Direct to indirect band gap transition induced by approximately dark states

Abstract Recent work suggests that crystal structures with two sublattice pairs per primitive cell can host “dark states”, electronic states that barely interact with light due to destructive interference, which makes them invisible in photoemission. In practice, however, dark states are only approximately dark, arising from near but imperfect translation symmetries. Here, we demonstrate a practical consequence of this in the semiconductor (NbSe 4 ) 3 I: Although its band structure indicates an almost direct gap, the material behaves optically like an indirect-gap semiconductor. Angle-resolved photoemission spectroscopy uncovers weak spectral-weight bands folded from a larger Brillouin zone, reflecting approximate intra-unit-cell symmetry. These states form a small direct band gap consistent with transport data but exhibit very low optical transition probability. Instead, optical absorption is dominated by higher-energy transitions involving bands with stronger spectral weight, effectively enlarging the observed optical gap. Our results show that dark states are approximate phenomena with significant consequences for optoelectronic properties.