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Since the correlated insulating states and superconductivity in magic angle twisted bilayer graphene were discovered, the twisted moiré superlattice has attracted a wide range of research interest, and even has brought a new field, “twistronics”, into being. In this review, we first give a history of experimentally discovering magic angle graphene and flat band, and then summarize the recent developments of twisted moiré superlattice, including twisted graphene systems and TMDCs, and finally introduce a notion of moiré superlattice quantum simulator.
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Keywords:
- moiré superlattice /
- correlated insulator /
- superconductivity /
- magnetism
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图 1 “魔角”石墨烯 (a) 摩尔超晶格和摩尔布里渊区示意图[12]; (b) 能带图[13]; (c) 半填充的莫特绝缘态和拱形的超导态[13]; (d) 3/4填充处的量子反常霍尔效应[36]
Fig. 1. Magic angle twisted bilayer graphene: (a) Moiré pattern and the mini Brillouin zone[12]; (b) band energy E of TBG at
$ \theta ={1.05}^{\circ } $ [13]; (c) phase diagram with mott insulating states at half filling and gate-tunable superconductivity domes nearby[13]; (d) quantum anomalous Hall effect near 3/4 filling and schematic band structure at full filling ($ \nu =4 $ ) and 3/4 filling ($ \nu =3 $ )[36].图 2 电场可调的多层石墨烯转角体系 (a) ABC堆垛的三层石墨烯/氮化硼摩尔超晶格中关联绝缘态和超导态[43]; (b) 转角双层-双层石墨烯(TDBG, 2+2)中的关联绝缘态[45]; (c) 转角单层-双层石墨烯(TMBG, 1+2)中的关联绝缘态[54]; (d) 转角三层石墨烯体系(MATTG, 1+1+1)中的超导态[56]
Fig. 2. Field tunable multilayer graphene twisted moiré superlattice systems: (a) Signatures of Mott insulator and the superconducting (SC) phase in ABC-trilayer graphene/hBN superlattice[43]; (b) correlated insulating states in twisted double bilayer graphene (TDBG)[45]; (c) correlated insulating states in twisted monolayer-bilayer graphene (TMBG)[54]; (d) MATTG phase diagrams, and the superconductivity is colored in blue[56].
图 3 转角过渡金属硫化物的关联效应 (a) WSe2/WS2异质摩尔超晶格半填充处的莫特绝缘态和不同填充处下的磁化率
$ \chi \propto g-{g}_{0} $ , 和Weiss常数$ \theta $ [60]; (b) WSe2/WS2质摩尔超晶格分数填充处的关联绝缘态[69]; (c) WSe2/WSe2同质摩尔超晶格的关联绝缘态[58]Fig. 3. Correlated insulating states in twisted TMD superlattice: (a) Signature of correlated insulator at half filling in WSe2/WS2 moiré superlattice[60]; (b) fractional insulating states in WSe2/WS2 moiré superlattice[69]; (c) transport signature of half filling insulator in twisted WSe2/WSe2 moiré superlattice[58].
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