Kagome metals

TL;DR

The kagome lattice uniquely blends geometric frustration, topological band structure features (Dirac points, flat bands, and van Hove singularities), and strong correlations, giving rise to a broad landscape of electronic orders. The paper surveys both single-particle theories and many-body phenomena, emphasizing the essential roles of spin–orbit coupling, phonons, and multi-orbital physics, and it details how realistic multisubspace models better capture the physics of AV$_3$Sb$_5$ and related compounds. It then catalogues the diverse material classes—binary and ternary kagome metals—highlighting representative compounds (Fe-, Co-, Mn-, Ni-, Nb-based, AV$_3$Sb$_5$, ScV$_6$Sn$_6$, AM$_6$X$_6$, etc.) and their intertwined topological and correlated states, including CDWs, unconventional superconductivity, PDWs, and topological edge modes. The review concludes with a discussion of open questions, such as constructing unified theories that treat electronic correlations and electron–phonon coupling on an equal footing, understanding strain/defect effects, and advancing towards truly two-dimensional kagome platforms for novel quantum phases and devices.

Abstract

Three important driving forces for creating qualitatively new phases in quantum materials are the topology of the materials' electronic band structures, frustration in the electrons' motion or magnetic interactions, and strong correlations between their charge, spin, and orbital degrees of freedom. In very few material systems do all of these aspects come together to contribute on an equal footing to stabilize new electronic states with unprecedented properties; however the search for such systems can be guided by models of configurational motifs or key sublattices that can host such physics. One of the most fascinating structural motifs for realizing this rich interplay of frustration, electronic topology, and electron correlation effects is the kagome lattice. In this review, we provide an overview of the theoretical underpinnings driving the physics of kagome lattices, and we then discuss experimental progress in realizing novel states enabled by kagome networks in crystalline materials. Different material classes are discussed with an emphasis on the phenomenologies of their electronic states and how they map to interactions arising from their kagome lattices.

Figures (31)

• Figure 1: Number of publications per year, and relative citations, from 2000 to 2024 in which the word kagome is mentioned. Data have been retrieved from the Web of Science platform, searching within all fields. The red dashed lines are guide to the eye to emphasize the surge of interest by the scientific community around 2019 that we ascribe to the experimental discovery of binary and ternary kagome metals ye_massive_2018ortiz2019new.
• Figure 2: (a) Structure of the ideal kagome lattice. A, B and C are the three sites in the unit cell. The blue triangles highlight the corner sharing configuration. (b) Band structure and corresponding density of states (DOS) in units of the hopping integral $t$ resulting from the three-sublattice structure of the kagome lattice shown in (a). The electron fillings $n = 3/12$ and $n = 5/12$ (grey horizontal plane) are located at VHS, as visible in the density of state plot from the two divergences symmetric to the location of the Dirac point. (c) Confinement of the electron wavefunction $\Psi$. Plus and minus signs indicate the phase of flat band eigenstate at neighboring sublattices. Any hoppings outside the hexagon (arrows) are canceled by destructive quantum interference, resulting in the perfect localization of electron in the blue-colored hexagon. (d) Fermi-surface distribution of the sublattice weight for the pure type VHS at filling $n = 5/12$. The Fermi surface touches the M point of the hexagonal BZ where the DOS diverges, as shown in (b). Its topology allows for three nesting vectors connecting parallel opposite sides of the Fermi surface, one of which is $\textbf{Q}_3 = (-\pi/2, \sqrt{3}\pi/2)$. The colors red, blue, and green label the major sublattice occupation of the Fermi surface states, in agreement with the sublattice coloring scheme of panel (a). $\tilde{\textbf{Q}}^{\pm}_3$ originate from opposite shifts of $\textbf{Q}_3$ and link states of similar sublattice weights. The labels I-VI are guides to the eye to help reading off the modulation of sublattice occupation weights encoded in $|u_{s,n=2}(\textbf{k})|^2$ for band $E^{(2)}$ and momenta $\textbf{k}$ along the Fermi surface. Panel (c) adapted from kang_topological_2020. Panel (d) adapted from kiesel_sublattice_2012.
• Figure 3: (a) Eigenvalues of the static non-interacting susceptibility $\chi^{0}_{s_1s_1s_3s_3}(\textbf{q},\omega = 0)$ along a high-symmetry path of the kagome BZ for the chemical potential set at the $p$--type VHS. The colors refer to the sublattice contributions in the susceptibility eigenvectors, following the color scheme given in Fig. \ref{['figure1']}(a) for the A, B and C sublattices. The dashed grey line, whose y-axis is at the right, reports the Lindhard function. (b) Same as panel (a) but for the chemical potential set at the $m$--type VHS.
• Figure 4: Eigenvalues of the two orbitals per site model of Eq. (\ref{['eq:H0_2orb']}) (blue lines) overlaying the band structure as obtained from the first-principles calculations in the absence of SOC (grey lines) for KV$_3$Sb$_5$. The red box highlights the energy-momentum region where the multiple VHS of both $p$-type and $m$-type character emerge below and above the Fermi level, respectively. The top right corner inset reports the real-space structure of the kagome V plane where the sign structure (blue or red lobes) and spatial orientation of the $B_{2g}$ and $B_{3g}$ orbitals is shown on the different lattice sites. Around the $\Gamma$ point, the arrows identify the electron pocket originating from the $p_z$ orbital of the Sb atom located at the center of the hexagon of the kagome lattice. Inset adapted from wu2021nature.
• Figure 5: Band structure induced by $d_{xy}$ (blue) and $d_{xz}/d_{yz}$ (red) orbitals on the kagome lattice (see top right corner inset) and corresponding pure and mixed nature of VHS. Adapted from denner2021analysis.