The quantum geometry of the electronic states in momentum space, distinct from real-space structural geometry, has attracted increasing interest that has advanced our understanding of quantum phenomena. An important physical manifestation is the recent discovery of anomalous Landau level spreading $\mathrm{\Delta }$ in relation to the maximal quantum distance $d$ of a singular flat band, such as that hosted in a kagome lattice. Strikingly, for a diatomic kagome lattice, we found that $\mathrm{\Delta }$ depends not only on $d$ but also $r$, the real-space diatomic distance. As $r$ increases, $\mathrm{\Delta }$ can even shrink to zero for the case of $d=1$. Interestingly, based on semiclassical theory, we derive that the dependence of $\mathrm{\Delta }$ on $r$ originates from the non-Abelian orbital magnetic moment generated by the bipartite nature of the diatomic kagome lattice with particle-hole symmetry, in analogy with the origin of electron spin from the Dirac equation. The revealed insights have broad implications in the quantum phenomena governed by the intriguing interplay of quantum and real-space geometry.

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• Electronic structure
• Flat bands
• Landau levels