Fig. 2: Bandstructure and shift current conductivity of the two-layer Rice-Mele model and its dependence on model parameters δ₂.

a Bandstructure of 2RM model without band mixing (dashed line) and with band mixing of ε = 0.1 (solid line). The red/black band refers to the first/second RM model, with intracell hopping strength \({v}_{i}=\frac{1}{2}({t}_{i}+{\delta }_{i})\), intercell hopping strength \({w}_{i}=\frac{1}{2}({t}_{i}-{\delta }_{i})\), and sublattice offset potential Δ_i, where i = 1, 2 indexing the different RM layers. A schematic description of the model is included, with ε coupling the different sublattice degrees of freedom between the chain. The parameters of 2RM are (t, δ₁, Δ₁, δ₂, Δ₂) = (1, 0.8, 0.7, 0.86, 0.6). b Shift current conductivity due to transitions between the red band (first RM model) with and without band mixing. The presence of mixing enhances the peak due to the transition at the band edge via virtual transitions through the second RM bands. c Bandstructure of the top two bands, with the orange dashed line denoting chemical potential at filling ν = 0.5. d Shift current conductivity due to transitions from band 2 to band 3, showing a large response at a low frequency determined by the energy gap of band 2 and 3 at ka = ±π.