Magic angles and flat Chern bands in alternating-twist multilayer graphene system

doi:10.1016/j.jmst.2021.09.040

Abstract

Abstract:

Based on the effective continuum model, we study alternating-twist multilayer graphene system and emergence of magic angles and flat band topology. All the alternating-twist multilayer graphene system (from triple layers to few layers) are found to have flat bands at magic angles where the area of AA stacking equals n-fold (n is an integer) electron cyclotron area. From the pseudo-Landau-level representation, there is always an isolated Dirac band in the alternating-twist graphene system constructed by odd number of layers. Since each pair of flat bands can be perceived as the zeroth pseudo-Landau-levels in two dimensional Dirac fermions, electron in the flat band pair can feel a pseudo-magnetic field with the same magnitude but the opposite sign. Calculated Chern number for each flat band is +1 (or -1) which can be tuned by twisting in the vicinity of magic angles or by gating. The concurrent appearance of strong correlation and band topology of flat bands in the alternating-twist multilayer graphene may pave an avenue for the new understanding of superconductivity observed in triple-layered graphene, and supply a new playground for realizing (quantum) anomalous Hall effect.

Key words: Alternating-twist multilayer graphene, Magic angle, Flat band, Band topology

Zhiyong Liu, Wenyuan Shi, Teng Yang, Zhidong Zhang. Magic angles and flat Chern bands in alternating-twist multilayer graphene system[J]. J. Mater. Sci. Technol., 2022, 111: 28-34.

Figures/Tables 4

Fig. 1. (a) A schematic picture of the ATMG: trilayer (left) and quadrilayer (right). (b) The Moiré supercell Brillouin zone of the alternating-twist multilayer graphene. Two large hexagons represent the first Brillouin zones of odd- and even-numbered graphene layers, and the small hexagon is the Moiré Brillouin zone.

Table 1. Magic angles of ATMG from numerical calculation ${{u}_{1}}=0.1\text{eV}$ and ${{u}_{2}}=0.1\text{eV}$ and also from analytical calculation by Eq. (11).

n	θ₁		θ₂		θ₃		θ₄
n	Ana.	Num.	Ana.	Num.	Ana.	Num.	Ana.	Num.
2	1.07	1.06	0.53	0.51	0.36	0.34	0.27	0.24
3	1.51	1.49	0.76	0.71	0.51	0.51	0.38	0.43
4	1.73	1.72	0.87	0.83	0.58	0.57	0.43	0.42
	0.66	0.65	0.33	0.31	0.22	0.22	0.17	0.15
5	1.86	1.84	0.93	0.94	0.62	0.68	0.46	0.47
	1.07	1.06	0.53	0.59	0.36	0.35	0.27	0.28
6	1.93	1.91	0.97	0.93	0.65	0.63	0.48	0.49
	1.34	1.32	0.67	0.63	0.44	0.40	0.33	0.27
	0.48	0.47	0.23	0.22	0.22	0.15	0.12	0.12

Fig. 2. The band structures of K valley of the ATMG systems with ${{u}_{1}}=0.1\text{eV}$ and ${{u}_{2}}=0.1\text{eV}$ at first magic angles. (a) Trilayer with twisted angle$\theta ={{1.49}^{\circ }}$; (b) Quadrilayer graphene with twisted angle θ=1.72°; (c) Five layers with twisted angle $\theta ={{1.84}^{\circ }}$ and (d) Six layers with twisted angle $\theta ={{1.91}^{\circ }}$.

Fig. 3. The Chern numbers of the two low-energy flat bands of ATMG on h-BN. (a) and (b) The band structures of alternating-twist trilayer and quadrilayer graphene on h-BN with θ=1.49° and θ=1.72°. (c) and (d) The Chern number of two flat bands of alternating-twist trilayer and quadrilayer graphene on h-BN tuned by gate potential V and twist angle near each magic angle.

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