Understanding the flat band in 1T-TaS2 using a rotated basis

Abstract

Electronic flat bands serve as a unique platform to achieve strongly-correlated phases. The emergence of a flat band around the Fermi level in 1T-TaS${}_2$ in accompany with the development of a $\sqrt{13}\times \sqrt{13}$ charge density wave (CDW) superlattice has long been noticed experimentally, but a transparent theoretical understanding remains elusive. We show that without CDW, the primary feature of the $1\times 1$ bands can be fitted by a simple trigonometric function, and physically understood by choosing a rotated ${\tilde{t}}_{2g}$ basis with the principle axes aligning to the tilted TaS${}_6$ octahedron. Using this basis, we trace the band evolution in the $\sqrt{13}\times \sqrt{13}$ superlattice by progressively including different CDW effects. We point out that CDW strongly rehybridizes the three ${\tilde{t}}_{2g}$ orbitals, which leads to the formation of a well-localized molecular orbital and spawns the flat band.