Valley-contrasting interband transitions and excitons in symmetrically biased dice model

We study the exciton states in the symmetrically biased dice model, the electronic structures of which have an isolated flat band between two dispersive bands. At 1/3 or 2/3 filling, the model describes a two-dimensional semiconductor with the band edge at two degenerate valleys. Because of qualitative changes in the eigenvectors resulting from the bias term, the interband transition between the flat band and a dispersive band is valley contrasting under circularly polarized light. In terms of an effective-mass model and a realistic electron-hole interaction, we numerically calculate the spectrum and wave functions of the intravalley excitons, which are treated as Wannier-Mott excitons. We also discuss the fine structures of the exciton spectrum induced by the intravalley and intervalley exchange interactions. The symmetrically biased dice model thereby proves to be a new platform for valley-contrasting optoelectronics.