Domain-Direct Band Gaps: Classification and Material Realization

Abstract

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.

Figures (5)

• Figure 1: Generalized classification of direct band gaps based on the geometry of their band-extremum sets in k-space.
• Figure 2: (a) Top view of the twisted bilayer graphite with a $\sqrt{39}$×$\sqrt{39}$ supercell at a twist angle of 27.8°. (b) Top and side views of the twisted diamond obtained after introducing interlayer hybridization, where different layers are indicated by different colors. (c) Top view highlighting the formation of three nanotube-like backbones arranged in a triangular pattern as a result of interlayer hybridization. (d) Enlarged views for detailed atomic configurations on the nanotube-like backbones.
• Figure 3: (a) TB-based band structures and total density of states (DOS). (b) 3D band structures of the highest valence band and the lowest conduction band in the kz = 0 plane of the 2D BZ (green-filled region). (c) The conventional high-symmetry paths for a 3D hexagonal lattice. (d) PBE-based band structures and total density of states (DOS). (e) Real-space partial charge density distribution corresponding to the conduction band minimum flat band. (f) Real-space partial charge density distribution corresponding to the valence band maximum flat band.
• Figure 4: In-plane projections of the direction-dependent Fermi velocities for the VBM (blue) and CBM (red) at the (a) K, (b) $\Gamma$, and (c) M points in kz=0 plane.
• Figure 5: PBE-calculated optical absorption spectra of diamond and the large-supercell structures 165-13-156-r567-0, 163-13-148-r6-0, and 159-26-148-r567-3. The corresponding PBE band gaps are indicated for each structure and their bands structures are shown in Fig.S16.