Loop currents in $A$V${}_3$Sb${}_5$ kagome metals: multipolar and toroidal magnetic orders

Abstract

Experiments in the recently discovered vanadium-based kagome metals have suggested that their charge-ordered state displays not only bond distortions, characteristic of a ``real" charge density-wave (rCDW), but also time-reversal symmetry-breaking, typical of loop currents described by an ``imaginary" charge density-wave (iCDW). Here, we combine density-functional theory, group-theory, and phenomenological modeling to investigate the complex charge-ordered states that arise from interactions between the low-energy van Hove singularities present in the electronic structure of $A$V${}_3$Sb${}_5$. We find two broad classes of mixed iCDW-rCDW configurations: triple-$\mathbf{Q}$ iCDW, triple-$\mathbf{Q}$ rCDW order, dubbed $3\mathbf{Q}$-$3\mathbf{Q}$, and double-$\mathbf{Q}$ iCDW, single-$\mathbf{Q}$ rCDW order, dubbed $2\mathbf{Q}$-$1\mathbf{Q}$. Moreover, we identify seven different types of iCDW order, stemming from the different vanadium-orbital and kagome-sublattice structures of the two pairs of van Hove singularities present above and below the Fermi level. While the $2\mathbf{Q}$-$1\mathbf{Q}$ states trigger an orthorhombic distortion that breaks the threefold rotational symmetry of the kagome lattice, the $3\mathbf{Q}$-$3\mathbf{Q}$ states induce various types of subsidiary uniform magnetic orders, from conventional ferromagnetism to magnetic octupolar, magnetic toroidal, and even magnetic monopolar order. We show that these exotic orders display unique magneto-striction, magneto-electric, and magneto-electric-striction properties that can be probed experimentally to identify which iCDW state is realized in these compounds. We briefly discuss the impact of an out-of-plane modulation of the charge order and the interplay between these complex charge-ordered states and superconductivity.

arXiv comment20 pages, 8 figures

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Cited by in corpus (62)

• Quantum states and intertwining phases in kagome materials
• AV${}_3$Sb${}_5$ Kagome Superconductors: Progress and Future Directions
• Chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5
• Correlated order at the tipping point in the kagome metal CsV${}_3$Sb${}_5$
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• Charge-loop current order and Z3 nematicity mediated by bond-order fluctuations in kagome metal AV3Sb5 (A=Cs,Rb,K)
• Loop-current charge density wave driven by long-range Coulomb repulsion on the kagome lattice
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• Theory of nematic charge orders in kagome metals
• Microscopic nature of the charge-density wave in kagome superconductor RbV${}_3$Sb${}_5$
• Intertwined van-Hove Singularities as a Mechanism for Loop Current Order in Kagome Metals
• Unconventional superconductivity protected from disorder on the kagome lattice
• Small Fermi pockets intertwined with charge stripes and pair density wave order in a kagome superconductor
• Quantum oscillations revealing topological band in kagome metal ScV6Sn6
• Impact of Sb degrees of freedom on the charge density wave phase diagram of the kagome metal CsV${}_3$Sb${}_5$
• Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals
• A New Era of Excitonic Insulators
• Superconductivity from Orbital-Selective Electron-Phonon Coupling in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$
• Probing octupolar hidden order via Janus impurities
• Absence of $E_{2g}$ nematic instability and dominant $A_{1g}$ response in the kagome metal CsV${}_3$Sb${}_5$
• Charge order above room-temperature in a prototypical kagome superconductor La(Ru${}_{1-x}$Fe${}_x$)${}_3$Si${}_2$
• Origin of $\pi$-shifted three-dimensional charge density waves in kagome metal AV${}_3$Sb${}_5$
• Probing orbital magnetism of a kagome metal CsV3Sb5 by a tuning fork resonator
• Phenomenology of bond and flux orders in kagome metals
• Kagome metals
• Superconductivity due to fluctuating loop currents
• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
• Low-Energy Electronic Structure in the Unconventional Charge-Ordered State of ScV${}_6$Sn${}_6$
• Search for orbital magnetism in the kagome superconductor $\mathrm{Cs}{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$ using neutron diffraction
• Frustrated charge density wave and quasi-long-range bond-orientational order in the magnetic kagome FeGe
• Existence of Hebel-Slichter peak in unconventional kagome superconductors
• Dynamical decoding of the competition between charge density waves in a kagome superconductor
• Exotic charge density waves and superconductivity on the Kagome Lattice
• Real-space Loop Current Pattern in Time-reversal-symmetry Breaking Phase in Kagome Metals
• Piezoresistivity as a Fingerprint of Ferroaxial Transitions
• Low temperature phase transitions under CDW state in kagome metals AV3Sb5 (A=Cs,Rb,K): Significance of mix-type Fermi surface electron correlations
• Quantifying magnetic field driven lattice distortions in kagome metals at the femto-scale using scanning tunneling microscopy
• Topological Quantum Computation on a Chiral Kondo Chain
• Electronic structure of $A$V${}_3$Sb${}_5$ kagome metals
• Revealing Rotational Symmetry Breaking Charge-density Wave Order in Kagome Superconductor (Rb, K)V${}_3$Sb${}_5$ by Ultrafast Pump-probe Experiments
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• Interplay of superconductivity and charge-density-wave order in kagome materials
• Evidence for reduced periodic lattice distortion within the Sb-terminated surface layer of the kagome metal CsV${}_3$Sb${}_5$
• Charge-density wave fluctuation driven composite order in the layered Kagome Metals
• Constraints on the orbital flux phase in $A$V${}_3$Sb${}_5$ from polar Kerr effect
• Origin of switchable quasiparticle-interference chirality in loop-current phase of kagome metals measured by scanning-tunneling-microscopy
• Unveiling the nature of electronic transitions in RbV${}_3$Sb${}_5$ with Avoided Level Crossing $\mu$SR
• Odd-parity quadrupole order and induced nonreciprocal transport in the kagome metal CsTi${}_3$Bi${}_5$ driven by quantum interference
• Nanoscale strain manipulation of smectic susceptibility in kagome superconductors
• Loop-current order through the kagome looking glass
• Phase-sensitive evidence for pair density waves in a kagome superconductor
• Magnetic field-induced momentum-dependent symmetry breaking in a kagome superconductor
• Kohn-Luttinger-like mechanism for unconventional charge density waves
• Orbital altermagnetism on the kagome lattice and possible application to $A$V${}_3$Sb${}_5$
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