Two dimensional twisted moiré superlattice
超晶格是一种具有较大周期的、人造的超结构, 类似于普通的晶格结构, 它也是一种周期性的势垒, 会形成迷你能带, 实现对材料物性的调制. 早在20世纪70年代, 人们就提出了以两种或多种晶格匹配的材料交替生长形成超晶格的概念, 即以三维材料为母体形成一维超晶格. 20世纪90年代, 人们可以采用微纳加工的手段在传统III-V族半导体异质结二维电子气中构造百纳米级别的人造二维超晶格结构. 进入21世纪后, 随着石墨烯、六方氮化硼和其他二维材料的发现和兴起, 这种原子级厚度的二维材料及其丰富的材料堆垛方式为二维超晶格的发展提供了绝佳机会. 其中, 最典型的两个代表是2013年兴起的石墨烯/六方氮化硼异质莫尔超晶格和2018年发现的魔角石墨烯. 前者是二维超晶格对单粒子能带改造的典范, 而后者更是因其平的能带结构及其关联绝缘体和超导的发现而备受关注, 成为凝聚态物理一个新兴的强关联体系.
二维转角莫尔超晶格的堆垛结构丰富可调, 不论是同质转角体系还是异质转角体系, 材料、层数、转角以及衬底都是独立可调的参数. 以多层石墨烯转角莫尔超晶格为例, 四层体系可以是转角双层-双层石墨烯(2+2), 也可以是转角单层-单层-单层-单层石墨烯(1+1+1+1), 甚至诸如(1+3)或者(1+2+1)等其他构型. 而且对于给定的一种堆垛结构, 超晶格的物态丰富可调, 被载流子浓度、空间电场、磁场、光和温度等多场调控. 这种丰富可调性造就了二维转角莫尔体系丰富的物理效应, 实现了关联绝缘体、超导体、陈绝缘体、量子反常霍尔效应、莫尔激子、激子绝缘体、维格纳晶体等各种奇异物态. 二维转角莫尔超晶格的发展促进了转移堆垛、电学输运测量、扫描显微和谱学技术、纳米光学等实验手段的进步, 也促进了材料及器件、超导、磁学、拓扑、光学等不同领域的学科交叉与融合.
为了使读者更加了解二维转角莫尔超晶格的最新进展, 本专题特别邀请了部分活跃在转角领域的青年学者撰文, 内容涵盖二维转角莫尔超晶格的制备和纳米光学表征、转角多层石墨烯莫尔超晶格的新奇物态、二维半导体双层莫尔超晶格的层间耦合, 以及该体系中的莫尔激子和激子绝缘体等理论和实验进展. 鉴于转角领域的快速发展, 本专题很难对转角莫尔体系进行全方位的介绍, 疏漏和不足之处恳请各位同仁批评指正.
2023, 72 (2): 027102.
doi: 10.7498/aps.72.20222145
Abstract +
Polariton is a quasiparticle generated from strong interaction between a photon and an electric or magnetic dipole-carrying excitation. These polaritons can confine light into a small space that is beyond the diffraction limit of light, thus have greatly advanced the development of nano photonics, nonlinear optics, quantum optics and other related research. Van der Waals two-dimensional (2D) crystals provide an ideal platform for studying nano-polaritons due to reduced material dimensionality. In particular, stacking and twisting offer additional degree of freedom for manipulating polaritons that are not available in a single-layer material. In this paper, we review the near-field optical characterizations of various structures and polaritonic properties of stacked/twisted 2D crystals reported in recent years, including domain structures of stacked few-layer graphene, moiré superlattice structures of twisted 2D crystals, twisted topological polaritons, and twisted chiral plasmons. We also propose several exciting directions for future study of polaritons in stacked/twisted 2D crystals.
2023, 72 (2): 027802.
doi: 10.7498/aps.72.20222080
Abstract +
Moiré superlattices formed by van der Waals materials with small lattice mismatch or twist angle open an unprecedented approach to generate flat bands that don’t exist in the “parent” materials, which provides a controllable platform for exploring quantum many body physics. Owing to the wide angle range for the existence of flat bands, as well as the valley-spin-locking band structure and the excellent optical properties, twisted semiconducting transition metal dichalcogenides (TMDs) heterostructures have recently attracted lots of attention. In this review, we discuss the exotic states discovered in the twisted TMDs heterostructures, including Mott insulator, generalized Wigner crystals, topological non-trivial states, and moiré excitons, how to manipulate these exotic states and related mechanisms, and finally some perspectives on the opportunities and challenges in this field.
2023, 72 (2): 027302.
doi: 10.7498/aps.72.20222046
Abstract +
In recent years, various novel phenomena have been observed in two-dimensional semiconductor moiré systems, including the moiré excitons, strongly-correlated electronic states and vertical ferroelectricity. To gain an insight into the underlying physical mechanisms of these intriguing phenomena, it is essential to understand the interlayer coupling form of the electrons in moiré systems. In this work, the position- and momentum-dependent interlayer coupling effects in two-dimensional semiconductor moiré superlattices are investigated. Starting from the monolayer Bloch basis, the interlayer coupling between two Bloch states are treated as a perturbation, and the coupling matrix elements in commensurate and incommensurate bilayer structures are obtained, which are found to depend on the momentum and the interlayer translation between the two layers. Under the effect of an external potential, the Bloch states form localized wavepackets, and their interlayer couplings are found to depend on the wavepacket width as well as the interlayer translation at the wavepacket center position. Meanwhile the momentum-dependence results in very different interlayer coupling forms for the ground-state $ \rm{S} $ -type and the excited-state $ {\rm{P}}^{\pm } $ -type wavepackets. It is shown that at a position where the interlayer coupling between two $ \rm{S} $ -type wavepackets vanishes, the coupling between an $ \rm{S} $ -type wavepacket and a $ {\rm{P}}^{+} $ -type wavepacket (or between an $ \rm{S} $ - type wavepacket and a $ {\rm{P}}^{-} $ -type wavepacket) reaches a maximum strength. This can be used to manipulate the valley-selective interlayer transport of the ground-state wavepackets through external electric and optical fields. Besides, the vertical ferroelectricity recently discovered in bilayer systems can be attributed to the charge redistribution induced by the coupling between conduction and valence bands in different layers. Using the obtained interlayer coupling form combined with a simplified tight-binding model for the monolayer, the vertical electric dipole density can be calculated whose form and order of magnitude accord with the experimental observations.
2023, 72 (6): 067101.
doi: 10.7498/aps.72.20230079
Abstract +
Interlayer electron and hole can be paired up through coulomb interaction to form an exciton insulator when their kinetic energy is substantially smaller than the interaction energy. The traditional platform to realize such an interlayer interaction is the double quantum well with dielectric material between electron and hole, for which an external magnetic field is required to generate Landau level flat bands that can reduce the kinetic energy of charged carriers. When both quantum wells are at the half filling of the lowest landau level, the electron-electron repulsive interaction, by the particle-hole transformation in one well, will be equivalent to electron-hole attractive interaction, from which interlayer exciton and its condensation can emerge. In a two-dimensional twisted homostructure or an angle aligned heterostructure, there exists a moiré superlattice, in which bands are folded into the mini-Brillouin zone by the large moiré period. Gap opening at the boundary of mini-Brillouin zone can form the well-known moiré flat band. This review will discuss how to use the moiré flat bands to generate exciton insulator in the absence of external magnetic field in transitional metal dichalcogenide (TMD) moiré heterostructure. Unlike the double quantum well where symmetric well geometry is used, the moiré related sample can have multiple different geometries, including monolayer TMD-hexagonal boron nitride-moiré structure, moiré-moiré structure, and monolayer TMD-bilayer TMD structure. The carriers in those structures can be well tuned to locate equally in different layers, and particle-hole transformation in the moiré first Hubbard band can transform the interlayer repulsive coulomb interaction into attractive interaction, which is the same as that in quantum well under magnetic field. We will show that by using differential contrast reflection spectrum, interlayer photoluminescence, 2s exciton sensing, quantum capacitance and microwave impedance microscopy, the signature of exciton fluid can be identified. The excitonic coherence features in those structures will promise by using the coulomb drag technique and counter flow technique in future. In general, exciton in moiré lattice is a promising candidate for studying the Bose-Hubbard model in solids and can well realize exciton superfluidity, excitonic mott insulator as well as the crossover between them.
2023, 72 (6): 067302.
doi: 10.7498/aps.72.20230120
Abstract +
In this review, we discuss the electronic structures, topological properties, correlated states, nonlinear optical responses, as well as phonon and electron-phonon coupling effects of moiré graphene superlattices. First, we illustrate that topologically non-trivial flat bands and moiré orbital magnetism are ubiquitous in various twisted graphene systems. In particular, the topological flat bands of magic-angle twisted bilayer graphene can be explained from a zeroth pseudo-Landau-level picture, which can naturally explain the experimentally observed quantum anomalous Hall effect and some of the other correlated states. These topologically nontrivial flat bands may lead to nearly quantized piezoelectric response, which can be used to directly probe the valley Chern numbers in these moiré graphene systems. A simple and general chiral decomposition rule is reviewed and discussed, which can be used to predict the low-energy band dispersions of generic twisted multilayer graphene system and alternating twisted multilayer graphene system. This review further discusses nontrivial interaction effects of magic-angle TBG such as the correlated insulator states, density wave states, cascade transitions, and nematic states, and proposes nonlinear optical measurement as an experimental probe to distinguish the different “featureless” correlated states. The phonon properties and electron-phonon coupling effects are also briefly reviewed. The novel physics emerging from band-aligned graphene-insulator heterostructres is also discussed in this review. In the end, we make a summary and an outlook about the novel physical properties of moiré superlattices based on two-dimensional materials.
