5$ ($A=$K,Rb,Cs). The intertwining of van Hove filling and sublattice interference suggests a three-fold charge density wave instability at T${\text{CDW}}$. From there, the charge order forming below T$_{\text{CDW}}$ can unfold into a variety of phases capable of exhibiting orbital currents and nematicity. We develop a Ginzburg Landau formalism to stake out the parameter space of kagome charge order. We find a nematic chiral charge order to be energetically preferred, which shows tentative agreement with experimental evidence.

Analysis of Charge Order in the Kagome Metal $A$V$_3$Sb$_5$ ($A=$K, Rb, Cs)

The paper presents a comprehensive theoretical investigation into the unconventional charge order observed in the kagome metal $A$V$3$Sb$_5$ ($A=$K, Rb, Cs). The study focuses on the formation of charge density waves (CDW) within these materials, driven primarily by electronic interactions. Specifically, the authors explore how van Hove singularities and sublattice interference contribute to a threefold CDW instability below the critical temperature $T{\text{CDW}}$, leading potentially to phases with orbital currents and nematicity.

Key Contributions

1. Theory of Electronically Mediated CDW: The authors develop a theory of charge density wave formation mediated by electronic interactions in $A$V$_3$Sb$_5$. By leveraging a Ginzburg Landau framework, they provide insights into different charge order parameters across the parameter space. A nematic chiral charge order emerges as energetically favorable, agreeing tentatively with experimental observations.

2. Sublattice Interference Phenomenon: At van Hove filling, distinct sublattice interference results in a preferred charge bond order (CBO) with $l=1$ angular momentum, challenging the conventional $l=0$ angular momentum in typical CDWs. This phenomenon is crucial for understanding the electronic instability mechanisms in kagome metals.

3. Interaction Strength Phase Diagram: The study contrasts charge density order (CDO) with CBO over varying interaction strengths (U/V ratio). It concludes that CBO dominates given the unique sublattice structure of the kagome lattice, reinforcing nearest-neighbor interactions in the $V$ channel.

4. Implications of Ginzburg Landau Analysis: The analysis reveals a propensity for nematicity through phase differences in CBO components below $T_{\text{CDW}}$, aligning with scanning tunneling microscopy findings. The interaction-driven currents and time-reversal symmetry breaking are notable, providing a basis for the phenomena observed in $A$V$_3$Sb$_5$.

Theoretical and Practical Implications

The investigation provides valuable insights for understanding the intricate mechanisms governing charge order in kagome metals. The theoretical models indicate a strong correlation between the electronic structure and emergent phases, like nematicity and orbital currents. Understanding these interactions is critical for advancing potential applications in complex quantum materials and offers a promising platform for further investigation of electronic correlation phenomena.

Future Directions

Given the findings, several avenues for continued research are suggested, including:

• Further experimental validation of the proposed nematic chiral charge order through advanced imaging techniques.
• Exploration of hydrostatic pressure effects on charge order parameters to elucidate the interaction strength mechanisms further.
• Investigation into superconducting pairing symmetries derived from charge order ground states in kagome metals.

In conclusion, the paper significantly contributes to understanding the electronic peculiarities of kagome metallic systems, providing a robust theoretical foundation for future study in correlated electron phenomena and topologically non-trivial phases.