The kagome lattice provides a fascinating playground to study geometrical frustration, topology and strong correlations. The newly discovered kagome metals AV3Sb5 (where A can refer to K, Rb or Cs) exhibit phenomena including topological band structure, symmetry-breaking charge-density waves and superconductivity. Nevertheless, the nature of the symmetry breaking in the charge-density wave phase is not yet clear, despite the fact that it is crucial in order to understand whether the superconductivity is unconventional. In this work, we perform scanning birefringence microscopy on all three members of this family and find that six-fold rotation symmetry is broken at the onset of the charge-density wave transition in all these compounds. We show that the three nematic domains are oriented at 120° to each other and propose that staggered charge-density wave orders with a relative π phase shift between layers is a possibility that can explain these observations. We also perform magneto-optical Kerr effect and circular dichroism measurements. The onset of both signals is at the transition temperature, indicating broken time-reversal symmetry and the existence of the long-sought loop currents in that phase. The interplay between superconductivity that might break time-reversal symmetry and charge order is a key issue in kagome materials. Now, optical measurements show that spatial and time-reversal symmetries are broken at the onset of charge order. 

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Three-state nematicity and magneto-optical Kerr effect in the charge density waves in kagome superconductors

Abstract When electric conductors differ from their mirror image, unusual chiral transport coefficients appear that are forbidden in achiral metals, such as a non-linear electric response known as electronic magnetochiral anisotropy (eMChA) 1–6 . Although chiral transport signatures are allowed by symmetry in many conductors without a centre of inversion, they reach appreciable levels only in rare cases in which an exceptionally strong chiral coupling to the itinerant electrons is present. So far, observations of chiral transport have been limited to materials in which the atomic positions strongly break mirror symmetries. Here, we report chiral transport in the centrosymmetric layered kagome metal CsV 3 Sb 5 observed via second-harmonic generation under an in-plane magnetic field. The eMChA signal becomes significant only at temperatures below $${T}^{{\prime} }\approx $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> <mml:mo>≈</mml:mo> </mml:mrow> </mml:math> 35 K, deep within the charge-ordered state of CsV 3 Sb 5 ( T CDW ≈ 94 K). This temperature dependence reveals a direct correspondence between electronic chirality, unidirectional charge order 7 and spontaneous time-reversal symmetry breaking due to putative orbital loop currents 8–10 . We show that the chirality is set by the out-of-plane field component and that a transition from left- to right-handed transport can be induced by changing the field sign. CsV 3 Sb 5 is the first material in which strong chiral transport can be controlled and switched by small magnetic field changes, in stark contrast to structurally chiral materials, which is a prerequisite for applications in chiral electronics. 

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Switchable chiral transport in charge-ordered kagome metal CsV3Sb5

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. These developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter. Recent key developments in the exploration of kagome materials are reviewed, including fundamental concepts of a kagome lattice, realizations of Chern and Weyl topological magnetism, flat-band many-body correlations, and unconventional charge-density waves and superconductivity. 

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Topological kagome magnets and superconductors.

Emergent charge order in pressurized kagome superconductor CsV3Sb5

The kagome lattice provides a fertile platform to explore novel symmetry-breaking states. Charge-density wave (CDW) instabilities have been recently discovered in a new kagome metal family, commonly considered to arise from Fermi-surface instabilities. Here we report the observation of Raman-active CDW amplitude modes in CsV3Sb5, which are collective excitations typically thought to emerge out of frozen soft phonons, although phonon softening is elusive experimentally. The amplitude modes strongly hybridize with other superlattice modes, imparting them with clear temperature-dependent frequency shift and broadening, rarely seen in other known CDW materials. Both the mode mixing and the large amplitude mode frequencies suggest that the CDW exhibits the character of strong electron-phonon coupling, a regime in which phonon softening can cease to exist. Our work highlights the importance of the lattice degree of freedom in the CDW formation and points to the complex nature of the mechanism. 

https://www.nature.com/articles/s41467-022-31162-1.pdf

Observation of anomalous amplitude modes in the kagome metal CsV3Sb5

Charge-density-wave-driven electronic nematicity in a kagome superconductor

Unidirectional electron–phonon coupling in the nematic state of a kagome superconductor

Electronic nematicity has been commonly observed in juxtaposition with unconventional superconductivity. Understanding the nature of the nematic state, as well as its consequence on the electronic band structure and superconductivity, has become a pivotal focus in condensed matter physics. Here we use spectroscopic imaging-scanning tunneling microscopy to visualize how the interacting quasiparticles organize themselves in the nematic state of kagome superconductor CsV$_{3-x}$Ti$_x$Sb$_5$, in which twofold symmetric (C$_2$) quasiparticle scattering interference of the vanadium kagome bands emerges below the bulk nematic transition temperature (T$_{nem}$). Surprisingly, we find that the coupling to collective modes, i.e., the phonon, dramatically alters the electrons self-energy and renormalizes the Fermi velocity of the in-plane vanadium d$_{xy/x^2-y^2}$ bands only along the C$_2$ direction, making the low-energy dispersion and electron dynamics highly nonequivalent along the three lattice directions. The anti-correlation between T$_{nem}$ and the superconducting transition temperature upon Ti substitution further suggests a possible competition between superconductivity and electron nematicity in this series, with a principal superconducting gap opening on the same V bands once the nematic state is totally suppressed. The organizing principle of these quasiparticles provides essential information for understanding the interplay between charge density wave and superconductivity in these kagome superconductors, and also reveals a previously unexplored form that expands the landscape for modelling electronic nematicity in systems where electron correlations and lattice degree of freedom act in concert.

Wanru Ma

Papers

Charge-density-wave-driven electronic nematicity in a kagome superconductor

Unidirectional electron–phonon coupling in the nematic state of a kagome superconductor

Unidirectional electron-phonon coupling as a"fingerprint'' of the nematic state in a kagome superconductor