Speaker
Description
We derive a set of general formulae for projecting a real space electronic interaction $V(\mathbf{r})$ on to orbital resolved bands in 3D, layered and monolayer lattices. The resulting k-space interaction $V(\mathbf{k}_1, \mathbf{k}_2, \mathbf{q}; n_1, n_2, n_3, n_4)$ resembles a vertex function, with momentum conservation up to a reciprocal lattice vector and an explicit dependence on the bands $n_1, n_2, n_3$ and $n_4$ corresponding to the ingoing and outgoing electrons. We apply this formalism to tight-binding models with higher order van Hove singularities, that are relevant to materials like the Kagome superconductors. We show that a general feature of such a band-projected interaction is that some k-space scatterings $\mathbf{k}_1, \mathbf{k}_2 \rightarrow \mathbf{k}_1 + \mathbf{q}, \mathbf{k}_2 – \mathbf{q}$ are accompanied by a much stronger interaction as compared to others. Such a hierarchy of interactions essentially results from the modulation of the real space interaction by lattice, orbital and band geometries. This can facilitate a more nuanced correlated-electron calculation with mean-field, parquet and functional renormalization group methods.