Emergent Superfluidity of Hard-Core Excitons in Single-Layer Breathing-Kagome Nb${}_3$Te${}_x$Cl${}_{8-x}$

We develop a microscopic theory of superfluidity for hard-core dark excitons on the triangular lattice by mapping the large-$U$ Bose–Hubbard model to an effective XXZ spin-$\frac{1}{2}$ Hamiltonian including virtual hopping processes. Within this framework, we identify the superfluid phase that emerges between the two Mott-insulating endpoints at fillings 0 and 1, and derive its mean-field structure via a canted-spin solution. We then construct the corresponding continuum Landau-Ginzburg (LG) functional and analyze phase fluctuations and vortex dynamics. In two dimensions, the superfluid–normal transition is shown to be governed by a Berezinskii–Kosterlitz–Thouless (BKT) mechanism with a stiffness determined by microscopic parameters. Our results provide a unified description connecting lattice-scale exciton dynamics to continuum critical behavior in triangular geometries.