Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures

Abstract

In this work, we study the synergistic correlated states in two distinct types of interacting electronic systems coupled by interlayer Coulomb interactions. We propose that this scenario can be realized in a new type of Coulomb-coupled graphene-insulator heterostructures with gate tunable band alignment. We find that, by virtue of the interlayer Coulomb coupling between the interacting electrons in the two layers, intriguing correlated physics that is not seen in either individual layer emerges in a cooperative and synergistic manner. Specifically, as a result of the band alignment, charge carriers can be transferred between graphene and the substrate under the control of gate voltages, which can yield a long-wavelength electronic crystal at the surface of the substrate. This electronic crystal exerts a superlattice Coulomb potential on the Dirac electrons in graphene, which generates subbands with reduced non-interacting Fermi velocity. As a result, $e$-$e$ Coulomb interactions within graphene would play a more important role, giving rise to a gapped Dirac state at the charge neutrality point, accompanied by interaction-enhanced Fermi velocity. Moreover, the superlattice potential can give rise to topologically nontrivial subband structures which are tunable by superlattice's constant and anisotropy. Reciprocally, the electronic crystal formed in the substrate can be substantially stabilized in such coupled bilayer heterostructure by virtue of the cooperative interlayer Coulomb coupling. We further perform high-throughput first principles calculations to identify a number of promising insulating materials as candidate substrates for graphene to demonstrate these effects. Our findings provide new insights into the physics of correlated and topological electronic states in graphene-based heterostructures.

Novel electrical properties of moiré graphene systems

“…往往存在着自旋极化的向列序态, 并且垂直磁场可 以诱发这类体系从自旋极化向列序态到谷极化陈 绝缘体态的拓扑相变 [83,84] . 而针对转角双层石墨烯 中声子性质的深度学习分子动力学研究, 发现了若 干极低频率的面外"弯曲"声子模式, 并且这些极低 频模式与电子耦合可能导致关联绝缘态以及电四 极矩序 [85] . 最后, 本综述将讨论一类新型石墨烯异 质结体系: 能带对齐的石墨烯和绝缘衬底形成的异 质结体系中的新奇物理.…”

“…阻 [15,16,[22][23][24][25][26][27]31,171,172] 等, 不仅取决于魔角双层石墨 烯的能带拓扑性和库仑关联效应, 还与该体系的声 子和电声耦合效应密切相关 [173][174][175][176][177][178][179][180][181][182][183][184] . 本节主要讨论 Liu等 [85] 利用深度学习分子动力学结合紧束缚模 型研究的魔角双层石墨烯体系的低频莫尔声子性 质和电声耦合效应.…”

“…具体而言, 首先对大转角、小体系的转角 石墨烯体系进行基于密度泛函理论的第一性原理 计算, 生成大量总能、力和应力的数据, 然后用这 些数据来训练神经网络, 生成一个碳原子之间的多 体经典势函数. 之后再把这个基于神经网络的经典 多体势函数外延到魔角双层石墨烯, 进行晶格弛豫 和声子谱的计算 [85] . 计算结果如图7所示.…”

“…特别地, 在魔角双层石墨烯中有很多低频的面外"弯曲"声 子模式, 且不能被双层石墨烯的面外声学支声子模 式单纯折叠到莫尔布里渊区来解释. 下面重点分析 这些莫尔尺度上的面外"弯曲"声子模式 [85] . (b)转角双层-双层石墨烯半填充处的实空间电荷分布 [83] ; (c)-(e)转角双层-单层石墨烯体系在不同Hubbard参数和磁场下衍生 出的不同陈数的绝缘态, 用红线标记 [83] Fig.…”

“…频率为 的声子 模式则是具有 对称性的四极矩模式, 它与另一 个频率相同的模式形成 点群的 表示. 这个模 式与平带电子的耦合相对较强, 有效电声耦合系数 接近 , 对电荷密度和电子结构具有重要影响 [85] .…”