Abstract
The van Hove singularity in density of states generally exists in periodic systems due to the presence of saddle points of energy dispersion in momentum space. We introduce a new type of van Hove singularity in two dimensions, resulting from high-order saddle points and exhibiting power-law divergent density of states. We show that high-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moiré superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field. Correlation effects from high-order van Hove singularity near Fermi level are also discussed.
Highlights
The van Hove singularity in density of states generally exists in periodic systems due to the presence of saddle points of energy dispersion in momentum space
We show that as the twist angle decreases below a critical value θc, the van Hove saddle point—which marks the change of topology in Fermi surface (Lifshitz transition)—undergoes a topological transition whereby a single saddle point splits into two new ones
We propose that proximity to such “high-order van Hove singularity”, which requires tuning to the critical twist angle or pressure, is an important factor responsible for correlated electron phenomena in twisted bilayer graphene (TBG) near half filling
Summary
An additional hole pocket (not present at θ 1⁄4 2) emerges out of each energy maximum and eventually intersects two Dirac pockets at two new saddle points on opposite sides of ΓM32 Λþ and ΛÀ are a pair of ordinary VHS points related by two-fold rotation, whose Fermi contours are two parabolas 2αðpx Ç β=~γÞ 1⁄4 ðγ ± ~γÞp2y, see Fig. 2f This behavior corresponds to the VHS in the calculated band structure at θ 1⁄4 1:05. Our unified description of two regimes of ordinary VHS (Λ0 and Λ ± ) using a single local energy dispersion (3) implies that the transition between them corresponds to the sign change of β In this process, energy contours at VHS changes from intersecting at one point Λ0 (Fig. 2d and e) to two points Λ ± (Fig. 2f). For the energy dispersion (3), we find the DOS analytically ρðEÞ
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