High-order minibands and interband Landau level reconstruction in graphene moire superlattice
Xiaobo Lu, Jian Tang, John R. Wallbank, Shuopei Wang, Cheng Shen, Shuang Wu, Peng Chen, Wei Yang, Jing Zhang, Kenji Watanabe, Takashi Taniguchi, Rong Yang, Dong… 展开作者
Xiaobo Lu, Jian Tang, John R. Wallbank, Shuopei Wang, Cheng Shen, Shuang Wu, Peng Chen, Wei Yang, Jing Zhang, Kenji Watanabe, Takashi Taniguchi, Rong Yang, Dongxia Shi, Dmitri K. Efetov, Vladimir I. Falko, Guangyu Zhang
The propagation of Dirac fermions in graphene through a long-period periodic potential would result in a band folding together with the emergence of a series of cloned Dirac points (DPs). In highly aligned graphene/hexagonal boron nitride (G/hBN) heterostructures, the lattice mismatch between the two atomic crystals generates a unique kind of periodic structure known as a moiré superlattice. Of particular interests is the emergent phenomena related to the reconstructed band-structure of graphene, such as the Hofstadter butterfly, topological currents, gate dependent pseudospin mixing, and ballistic miniband conduction. However, most studies so far have been limited to the lower-order minibands, e.g. the 1st and 2nd minibands counted from charge neutrality, and consequently the fundamental nature of the reconstructed higher-order miniband spectra still remains largely unknown. Here we report on probing the higher-order minibands of precisely aligned graphene moiré superlattices by transport spectroscopy. Using dual electrostatic gating, the edges of these high-order minibands, i.e. the 3rd and 4th minibands, can be reached. Interestingly, we have observed interband Landau level (LL) crossinginducing gap closures in a multiband magneto-transport regime, which originates from band overlap between the 2nd and 3rd minibands. As observed high-order minibands and LL reconstruction qualitatively match our simulated results. Our findings highlight the synergistic effect of minibands in transport, thus presenting a new opportunity for graphene electronic devices.
We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields B_{p/q}= pϕ_0/(qS) providing rational magnetic flux through a unit cell of the moire superlattice created by a hexagonal substrate for electrons in graphene. The Dirac-type features in the minibands at B=B_{p/q} determine a hierarchy of gaps in the surrounding fractal spectrum, and show that these minibands have topological insulator properties. Using the additional $q$-fold degeneracy of magnetic minibands at B_{p/q}, we trace the hierarchy of the gaps to their manifesta…
We present a phenomenological theory of the low energy moiré minibands of Dirac electrons in graphene placed on an almost commensurate hexagonal underlay with a unit cell pproximately three times larger than that of graphene.A slight incommensurability results in a periodically modulated intervalley scattering for electrons in graphene. In contrast to the perfectly commensurate Kekulé distortion of graphene, such supperlattice perturbation leaves the zero energy Dirac cones intact, but is able to open a band gap at the edge of the first moiré subbband, asymmetrically in the conduction and vale…
We identify features in the angle-resolved photoemission spectra (ARPES) arising from the periodic pattern characteristic for graphene heterostructure with hexagonal boron nitride (hBN). For this, we model ARPES spectra and intensity maps for five microscopic models used previously to describe moire superlattice in graphene/hBN systems. We show that detailed analysis of these features can be used to pin down the microscopic mechanism of the interaction between graphene and hBN. We also analyze how the presence of a moire-periodic strain in graphene or scattering of photoemitted electrons off h…
Moiré superlattices open an unprecedented opportunity for tailoring interactions between quantum particles and their coupling to electromagnetic fields. Strong superlattice potential generates moiré minibands of excitons -- bound pairs of electrons and holes that reside either in a single layer (intralayer excitons) or two separate layers (interlayer excitons). The twist-angle-controlled interlayer hybridization of carriers can also mix the two types of excitons to combine the strengths of both. Here, we report a direct observation of spatially mixed moiré excitons in angle-aligned WSe2/WS2 an…
We demonstrate a generic mechanism to realize topological flat minibands by confining massive Dirac fermions in a periodic moiré potential, which can be achieved in a heterobilayer of transition metal dichalcogenides. We show that the topological phase can be protected by the symmetry of moiré potential and survive to arbitrarily large Dirac band gap. We take the MoTe$_2$/WSe$_2$ heterobilayer as an example and find that the topological phase can be driven by a vertical electric field. By projecting the Coulomb interaction onto the topological fat minibands, we identify a correlated Chern insu…
A Catalogue of Topological Moiré Bands in Twisted Semiconductors
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所与凝聚态物理北京国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Condensed Matter Physics Data Center of Chinese Academy of Sciences（中国科学院凝聚态物理数据中心）
We investigate the optical properties of interlayer excitons in heterobilayer transition metal dichalcogenides where moiré pattern is introduced by heterostrain, in comparison with that introduced by twisting (and/or lattice mismatch). Besides being a cause of the moiré texture, strain also effectively introduces a constant gauge potential on either electron or hole, which shifts the dispersion of kinetic energy with respect to the excitonic crystal momenta in the moiré superlattices.This leads to distinct exciton mini-band dispersions and light coupling properties from the twisting induced mo…
Geometrical moiré patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moiré superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band ed…
Van der Waals heterostructures of graphene and hexagonal boron nitride feature a moiré superlattice for graphene's Dirac electrons. Here, we review the effects generated by this superlattice, including a specific miniband structure featuring gaps and secondary Dirac points, and a fractal spectrum of magnetic minibands known as Hofstadter's butterfly.
Studies on two-dimensional electron systems in a strong magnetic field first revealed the quantum Hall (QH) effect, a topological state of matter featuring a finite Chern number (C) and chiral edge states. Haldane later theorized that Chern insulators with integer QH effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (TLG/hBN) moiré superlattice provides an attractive platform to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent electrically tunable …
We investigate theoretically the interplay between the effects of a perpendicular electric field and incommensurability at the interface on the electronic properties of a heterostructure of bilayer graphene and a semiconducting substrate with a unit cell almost three times larger then that of graphene. It is known that the former introduces an asymmetry in the distribution of the electronic wave function between the layers and opens a band gap in the electronic spectrum. The latter generates a long wavelength periodic moiré perturbation of graphene electrons which couples states in inequivalen…
Bilayer graphene was theorized to host a moire miniband with flat dispersion if the layers are stacked at specific twist angles known as the magic angles. Recently, such twisted bilayer graphene (tBLG) with the first magic angle twist was reported to exhibit correlated insulating state and superconductivity, where the presence of the flat miniband in the system is thought to be essential for the emergence of these ordered phases in the transport measurements. Tunneling spectroscopy and electronic compressibility measurements in tBLG have revealed a van Hove singularity that is consistent with …
$\mathbb Z_2$-Nontrivial Moiré Minibands and Interaction-Driven Quantum Anomalous Hall Insulators in Topological Insulator Based Moiré Heterostructures
Rational design of artificial lattices yields effects unavailable in simple solids, and vertical superlattices of multilayer semiconductors are already used in optical sensors and emitters. Manufacturing lateral superlattices remains a much bigger challenge, with new opportunities offered by the use of moire patterns in van der Waals heterostructures of graphene and hexagonal crystals such as boron nitride (h-BN). Experiments to date have elucidated the novel electronic structure of highly aligned graphene/h-BN heterostructures, where miniband edges and saddle points in the electronic dispersi…
Bandwidth-Limited Critical Currents in Electrically Tunable Moiré Bands
ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学技术研究院）；Massachusetts Institute of Technology（麻省理工学院）；National Graphene Institute, University of Manchester（国家石墨烯研究所，曼彻斯特大学）；Dept. of Physics & Astronomy, University of Manchester（物理与天文学系，曼彻斯特大学）；COMMIT, Department of Physics and NANOlight Center of Excellence, University of Antwerp（安特卫普大学物理系及NANOlight卓越中心）
Using a general symmetry-based approach, we provide a classification of generic miniband structures for electrons in graphene placed on substrates with the hexagonal Bravais symmetry. In particular, we identify conditions at which the first moiré miniband is separated from the rest of the spectrum by either one or a group of three isolated mini Dirac points and is not obscured by dispersion surfaces coming from other minibands. In such cases the Hall coefficient exhibits two distinct alternations of its sign as a function of charge carrier density.
Flat bands in twisted moire superlattices support a variety of topological and strongly correlated phenomena along with easily tunable electrical and optical properties. Here, we demonstrate the existence of tunable, long-lived, and flat intraband and interband terahertz plasmons in twisted double bilayer graphene. We show that the interband plasmons originate from the presence of a Van Hove singularity in the joint density of states and a finite Berry connection between the pair of bands involved. We find that the gapped interband plasmon mode has a universal dispersion, and the plasmon gap i…
Twistronic heterostructures have recently emerged as a new class of quantum electronic materials with properties determined by the twist angle between the adjacent two-dimensional materials. Here we study moiré superlattice minibands in graphene (G) encapsulated in hexagonal boron nitride (hBN) with an almost perfect alignment with both the top and bottom hBN crystals. We show that, for such an orientation of the unit cells of the hBN layers that locally breaks inversion symmetry of the graphene lattice, the hBN/G/hBN structure features a Kagomé network of topologically protected chiral states…
We have studied a 50/50Åsuperlattice of GaAs/Al$_{0.21}$Ga$_{0.79}$As composition, modulation-doped with Si, to produce $n=1.4\times 10^{12}$ cm$^{-2}$ electrons per superlattice period. The modulation-doping was tailored to avoid the formation of Tamm states, and photoluminescence due to interband transitions from extended superlattice states was detected. By studying the effects of a quantizing magnetic field on the superlattice photoluminescence, the miniband energy width, the reduced effective mass of the electron-hole pair, and the band gap renormalization could be deduced.
Beyond the Flat-Band Paradigm: Open Orbits as a Route to Correlated States in Dispersive Moiré Minibands
National University of Singapore（新加坡国立大学）；Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学和纳米技术研究所（ICN2，CSIC和BIST））；ICREA–Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚高级研究学院（ICREA））；Institute of Materials Research & Engineering (IMRE), Agency for Science, Technology and Research (A*STAR)（材料研究与工程学院（IMRE），科学技术研究局（A*STAR））；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；University of Manchester（曼彻斯特大学）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
We study the superlattice minibands produced by the interplay between moiré pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moiré miniband features in BLG, where they are affected by the interlayer asymmetry of BLG-hBN heterostructure and trigonal warping characteristic for electrons in Bernal-stacked bilayers with those found in monolayer graphene.
The electronic bands of twisted bilayer graphene (TBLG) with a large-period moiré superlattice fracture to form narrow Bloch minibands that are spectrally isolated by forbidden energy gaps from remote dispersive bands. When these gaps are sufficiently large, one can study a band-projected Hamiltonian that correctly represents the dynamics within the minibands. This inevitably introduces nontrivial geometrical constraints that arise from the assumed form of the projection. Here we show that this choice has a profound consequence in a low-energy experimentally-observable signature which therefor…
In conventional light harvesting devices, the absorption of a single photon only excites one electron, which sets the standard limit of power-conversion efficiency, such as the Shockley-Queisser limit. In principle, generating and harnessing multiple carriers per absorbed photon can improve the efficiency and possibly overcome this limit. Here, we report the observation of multiple hot carrier collection in graphene-boron-nitride Moire superlattice structures. A record-high zero-bias photoresponsivity of 0.3 ampere per watt, equivalently, an external quantum efficiency exceeding 50 percent, is…
Mott insulator plays a central role in strongly correlated physics, where the repulsive Coulomb interaction dominates over the electron kinetic energy and leads to insulating states with one electron occupying each unit cell. Doped Mott insulator is often described by the Hubbard model3, which can give rise to other correlated phenomena such as unusual magnetism and even high-temperature superconductivity. A tunable Mott insulator, where the competition between the Coulomb interaction and the kinetic energy can be varied in situ, can provide an invaluable model system for the study of Mott phy…
Within a two-band tight binding model, we investigate the dynamics of electrons with Markoffian dephasing under the influence of static electric fields. With the help of both numerical and analytic calculations we find that the dephasing ultimately takes electrons which are initially located in one miniband to equal population of the two minibands, instead of undergoing persistent Rabi flop, as they do in the absence of scattering. Miniband localization is wholly destroyed by the intervention of dephasing. We also obtain the effective decay time for the approach to equal band populations under…
Ultra-small-angle graphene twistronics with monolayer spacers: From interlayer hybridisation and moiré effects to high-temperature magnetotransport oscillations
University of Manchester（曼彻斯特大学）；National Graphene Institute, University of Manchester（国家石墨烯研究所，曼彻斯特大学）；City University of Hong Kong（香港城市大学）；National University of Singapore（新加坡国立大学）；Institute for Functional Intelligent Materials, National University of Singapore（功能智能材料研究所，新加坡国立大学）
High-field Josephson effect enabled by a moiré Hofstadter spectrum
Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Nanomaterials and Nanotechnology Research Center (CINN-CSIC), Universidad de Oviedo (UO)（阿斯图里亚斯大学纳米材料与纳米技术研究中心（CINN-CSIC））；Yale University（耶鲁大学）；Aalto University（阿尔托大学）；National Institute for Materials Science（国立材料研究所）
We investigate the magnetic minibands of a heterostructure consisting of bilayer graphene (BLG) and hexagonal boron nitride (hBN) by numerically diagonalizing a two-band Hamiltonian that describes electrons in BLG in the presence of a moire potential. Due to inversion-symmetry breaking characteristic for the moire potential, the valley symmetry of the spectrum is broken, but despite this, the zero-energy Landau level in BLG survives, albeit with reduced degeneracy. In addition, we derive effective models for the low-energy features in the magnetic minibands and demonstrate the appearance of se…
We theoretically study the effect of magnetic moiré superlattice on the topological surface states by introducing a continuum model of Dirac electrons with a single Dirac cone moving in the time-reversal symmetry breaking periodic pontential. The Zeeman-type moiré potentials generically gap out the moiré surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\pm1$. This result provides a promising platform for realizing the time-reversal breaking correlated topological phases. In a $C_6$ periodic potential, when the scalar $U_0$ and Zeeman $Δ_1$ moiré potential s…
The flat bands resulting from moiré superlattices in magic-angle twisted bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated electron phenomena such as correlated insulators and superconductivity. More recently, orbital magnetism associated with correlated Chern insulators was found in this class of layered structures centered at integer multiples of n0, the density corresponding to one electron per moiré superlattice unit cell. Here we report the experimental observation of ferromagnetism …
Understanding the mechanism of high temperature (high Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high Tc superconductivity arises from a doped Mott insulator as described by the Hubbard model. An exact solution of the Hubbard model, however, is extremely challenging due to the strong electron-electron correlation. Therefore, it is highly desirable to experimentally study a model Hubbard system in which the unconventional superconductivity can be continuously tuned by varying the Hubbard parameters. Here we report signatures of tunable su…
Moiré superlattices provide a powerful tool to engineer novel quantum phenomena in two-dimensional (2D) heterostructures, where the interactions between the atomically thin layers qualitatively change the electronic band structure of the superlattice. For example, mini-Dirac points, tunable Mott insulator states, and the Hofstadter butterfly can emerge in different types of graphene/boron nitride moiré superlattices, while correlated insulating states and superconductivity have been reported in twisted bilayer graphene moiré superlattices. In addition to their dramatic effects on the single pa…
We investigate the physics of photonic band structures of the moiré patterns that emerged when overlapping two uni-dimensional (1D) photonic crystal slabs with mismatched periods. The band structure of our system is a result of the interplay between intra-layer and inter-layer coupling mechanisms, which can be fine-tuned via the distance separating the two layers. We derive an effective Hamiltonian that captures the essential physics of the system and reproduces all numerical simulations of electromagnetic solutions with high accuracy. Most interestingly, \textit{magic distances} corresponding…
In stacks of two-dimensional crystals, mismatch of their lattice constants and misalignment of crystallographic axes lead to formation of moiré patterns. We show that moiré superlattice effects persist in twisted bilayer graphene (tBLG) with large twists and short moiré periods. Using angle-resolved photoemission, we observe dramatic changes in valence band topology across large regions of the Brillouin zone, including the vicinity of the saddle point at $M$ and across 3 eV from the Dirac points. In this energy range, we resolve several moiré minibands and detect signatures of secondary Dirac …
Twisting van der Waals heterostructures to induce correlated many-body states provides a novel tuning mechanism in solid-state physics. In this work, we theoretically investigate the fate of the surface Dirac cone of a three-dimensional topological insulator subject to a superlattice potential. Using a combination of diagrammatic perturbation theory, lattice model simulations, and ab initio calculations we elucidate the unique aspects of twisting a single Dirac cone with an induced moiré potential and the role of the bulk topology on the reconstructed surface band structure. We report a dramat…
We model optical absorption of monolayer and bilayer graphene on hexagonal boron nitride for the case of closely-aligned crystal lattices. We show that perturbations with different spatial symmetry can lead to similar absorption spectra. We suggest that a study of the absorption spectra as a function of the doping for almost completely full first miniband is necessary to extract meaningful information about the moire characteristics from optical absorption measurements and to distinguish between various theoretical proposals for the physically realistic interaction. Also, for bilayer graphene,…
Parity- and Chirality-Selected Dirac Masses in Hybrid Moiré--1D Superlattices
Arts and Sciences, NYU Shanghai（纽约大学上海分校文理学院）；NYU-ECNU Institute of Physics at NYU Shanghai（纽约大学上海分校纽约大学-华东师范大学物理研究所）；Department of Physics, New York University（纽约大学物理系）；Department of Physics, Hanyang University（汉阳大学物理系）
