Session S07: Charge Density Waves in Kagome Metals

Evidence of Time-Reversal and Rotational Symmetry Breaking in the Charge Density Wave States in Kagome Superconductors

The kagome lattice provides a fascinating playground to study geometrical frustration, topology and strong correlations. The newly discovered kagome metals AV₃Sb₅ (A = K, Rb, Cs) exhibit exotic phases including charge density waves (CDWs) and superconductivity, with debated properties such as time reversal symmetry breaking (TRSB) and six-fold rotational symmetry breaking in the CDW phase. In our study, we perform scanning birefringence and circular dichroism (CD) microscopy on CsV₃Sb₅. The emergence of opposite CD domains within the same birefringence domain, along with field-induced CD switching, indicate broken time-reversal symmetry. Furthermore, ultrafast pump-probe reflectivity measurements reveal a splitting of charge density wave induced phonon modes in all three birefringence domains. Such a breaking in degeneracy corroborates the six-fold rotation symmetry breaking in the charge ordered phase.   

Phonon mixing in the charge density wave state of ScV6Sn6

Kagome metals are widely recognized, versatile platforms for exploring topological properties, unconventional electronic correlations, magnetic frustration, and superconductivity. In the RV₆Sn₆ family of materials (R = Sc, Y, Lu), ScV₆Sn₆ hosts an unusual charge density wave ground state as well as structural similarities with the AV₃Sb₅ system (A = K, Cs, Rb). In this work, we combine Raman scattering spectroscopy with first-principles lattice dynamics calculations to reveal phonon mixing processes in the charge density wave state of ScV₆Sn₆. In the low temperature phase, we find at least four new peaks in the vicinity of the V-containing totally symmetric mode near 240 cm⁻¹ suggesting that the density wave acts to mix modes of P6/mmm and R ̅3m symmetry - a result that we quantify by projecting phonons of the high symmetry state onto those of the lower symmetry structure. We also test the stability of the short-range ordered density wave state under compression and propose that both physical and chemical pressure quench the effect. We discuss these findings in terms of symmetry and the structure-property trends that can be unraveled in this system.   

Gap anisotropy, enhanced phonon-phonon coupling, and unusual Fano shape of the amplitude mode in CsV3Sb5

Our polarization-resolved Raman spectra of the kagome metal CsV₃Sb₅ show a small but significant anisotropy of a large gap in the electronic excitation spectrum below the charge density wave (CDW) transition at T_CDW = 95K which escaped detection so far. The projections observed in A_1g and E_2g symmetry suggest that a gap may open up also on the Fermi surface encircling the Γ-point. The simulations using density-functional theory (DFT) reproduce the observed spectral changes and show that both energy considerations and spectroscopy support the tri-hexagonal rather than the Star of David distortion which cannot be distinguished on the basis of the phonon selection rules. The temperature-dependent line width of the low-energy optical A_1g mode indicates enhanced phonon-phonon coupling below T_CDW. The A_1g amplitude mode (AM) develops an unexpected Fano- type line shape which describes the strong coupling of an isolated oscillator and a continuum. The large electronic gap, the enhanced anharmonic phonon-phonon coupling, and the Fano shape of the AM combined are more supportive of a strong-coupling phonon-driven CDW transition than of a Fermi surface instability or an exotic mechanism.   

Spectroscopic Signature of an Unconventional Charge-Ordered State in the Kagomé Vanadate ScV6Sn6

Kagomé materials are an emerging platform for studying a variety of intertwined phases, including superconductivity, charge density waves, and magnetism. Here, we report the low-energy electronic structure of the recently-discovered kagomé vanadate ScV₆Sn₆ that exhibits a charge density wave, using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) measurements. The ARPES data reveal the presence of multiple van Hove singularities (vHSs) at the M point of the Brillouin zone just below the Fermi level, but minimal changes to the electronic structure across the CDW transition. STM quasiparticle interference (QPI) measurements show strong dispersing features deep in the CDW phase. The observed QPI is inconsistent with scattering theory which assumes scattering of quasiparticles by point-like impurities that generally gives a good description of the STM QPI. Instead, reconciling the ARPES and STM measurements requires the presence of a strong momentum dependence of the scattering potential that peaks at the CDW wavevector deep in the ordered phase, which we attribute to an unconventional CDW associated with a nearby instability.   

Scanning tunneling microscopy study of charge density wave kagome metal ScV6Sn6

Kagome lattices have received significant attention due to their potential to concurrently exhibit multiple novel quantum phenomena such as flat bands, topologically protected bands, and van Hove singularities related to charge density Waves (CDW). ScV₆Sn₆ is a new kagome metal which displays an unusual CDW pattern in its low-temperature phase below 92K. Its unit cell includes a pair of mirror-related V-Sn kagome layers separated by a honeycomb lattice of Sn. We investigate both the high-temperature and low-temperature phases of ScV₆Sn₆ using scanning tunneling microscopy/spectroscopy (STM/S). Topographic images and dI/dV maps of cleaved samples show two different surface terminations with distinct density of states near the Fermi level. A direct comparison of atomic resolution STM/S measurements and density functional theory simulations attribute these two terminations to the honeycomb Sn and kagome layers. The charge density of the Sn-terminated surface decays more slowly into the vacuum than that of the kagome-terminated surface. The significant difference in the decay lengths must be considered while characterizing the electronic structures of ScV₆Sn₆ with STM and other surface-sensitive methods.   

Phase diagrams of charge density waves in kagome metals from first principles

Charge density waves (CDWs), the periodic modulation of charge density arising from electron-electron interaction and/or electron-phonon coupling, have been central themes of modern condensed matter physics, as studied in multiple compounds including transition metal dichalcogenides, cuprates, nickelates, and recently kagome metals. Among them, CDWs in kagome metals have attracted significant attention due to their intriguing characteristics including time-reversal symmetry breaking and their interplay with superconductivity and nematic phases. In this talk, we present our comprehensive first principles study on kagome metals ScV₆Sn₆ and LaRu₃Si₂ that host multiple competing CDW instabilities. We carefully identify competing CDW states by considering multi-phonon effects. We discuss the crucial role of finite temperature effects through anharmonic lattice vibrations in the formation of CDWs. We also show various phase diagrams highlighting the role of lattice parameter, strain, and pressure. Our theory is consistent with experimental reports.     

Tiny Sc Allows the Chains to Rattle: Impact of Lu and Y Doping on the Charge Density Wave in ScV6Sn6

Kagome metals have revealed exciting and unexpected physics in recent years. For example, the RV₆Sn₆ compounds of the HfGe₆Ge₆ family show interesting electronic states and magnetism. Surprisingly, only the scandium version of these rare earth materials (ScV₆Sn₆) develops a charge density wave (CDW) at low temperature.[1] We use careful crystallography and chemical tuning with Lu and Y doping to answer what makes ScV₆Sn₆ special. Our results reveal that the small size of the Sc atom leaves room for Sn and Sc atoms to rattle and ultimately displace to form the CDW modulation. This not only address why only ScV₆Sn₆ develop charge order but also provides an unusual variation on the common correspondence between physical and chemical pressure.[2]

[1] H. W. S. Arachchige, et al. Phys. Rev. Lett. 129, 216402 (2022) https://doi.org/10.1103/PhysRevLett.129.216402 

[2] W. R. Meier, et al. J. Am. Chem. Soc. 145 (38), 20943 (2023) https://doi.org/10.1021/jacs.3c06394    

Impact of transition-metal doping on charge density wave in ScV6Sn6

The transition metal kagome layers of HfFe6Ge6-type compounds give rise to diverse and novel electronic and magnetic properties. ScV6Sn6 produces a charge density wave (CDW) below 92K and ScMn6Sn6 exhibits antiferromagnetism below 390K as well as anomalous Nernst and Hall effects. Considering the resistance of ScV6Sn6 to doping by chromium, we investigate the mutual doping capability of ScV6Sn6 and ScMn6Sn6 by synthesizing crystals of Sc(V1-xMnx)Sn6, where 0   

Competing itinerant and local spin interactions in kagome metal FeGe

Two-dimensional kagome metals with corner-sharing triangles provide a platform for exploring strong electron correlations and band topology due to their geometrically frustrated structure. In these systems, comparable energy scales among spin, lattice, and electronic dynamics lead to competing quantum phases such as charge density wave (CDW), magnetic order, and superconductivity. Kagome metal FeGe, for instance, shows various phases: A-type antiferromagnetic (AFM) order around 400 K, a CDW phase with AFM moment below 100 K, and a c-axis double cone AFM near 60 K. Using neutron scattering, we detected gapless incommensurate spin excitations related to the double cone AFM at temperatures surpassing the mentioned phase transitions. Commensurate spin waves adhere to the Bose population factor, while incommensurate ones show deviation, peaking at T_Canting, indicative of a second-order magnetic phase transition. Density functional theory calculations suggest the incommensurate structure originates from the nested Fermi surfaces and spin density wave order formation. The temperature variation of these excitations hints at a connection between spin density wave and CDW order, possibly because of flat electronic bands near the Fermi level.   

Topological Nernst, Anomalous Nernst, and Anomalous Thermal Hall effect in the Kagome magnet YMn6Sn4Ge2

RMn₆Sn₆ (R = rare earth elements) are magnetic compounds that form in a Kagome lattice structure. Among the family, YMn₆Sn₆ has attracted much interest, as it hosts multiple competing magnetic phases, magnetization driven Lifshitz transitions, Dirac points, flat bands, and anomalous Nernst and Hall effect. To study how the magnetic structures can be tuned by Ge substitution, YMn₆Sn₄Ge₂ has been recently synthesized and demonstrates distinct magnetic phases from the parent compound’s transverse conical spiral and fan-like phases. In this study, we performed thermal and thermoelectric measurements on YMn₆Sn₄Ge₂ to understand how transport properties can be affected by magnetic structures. We observed a topological Nernst effect, along with an anomalous Nernst and thermal Hall effect, which differs from the parent compound.  Our study reveals the non-trivial topological nature of YMn₆Sn₄Ge₂ and the sensitivity of its magnetic structure to Ge-substitution.    

Magnetism, lattice dynamics, and anomalous Hall conductivity in kagome metal KMn3Sb5

Kagome metals are reported to exhibit remarkable properties, including superconductivity, charge density wave order, and a large anomalous Hall conductivity (AHC), which facilitate the implementation of spintronic devices. In this work, we theoretically study a novel kagome metal based on Mn magnetic sites in a KMn₃Sb₅ stoichiometry. By means of first-principles density functional theory calculations, we demonstrate that the studied compound is dynamically stable, locking the ferromagnetic order as the ground state configuration, thus preventing the charge-density-wave state as reported in its vanadium-based counterpart KV₃Sb₅. Our calculations reveal that KMn₃Sb₅ exhibits an out-of-plane (001) ferromagnetic response as the ground state, allowing for the emergence of topologically protected Weyl nodes near the Fermi level and nonzero AHC in this centrosymmetric system. We obtain a tangible AHC σ_xy = 314 S·cm⁻¹ component, which is comparable to that of other kagome metals. Finally, we explore the effect of the on-site Coulomb repulsion (+U) on the structural and electronic properties and find that, although the lattice parameters and σ_xy moderately vary with increasing +U, KMn₃Sb₅ stands as an ideal stable ferromagnetic kagome metal with a large AHC response.   

Anharmonic melting of the 3D charge-density wave in the kagome metal CsV3Sb5

The CDW mechanism and resulting structure of the AV3Sb5 family of Kagome metals has posed a puzzling challenge since their discovery four years ago. Thus far, attempts to theoretically study the CDW have overlooked the importance of anharmonic effects. Here, we employ a non-perturbative treatment of anharmonicity to conduct a comprehensive exploration of the mechanisms governing the formation and melting of the initial charge-density wave (CDW) transition in CsV3Sb5. Our results reveal that the CDW transition at T ~ 94 K is driven by the large electron-phonon coupling within the material, while the eventual melting of the CDW state is attributed to the robust anharmonic effects of the lattice. Additionally, the CDW is primarily triggered by the unstable phonons at the L point, with the M phonons not playing any essential role. Despite the second-order nature of the phase transition, our examination of the spectral function at the L point suggests that observing softening experimentally may prove to be exceedingly challenging due to the large electron-phonon linewidth. Finally, the second-order nature of the CDW transition, enables us to narrow down the potential space groups that may emerge.

Taken together, our theoretical framework successfully anticipates various facets of the CDW transition, encompassing the transition temperature, the absence of M mode condensation, and the observed lack of softening. This significant agreement with experimental data carries two noteworthy implications:

(1) The study of the CDW mechanism can be decoupled from phenomena arising in the CDW phase.

(2) Quantum effects of the lattice may also exert a crucial influence on the emergent physics in the CDW state, akin to their role in the CDW mechanism.