Dual Haldane sphere and quantized band geometry in chiral multifold fermions

We show that the chiral multifold fermions present a dual Haldane sphere problem in momentum space. Owing to the Berry monopole at the degenerate point, a dual Landau level emerges in the trace of quantum metric, with which a quantized geometric invariant is defined through a surface integration. We further demonstrate potential manifestations in the measurable, physical observables. With a lower bound derived for the finite spread of Wannier functions, anomalous phase coherence is identified accordingly for the flat band superconductivity. We briefly comment on the stability of these results under perturbations. Potential experimental probes of the quantum metric are also discussed.

Automated summary

Through investigating the chiral multifold fermions, it was discovered that a dual Haldane sphere problem exists in momentum space. A quantized geometric invariant was defined through a surface integration in the trace of quantum metric. Potential manifestations in measurable physical observables were demonstrated, and anomalous phase coherence for flat band superconductivity was identified with a lower bound derived for the finite spread of Wannier functions. The stability of these results under perturbations was briefly commented on, along with potential experimental probes of the quantum metric.