Three-dimensional flat bands and possible interlayer triplet pairing superconductivity in the alternating twisted NbSe$_2$ moiré bulk

TL;DR

This work uses first-principles calculations to demonstrate that alternating twisted NbSe$_2$ moiré bulk hosts three-dimensional flat bands for twist angles $\le 7.31^\circ$, driven by spontaneous structural relaxation and strong interlayer coupling. The flat bands exhibit $k_z$-dependent dispersion, confirming a 3D character, and the system's out-of-plane mirror symmetry points to interlayer triplet pairing mechanisms that differ from those in twisted bilayers. A Coulomb-interaction analysis shows enhanced 3D interactions at small $q$, placing the system in a strong-coupling regime conducive to correlated states. A symmetry-guided continuum model indicates that nonzero $k_z$ enhances interlayer triplet pairing susceptibility, suggesting robust bulk triplet superconductivity in the moiré bulk and motivating experimental exploration of 3D moiré superconductivity in NbSe$_2$-based systems.

Abstract

Moiré superlattices hosting flat bands and correlated states have emerged as a focal topic in condensed matter research. Through first-principles calculations, we investigate three-dimensional flat bands in alternating twisted NbSe$_2$ moiré bulk structures. These structures exhibit enhanced interlayer interactions compared to twisted bilayer configurations. Our results demonstrate that moiré bulks undergo spontaneous large-scale structural relaxation, resulting in the formation of remarkably flat energy bands at twist angles $\leq$ 7.31°. The $k_z$-dependent dispersion of flat bands across different moiré bulks reveals their intrinsic three-dimensional character. The presence of out-of-plane mirror symmetry in these moiré bulk structures suggests possible interlayer triplet superconducting pairing mechanisms that differ from those in twisted bilayer systems. Our work paves the way for exploring potential three-dimensional flat bands in other moiré bulk systems.

Figures (6)

• Figure 1: (a) The top view of monolayer NbSe$_2$. (b) The side view of alternating twisted NbSe$_2$ moiré bulk. The unit cell of moiré bulk is remarked by black dashed lines. (c) The unrelaxed structure of alternating $6.01^{\circ}$-twisted NbSe$_2$ moiré bulk. (d) The relaxed structure of alternating $6.01^{\circ}$-twisted NbSe$_2$ moiré bulk. Compared to unrelaxed structure, obvious expansion of MM region exists in the relaxed structure.
• Figure 2: The atomic displacements in the top layer (a) and bottom layer (b) in the unitcell of alternating $13.17^{\circ}$-twisted NbSe$_2$ moiré bulk are shown, the length of red vectors on each atom refers to atomic displacement amplitude with scaling factor of 25. Here atomic displacements in the top layer (c) and bottom layer (d) in the unitcell of alternating $4.41^{\circ}$-twisted NbSe$_2$ moiré bulk are also present with scaling factor of 3. One can see Fig. S2 for more clear displacement distributions.
• Figure 3: The energy bands of alternating twisted NbSe$_2$ moiré bulk with unrelaxed and relaxed structures. Here we highlighted the energy bands whose energy is closest to Fermi level.
• Figure 4: Band structures in twisted 13.17° and 6.01° $NbSe_2$ with a rotation center of MX and MM (result of main text) respectively.
• Figure 5: (a) The average bandwidths of energy bands highlighted in the Fig.3 in different alternating twisted NbSe$_2$ moiré bulk. (b) The calculated density of states per atom of different twisted NbSe$_2$ bulk.