Theory of the charge-density wave in $A$V${}_3$Sb${}_5$ kagome metals

Abstract

The family of metallic kagome compounds $A$V${}_3$Sb${}_5$ ($A$=K, Rb, Cs) was recently discovered to exhibit both superconductivity and charge order. The nature of the charge-density wave (CDW) phase is presently unsettled, which complicates the interpretation of the superconducting ground state. In this paper, we use group-theory and density-functional theory (DFT) to derive and solve a phenomenological Landau model for this CDW state. The DFT results reveal three unstable phonon modes with the same in-plane momentum but different out-of-plane momenta, whose frequencies depend strongly on the electronic temperature. This is indicative of an electronically-driven CDW, stabilized by features of the in-plane electronic dispersion. Motivated by the DFT analysis, we construct a Landau free-energy expansion for coupled CDW order parameters with wave-vectors at the $M$ and $L$ points of the hexagonal Brillouin zone. We find an unusual trilinear term coupling these different order parameters, which can promote the simultaneous condensation of both CDWs even if the two modes are not nearly-degenerate. We classify the different types of coupled multi-$\mathbf{Q}$ CDW orders, focusing on those that break the sixfold rotational symmetry and lead to a unit-cell doubling along all three crystallographic directions, as suggested by experiments. We determine a region in parameter space, characterized by large nonlinear Landau coefficients, where these phases - dubbed staggered tri-hexagonal and staggered Star-of-David - are the leading instabilities of the system. Finally, we discuss the implications of our results for the kagome metals.

17 pages, 11 figures

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Cited by in corpus (105)

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• Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5
• Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors
• Charge density wave in kagome lattice intermetallic ScV6Sn6
• Quantum states and intertwining phases in kagome materials
• AV${}_3$Sb${}_5$ Kagome Superconductors: Progress and Future Directions
• Tunable nodal kagome superconductivity in charge ordered RbV3Sb5
• Charge order breaks time-reversal symmetry in CsV${}_3$Sb${}_5$
• Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagome superconductors
• Charge order landscape and competition with superconductivity in kagome metals
• Possible star-of-David pattern charge density wave with additional modulation in the kagome superconductor CsV${}_3$Sb${}_5$
• Loop currents in $A$V${}_3$Sb${}_5$ kagome metals: multipolar and toroidal magnetic orders
• Temperature-driven reorganization of electronic order in CsV${}_3$Sb${}_5$
• Coexistence of Tri-Hexagonal and Star-of-David Pattern in the Charge Density Wave of the Kagome Superconductor AV${}_3$Sb${}_5$
• Bulk evidence of anisotropic $s$-wave pairing with no sign change in the kagome superconductor CsV${}_3$Sb${}_5$
• Softening of a flat phonon mode in the kagome ScV${}_6$Sn${}_6$
• Charge density wave order in kagome metal AV${}_3$Sb${}_5$ (A= Cs, Rb, K)
• Spatial symmetry constraint of charge-ordered kagome superconductor CsV${}_3$Sb${}_5$
• Conjoined Charge Density Waves in the Kagome Superconductor CsV3Sb5
• Spin-phonon coupling driven Charge density wave in a Kagome Magnet
• Correlated order at the tipping point in the kagome metal CsV${}_3$Sb${}_5$
• Structural evolution of the kagome superconductors $A$V${}_3$Sb${}_5$ ($A$ = K, Rb, and Cs) through charge density wave order
• Observation of electronic nematicity driven by three-dimensional charge density wave in kagome lattice KV${}_3$Sb${}_5$
• Unidirectional coherent quasiparticles in the high-temperature rotational symmetry broken phase of AV3Sb5 kagome superconductors
• Order-disorder Peierls instability in the kagome metal (Cs,Rb)V${}_3$Sb${}_5$
• Electronic nematicity without charge density waves in titanium-based kagome metal
• Phonon promoted charge density wave in topological kagome metal ScV${}_6$Sn${}_6$
• Superconductivity from repulsive interactions on the kagome lattice
• Theory of nematic charge orders in kagome metals
• The effect of the interlayer ordering on the Fermi surface of Kagome superconductor CsV${}_3$Sb${}_5$ revealed by quantum oscillations
• Enhanced Spin-polarization via Partial Ge1-dimerization as the Driving Force of the 2$\times$2$\times$2 CDW in FeGe
• Three-dimensional energy gap and origin of charge-density wave in kagome superconductor KV3Sb5
• Origin of Charge Density Wave in Layered Kagome Metal CsV${}_3$Sb${}_5$
• Dynamical Study of the Origin of the Charge Density Wave in $A$V${}_3$Sb${}_5$ ($A=$K, Rb, Cs) Compounds
• Intertwined van-Hove Singularities as a Mechanism for Loop Current Order in Kagome Metals
• Multidome superconductivity in charge density wave kagome metals
• Frustrated charge order and cooperative distortions in ScV6Sn6
• Tuning charge-density wave order and superconductivity in the kagome metals KV${}_3$Sb${}_{5-x}$Sn${}_x$ and RbV${}_3$Sb${}_{5-x}$Sn${}_x$
• Unconventional superconductivity protected from disorder on the kagome lattice
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Small Fermi pockets intertwined with charge stripes and pair density wave order in a kagome superconductor
• Electronic properties of correlated kagomé metals AV${}_3$Sb${}_5$(A = K, Rb, Cs): A perspective
• Electronic Landscape of Kagome Superconductors $\text{A}$V${}_3$Sb${}_5$ ($\text{A}$ = K, Rb, Cs) from Angle-Resolved Photoemission Spectroscopy
• Monolayer Kagome Metals AV${}_3$Sb${}_5$
• Impact of Sb degrees of freedom on the charge density wave phase diagram of the kagome metal CsV${}_3$Sb${}_5$
• Stability frontiers in the AM${}_6$X${}_6$ kagome metals: The LnNb${}_6$Sn${}_6$ (Ln:Ce-Lu,Y) family and density-wave transition in LuNb${}_6$Sn${}_6$
• Superconductivity from Orbital-Selective Electron-Phonon Coupling in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$
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• Charge density wave and superconductivity in the kagome metal CsV${}_3$Sb${}_5$ around a pressure-induced quantum critical point
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• The structure of kagome superconductors CsV${}_3$Sb${}_5$ in the charge density wave states
• Charge order above room-temperature in a prototypical kagome superconductor La(Ru${}_{1-x}$Fe${}_x$)${}_3$Si${}_2$
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• Origin of $\pi$-shifted three-dimensional charge density waves in kagome metal AV${}_3$Sb${}_5$
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• Strong-coupling superconductivity and weak vortex pinning in Ta-doped CsV${}_3$Sb${}_5$ single crystals
• Electronic Correlations and Evolution of the Charge-Density Wave in the Kagome Metals $A$V${}_3$Sb${}_5$ ($A$ = K, Rb, Cs)
• Kagome metals
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• Phonon collapse and anharmonic melting of the 3D charge-density wave in kagome metals
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• Search for orbital magnetism in the kagome superconductor $\mathrm{Cs}{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$ using neutron diffraction
• Observation of anomalous amplitude modes in the kagome metal CsV${}_3$Sb${}_5$
• Orbital-selective effect of spin reorientation on the Dirac fermions in a non-charge-ordered kagome ferromagnet Fe${}_3$Ge
• Dynamical decoding of the competition between charge density waves in a kagome superconductor
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• Visualizing the internal structure of the charge-density-wave state in CeSbTe
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• Interplay between Chiral Charge Density Wave and Superconductivity in Kagome Superconductors: A Self-consistent Theoretical Analysis
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• Kohn-Luttinger-like mechanism for unconventional charge density waves
• Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids
• Inter-Layer Correlation of Loop Current Charge Density Wave on the Bilayer Kagomé Lattice
• Orbital altermagnetism on the kagome lattice and possible application to $A$V${}_3$Sb${}_5$
• Hexagonal-to-base-centered-orthorhombic $4Q$ charge density wave order in kagome metals KV${}_3$Sb${}_5$, RbV${}_3$Sb${}_5$, and CsV${}_3$Sb${}_5$
• Effective Ionic Valence and Local Magnetic Moment in Kagome Superconductors
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