Diatomic Kagome Lattices

Updated 23 October 2025

Diatomic kagome lattices are two-dimensional networks featuring two inequivalent sites per cell and corner-sharing triangles that enable complex band topologies.
They exhibit coexisting Dirac cones, flat bands, and symmetry-induced band inversions, which foster diverse topological and magnetic quantum phases.
Tunable through chemical composition, strain, and substrate manipulation, these lattices offer promising platforms for spintronics and topological electronics.

Diatomic kagome lattices are two-dimensional networks in which the conventional kagome motif—corner-sharing triangles—incorporates two inequivalent sites or sublattices per unit cell. This structural modification yields a broad variety of novel physical behaviors compared to the simple kagome lattice, including diverse realizations of band topology, magnetic frustration, strongly correlated states, and emergent topological phases. Diatomic kagome lattices are realized in crystalline transition metal compounds, metal-organic frameworks, ultracold atom systems, engineered heterostructures, and designer 2D materials. Their significance arises from the coexistence of Dirac cones, (nearly) flat bands, topologically protected states, and complex magnetism rooted in geometric frustration.

1. Structural Principles and Synthesis

Diatomic kagome lattices are characterized by their two-atom basis per primitive cell. The distinction between sites may arise from chemical composition (as in honeycomb–kagome heterolayers and ligand-decorated frameworks), electronic environment (as in breathing-kagome and kagome-in-honeycomb materials), or dimerization and bond alternation (as in kagome–triangular magnets):

System class	Sublattice distinction	Material or platform
Transition-metal pnictides/chalcogenides	Ineq. transition-metal/bismuth	$A$ Ti $_3$ Bi $_5$ $(A=$ Cs, Rb) (Werhahn et al., 2022)
Metal–organic frameworks (MOFs)	Metal vs. ligand site	$\mathrm{M}_3\mathrm{C}_6\mathrm{O}_6$ (Shaiek et al., 2022), MOF-74
Honeycomb–kagome heterolayers	Layer type (honeycomb/kagome)	Twisted/Lattice-mismatched HK (Bark et al., 20 Feb 2025)
Kagome-in-honeycomb “KIH” lattices	Kagome sublattice in graphene host	$(\text{MN}_4)_3\text{C}_{32}$ (M=Pt/Mn) (Dong et al., 6 Mar 2024)
Rydberg atom arrays	Paired/kagome via interactions	Cold atom arrays (Lozovik et al., 2019)

Synthetic routes include direct solid-state synthesis for bulk compounds (Werhahn et al., 2022), surface synthesis and epitaxy for 2D MOFs (Shaiek et al., 2022), optical superlattices for ultracold atoms (Jo et al., 2011), and template-driven atomic rearrangements (“kagomerization”) via capping monolayers such as h-BN on transition-metal substrates (Zhou et al., 2023, Kim et al., 2017).

2. Electronic Structure: Dirac Cones, Flat Bands, and Band Inversions

A key hallmark of kagome-based geometries is the coexistence of linearly dispersing Dirac cones and flat bands. In diatomic variants, site (or bond) alternation and chemical inequivalence add complexity to the band structure. Tight-binding (TB) and DFT calculations (Barreteau et al., 2017, Xu et al., 2023, Dong et al., 6 Mar 2024) reveal:

In ligand-decorated or honeycomb–kagome lattices, band theory predicts the following typical features:
- Dispersive bands with Dirac (and sometimes quadratic) crossings at symmetry points (usually $K$ or $\Gamma$ ).
- Flat bands associated with specific site/orbital symmetries; can be Kagome-centered, ligand-centered (A $_2$ /E), or metal-centered.
- In “kagome-in-honeycomb” $(\text{MN}_4)_3\text{C}_{32}$ , Dirac cones coexist with a flat band at $E_F$ ; SOC gaps the crossing, realizing a quantum spin Hall or quantum anomalous Hall phase (Dong et al., 6 Mar 2024).
- In honeycomb–kagome bilayers (HK heterolayers), hybridization drives Dirac cones toward $\Gamma$ where they merge to produce a higher-order topological phase (Bark et al., 20 Feb 2025).
The dispersionless flat band arises as the eigenfunction’s amplitude undergoes destructive interference around the hexagonal loops, trapping electrons. This band is robust but can be made dispersive by symmetry breaking, additional hopping, or applied strain (Xu et al., 2023).
Strain and symmetry breaking play critical roles:
- Uniaxial strain shifts Dirac points and reshapes the flat band into a partially flat band with highly anisotropic effective masses—enabling the engineering of directionally dependent transport and interaction effects (Xu et al., 2023).
- In breathing kagome lattices, bond alternation results in band inversions either at $K$ or $\Gamma$ , triggering different topological phases (Jung et al., 2021, Bark et al., 20 Feb 2025).

3. Magnetism, Correlation, and Quantum Phases

The magnetic properties of diatomic kagome lattices are governed by strong frustration originating from the geometry, further enriched by the inequivalence of sites/bonds:

Heisenberg antiferromagnets on such lattices allow for two distinct exchange couplings ( $J_{AA}$ $J_{AA}$ , $J_{AB}$ $J_{A B}$ ), yielding a phase diagram that spans:
- Ferrimagnetic order for dominant $J_{AB}$ (bipartite regime).
- Highly frustrated, decoupled clusters for weak $J_{AB}$ ( $J_2 \gg J_1$ limit).
- Extensive low-lying singlet manifolds at intermediate ratios, with quantum resonance among different local singlet “loops” (Rousochatzakis et al., 2013).
Inequivalent resonance loops (e.g., of length 4 and 6) stabilize non-trivial valence bond crystals, breaking lattice symmetries and supporting RVB (resonating valence bond) liquids or crystals (Rousochatzakis et al., 2013).
In metal–organic kagome monolayers with magnetic centers (e.g., Mn $_3$ C $_6$ O $_6$ ), local moments are strongly frustrated; substrate charge transfer can tune the balance between spin-liquid-like antiferromagnetic coupling and ferromagnetic order, with direct consequences for quantum anomalous Hall states (Shaiek et al., 2022).

4. Topological Phenomena: Higher-Order Insulators, Valley Hall, and Chiral Edge States

Band topology in diatomic kagome systems is exceptionally rich:

Higher-order topological insulators (HOTIs) arise in “breathing” kagome lattices, where corner-localized zero modes emerge when bond anisotropy leads to Wannier center shifts (Jung et al., 2021, Bark et al., 20 Feb 2025). The topological invariant is often a quadrupole moment $Q^{(6)}$ or an obstructed atomic limit.
Valley Hall phases are realized when inversion or mirror symmetry is broken (e.g., by sublattice mass, bond alternation, or lattice deformation). The resulting Berry curvature is sharply localized at $K/K'$ valleys, with protected valley Chern numbers and robust one-way edge states at domain walls (Lera et al., 2018).
Quantum anomalous Hall (QAH) and quantum spin Hall (QSH) phases are induced by intrinsic SOC:
- (PtN $_4$ ) $_3$ C $_{32}$ : QSH state; (MnN $_4$ ) $_3$ C $_{32}$ : QAH state with Chern number $C=1$ and chiral edge states (Dong et al., 6 Mar 2024).
- Edge state calculations confirm helical or chiral channel formation in these systems.

5. Designer Platforms and Strain Engineering

Diatomic kagome lattices can be engineered in cold atom, photonic, or electronic platforms and controlled through external parameters:

Ultracold atom optical lattices, realized by superimposing lattices of different wavelengths to form site-depleted kagome structures, allow for “on-demand” manipulation of frustration and paper of flat-band physics (Jo et al., 2011). Extension to mixtures of atomic species naturally realizes diatomic patterns.
Kagomerization, i.e., the structurally driven formation of kagome morphology from a hexagonal atomic layer capped with h-BN, allows for robust realization of 2D kagome networks in transition-metal monolayers supported on fcc(111) heavy metals. This process is generic and enables the stabilization of topological skyrmions, bimerons, and related solitons via interfacial redistribution of exchange, anisotropy, and DMI parameters (Zhou et al., 2023).
Strain engineering—uniaxial or biaxial—is effective for tuning band inversions, manipulating the relative dispersion of flat and Dirac bands, and driving topological phase transitions (Xu et al., 2023, Kim et al., 2017).

6. Experimental Signatures and Applications

Characteristic observables and device implications include:

STM and ARPES measurements are able to resolve domain-dependent local DOS in moiré superlattices or heterostructure networks, revealing the spatial variation of metallic and insulating character, and providing direct evidence of HOTI corner states or domain-wall edge modes (Bark et al., 20 Feb 2025, Jung et al., 2021).
Quantum oscillations and conventional Fermi liquid behavior in kagome metals (e.g., CsTi $_3$ Bi $_5$ , RbTi $_3$ Bi $_5$ ) confirm the persistence of kagome-derived Dirac bands and multi-orbital complex Fermi surfaces even when no clear topological signature is present (Werhahn et al., 2022).
Surface- and interface-synthesized MOFs and atomic lattices are prime platforms for spintronic and topological electronics applications—especially when the Fermi level can be tuned into the flat band regime for correlated and potentially superconducting phases (Shaiek et al., 2022, Kim et al., 2017, Dong et al., 6 Mar 2024).
The presence of flat bands amplifies correlation effects and may promote superconductivity, fractionalization, or magnetic soliton formation—opening prospects for quantum information, low-power computing, and robust non-Abelian state-based electronics.

7. Theoretical Formalism and Future Research

The theoretical description of diatomic kagome lattices relies on advanced tight-binding, DFT, model Hamiltonians, and many-body techniques:

Hamiltonians are constructed to capture inequivalent hopping integrals, on-site potentials, SOC, and interactions:

$H = - \sum_{\langle ij \rangle} t_{ij} c^\dagger_i c_j + \Delta \sum_{i \in B} n_i + \dots$

$H_{\text{SOC}} = i\lambda_{ij} \sum_{\langle\langle i,j \rangle\rangle} \left( \mathbf{d}_{ij} \times \mathbf{d}_{ik} \right) \cdot \mathbf{s}$

where $t_{ij}$ are hopping parameters (possibly direction-dependent), $\Delta$ is a sublattice potential, and $\lambda_{ij}$ are SOC strengths.
Topological invariants are computed via Wannier charge centers or Berry curvature integrals over the Brillouin zone, e.g.:

$\mathbb{Z}_2 = \int_{\text{half BZ}} \mathcal{A}_k \cdot dk \quad ; \quad C = \frac{1}{2\pi} \int_{\text{BZ}} \mathcal{F}(k) d^2k$
Quantum dimer models, RVB theory, and exact diagonalization are essential tools for describing frustrated magnetism, low-lying singlet manifolds, and valence bond crystals.
Future research is poised to further integrate electron–electron interactions (beyond-DFT and DMFT methods), paper moiré and domain architectures for emergent correlated topological phases, and enable device-level engineering of topologically protected states with intricate control over symmetry, doping, and external fields.

Diatomic kagome lattices are thus at the intersection of geometric frustration, correlation effects, and band topology, enabling a suite of quantum phases—HOTI, QSH, QAH, RVB spin liquids, and more—across a spectrum of material platforms. Their flexibility in structure and function continues to propel theoretical and experimental advances in quantum materials science (Wildeboer et al., 2011, Rousochatzakis et al., 2013, Barreteau et al., 2017, Lera et al., 2018, Jung et al., 2021, Shaiek et al., 2022, Werhahn et al., 2022, Xu et al., 2023, Zhou et al., 2023, Dong et al., 6 Mar 2024, Bark et al., 20 Feb 2025).