Domain-Direct Band Gaps: Classification and Material Realization
The conventional classification of direct band-gap semiconductors relies on point-like extrema in momentum space. Here, we introduce the concept of domain-direct band gaps, where the conduction-band minimum (CBM) and valence-band maximum (VBM) form extended manifolds in the Brillouin zone. We demonstrate this concept through the material realization of an extreme two-dimensional-two-dimensional (2D-2D) domain-direct band gap in twisted diamond. First-principles calculations show that both the CBM and VBM exhibit nearly flat 2D manifolds in the kx-ky plane with minimal energy variation (a few meV), yielding a direct band gap of 3.264 eV. In contrast, strong dispersion along the out-of-plane kz direction induces anisotropic carrier dynamics, with strongly suppressed in-plane Fermi velocities (down to about 10$^1$-10$^3$ m/s in certain directions) and much larger out-of-plane velocities (about 10$^6$ m/s). The nearly flat CBM and VBM manifolds enhance the joint density of states, leading to a pronounced optical absorption peak at the band gap onset. This new type of domain-direct gap, coupled with strong directional anisotropy, opens up opportunities for anisotropic optoelectronic applications. Our results establish domain-direct band gaps as a new class of semiconductors, demonstrating their feasibility in real materials.