Figure 1: Superfluid transport and Wannier functions. | Nature Communications

Figure 1: Superfluid transport and Wannier functions.

From: Superfluidity in topologically nontrivial flat bands

Figure 1

(a) Localized Wannier functions are obtained from the Bloch functions of a set of bands, called a composite band24,25. To have superfluidity in a flat band, the pairing takes place only in a subset of the bands within the composite band, for example, in a single flat band. While the Wannier functions built from the Bloch functions of the band where pairing takes place are delocalized due to the nonzero Chern number25 C0 (b) the Wannier functions of the composite band are exponentially localized (c). We show that the superfluid weight Ds in a flat band is given by the Brillouin-zone average of the quantum metric26,27, which is the real part of an invariant . (d) The imaginary part of gives the Chern number C. The positivite semidefiniteness of leads to the bound Ds|C| on the superfluid weight.

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