Magic angle hierarchy in twisted graphene multilayers

By E. Khalaf, A. Kruchkov, G. Tarnopolsky, Ashvin Vishwanath. Physical review B, 2019

195 citations recorded by the source corpus.

Author(s): Khalaf, E; Kruchkov, AJ; Tarnopolsky, G; Vishwanath, A | Abstract: © 2019 American Physical Society. When two monolayers of graphene are stacked with a small relative twist angle, the resulting band structure exhibits a remarkably flat pair of bands at a sequence of "magic angles" where correlation effects can induce a host of exotic phases. Here we study a class of related models of n-layered graphene with an alternating relative twist angle ±θ which exhibits magic angle flat bands coexisting with several Dirac dispersing bands at the moire K point. Remarkably, we find that the Hamiltonian for the multilayer system can be mapped exactly to a set of decoupled bilayers at different angles, revealing a remarkable hierarchy mathematically relating all these magic angles to the TBG case. For the trilayer case (n=3), we show that the sequence of magic angle is obtained by multiplying the bilayer magic angles by 2, whereas the quadrilayer case (n=4) has two sequences of magic angles obtained by multiplying the bilayer magic angles by the golden ratio φ=(5+1)/2≈1.62 and its inverse. We also show that for larger n, we can tune the angle to obtain several narrow (almost flat) bands simultaneously and that for n→∞, there is a continuum of magic angles for θ2. Furthermore, we show that tuning several perfectly flat bands for a small number of layers is possible if the coupling between different layers is different. The setup proposed here can be readily achieved by repeatedly applying the "tear and stack" method without the need of any extra tuning of the twist angle and has the advantage that the first magic angle is always larger than the bilayer case.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/696e625d5b2af57d5897b610a50b68f5abb2eb00

Citations in the corpus

• Theory of zero-field superconducting diode effect in twisted trilayer graphene (2021, unknown): “…the representation of the symmetries in table 1; these operators are related to c k ; ρ, l ,η, s , G by a unitary transformation in layer space [38], c r ; ρ, l ,η, s = V l ,ℓ ψ r ; ρ,ℓ,η, s , such that ℓ = 1 , 2 correspond to the mirror-even (invariant under σ h which interchanges the top and…”