Correlated electron-hole state in twisted double-bilayer graphene

Keldysh Field Theory of Dynamical Exciton Condensation Transitions in Nonequilibrium Electron-Hole Bilayers

Recent experiments have realized steady-state electrical injection of interlayer excitons in electron-hole bilayers subject to a large bias voltage. In the ideal case in which interlayer tunneling is negligibly weak, the system is in quasiequilibrium with a reduced effective band gap. Interlayer tunneling introduces a current and drives the system out of equilibrium. In this work we derive a nonequilibrium field theory description of interlayer excitons in biased electron-hole bilayers. In the large bias limit, we find that p-wave interlayer tunneling reduces the effective band gap and increases the effective temperature for intervalley excitons. We discuss possible experimental implications for InAs/GaSb quantum wells and transition metal dichalcogenide bilayers.

Strongly coupled magneto-exciton condensates in large-angle twisted double bilayer graphene

Excitons, pairs of electrons and holes, undergo a Bose-Einstein condensation at low temperatures. An important platform to study excitons is double-layer two-dimensional electron gases, with two parallel planes of electrons and holes separated by a thin insulating layer. Lowering this separation (d) strengthens the exciton binding energy, however, leads to the undesired interlayer tunneling, resulting in annihilation of excitons. Here, we report the observation of a sequences of robust exciton condensates (ECs) in double bilayer graphene twisted to ~ 10° with no insulating mid-layer. The large momentum mismatch between two graphene layers suppresses interlayer tunneling, reaching a d ~ 0.334 nm. Measuring the bulk and edge transport, we find incompressible states corresponding to ECs when both layers are in half-filled N = 0, 1 Landau levels (LLs). Theoretical calculations suggest that the low-energy charged excitation of ECs can be meron-antimeron or particle-hole pair, which relies on both LL index and carrier type. Our results establish a novel platform with extreme coupling strength for studying quantum bosonic phase.

Interplay of Landau Quantization and Interminivalley Scatterings in a Weakly Coupled Moiré Superlattice

Double-layer quantum systems are promising platforms for realizing novel quantum phases. Here, we report a study of quantum oscillations (QOs) in a weakly coupled double-layer system composed of a large-angle twisted-double-bilayer graphene (TDBG). We quantify the interlayer coupling strength by measuring the interlayer capacitance from the QOs pattern at low temperatures, revealing electron-hole asymmetry. At high temperatures when SdHOs are thermally smeared, we observe resistance peaks when Landau levels (LLs) from two moiré minivalleys are aligned, regardless of carrier density; eventually, it results in a 2-fold increase of oscillating frequency in D, serving as compelling evidence of the magneto-intersub-band oscillations (MISOs) in double-layer systems. The temperature dependence of MISOs suggests that electron-electron interactions play a crucial role and the scattering times obtained from MISO thermal damping are correlated with the interlayer coupling strength. Our study reveals intriguing interplays among Landau quantization, moiré band structure, and scatterings.

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and-by studying the backscattering between counter-propagating edge states-the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.

Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Symmetry-Broken Chern Insulators in Twisted Double Bilayer Graphene

Twisted double bilayer graphene (tDBG) has emerged as a rich platform for studying strongly correlated and topological states, as its flat bands can be continuously tuned by both a perpendicular displacement field and a twist angle. Here, we construct a phase diagram representing the correlated and topological states as a function of these parameters, based on measurements of over a dozen tDBG devices encompassing two distinct stacking configurations. We find a hierarchy of symmetry-broken states that emerge sequentially as the twist angle approaches an apparent optimal value of θ ≈ 1.34°. Nearby this angle, we discover a symmetry-broken Chern insulator (SBCI) state associated with a band filling of 7/2 as well as an incipient SBCI state associated with 11/3 filling. We further observe an anomalous Hall effect at zero field in all samples supporting SBCI states, indicating spontaneous time-reversal symmetry breaking and possible moiré unit cell enlargement at zero magnetic field.

A quantum ruler for orbital magnetism in moiré quantum matter

For almost a century, magnetic oscillations have been a powerful "quantum ruler" for measuring Fermi surface topology. In this study, we used Landau-level spectroscopy to unravel the energy-resolved valley-contrasting orbital magnetism and large orbital magnetic susceptibility that contribute to the energies of Landau levels of twisted double-bilayer graphene. These orbital magnetism effects led to substantial deviations from the standard Onsager relation, which manifested as a breakdown in scaling of Landau-level orbits. These substantial magnetic responses emerged from the nontrivial quantum geometry of the electronic structure and the large length scale of the moiré lattice potential. Going beyond traditional measurements, Landau-level spectroscopy performed with a scanning tunneling microscope offers a complete quantum ruler that resolves the full energy dependence of orbital magnetic properties in moiré quantum matter.

Orbitally Controlled Quantum Hall States in Decoupled Two-Bilayer Graphene Sheets

The authors report on integer and fractional quantum Hall states in a stack of two twisted Bernal bilayer graphene sheets. By exploiting the momentum mismatch in reciprocal space, the single-particle tunneling between both bilayers is suppressed. Since the bilayers are spatially separated by only 0.34 nm, the stack benefits from strong interlayer Coulombic interactions. These interactions can cause the formation of a Bose-Einstein condensate. Indeed, such a condensate is observed for half-filling in each bilayer sheet. However, only when the partially filled levels have orbital index 1. It is absent for partially filled levels with orbital index 0. This discrepancy is tentatively attributed to the role of skyrmion/anti-skyrmion pair excitations and the dependence of the energy of these excitations on the orbital index. The application of asymmetric top and bottom gate voltages enables to influence the orbital nature of the electronic states of the graphene bilayers at the chemical potential and to navigate in orbital mixed space. The latter hosts an even denominator fractional quantum Hall state at total filling of -3/2. These observations suggest a unique edge reconstruction involving both electrons and chiral p-wave composite fermions.

A Wrinkling and Etching-Assisted Regrowth Strategy for Large-Area Bilayer Graphene Preparation on Cu

Bilayer graphene is a contender of interest for functional electronic applications because of its variable band gap due to interlayer interactions. Graphene growth on Cu is self-limiting, thus despite the fact that chemical vapor deposition (CVD) has made substantial strides in the production of monolayer and single-crystal graphene on Cu substrates, the direct synthesizing of high-quality, large-area bilayer graphene remains an enormous challenge. In order to tackle this issue, we present a simple technique using typical CVD graphene growth followed by a repetitive wrinkling-etching-regrowth procedure. The key element of our approach is the rapid cooling process that causes high-density wrinkles to form in the monolayer area rather than the bilayer area. Next, wrinkled sites are selectively etched with hydrogen, exposing a significant portion of the active Cu surface, and leaving the remaining bilayer areas, which enhance the nucleation and growth of the second graphene layer. A fully covered graphene with 78 ± 2.8% bilayer coverage and a bilayer transmittance of 95.6% at room temperature can be achieved by modifying the process settings. Bilayer graphene samples are examined using optical microscopy (OM), scanning electron microscopy (SEM), Raman spectroscopy, and an atomic force microscope (AFM) during this process. The outcomes of our research are beneficial in clarifying the growth processes and future commercial applications of bilayer graphene.

Unconventional correlated insulator in CrOCl-interfaced Bernal bilayer graphene

The realization of graphene gapped states with large on/off ratios over wide doping ranges remains challenging. Here, we investigate heterostructures based on Bernal-stacked bilayer graphene (BLG) atop few-layered CrOCl, exhibiting an over-1-GΩ-resistance insulating state in a widely accessible gate voltage range. The insulating state could be switched into a metallic state with an on/off ratio up to 10⁷ by applying an in-plane electric field, heating, or gating. We tentatively associate the observed behavior to the formation of a surface state in CrOCl under vertical electric fields, promoting electron-electron (e-e) interactions in BLG via long-range Coulomb coupling. Consequently, at the charge neutrality point, a crossover from single particle insulating behavior to an unconventional correlated insulator is enabled, below an onset temperature. We demonstrate the application of the insulating state for the realization of a logic inverter operating at low temperatures. Our findings pave the way for future engineering of quantum electronic states based on interfacial charge coupling.

A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp²carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.

Facile Fabrication of a Bio-Inspired Leaf Vein-Based Ultra-Sensitive Humidity Sensor with a Hygroscopic Polymer

Bio-inspired materials have received significant interest in the development of flexible electronics due to their natural grid structures, especially natural leaf vein networks. In this work, a bio-inspired leaf vein-based flexible humidity sensor is demonstrated. The proposed sensor is composed of a leaf/Al/glycerin/Ag paste. The Al-deposited leaf vein networks are used as a bottom electrode with a resistance of around 100 Ω. The humidity sensor responds well to relative humidity (RH) levels ranging from 15% to 70% at room temperature. The fabricated humidity sensor exhibits an ultra-sensitive response to different humidity conditions due to the biodegradable insulating hygroscopic polymer (glycerin), specifically the ionic conductivity reaction. To further verify the presence of ionic conduction, the device performance is tested by doping NaCl salt into the hygroscopic polymer sensing layer. In addition, both the repeatability and flexibility of the sensor are tested under different bending angles (0°, 90°, 180°, and 360°). The bioinspired ultrasensitive humidity sensor with a biocompatible and biodegradable sensing layer holds great potential, especially for health care applications (e.g., respiratory monitoring) without causing any body harm.

Interlayer Electron-Hole Friction in Tunable Twisted Bilayer Graphene Semimetal

Charge-neutral conducting systems represent a class of materials with unusual properties governed by electron-hole (e-h) interactions. Depending on the quasiparticle statistics, band structure, and device geometry these semimetallic phases of matter can feature unconventional responses to external fields that often defy simple interpretations in terms of single-particle physics. Here we show that small-angle twisted bilayer graphene (SA TBG) offers a highly tunable system in which to explore interactions-limited electron conduction. By employing a dual-gated device architecture we tune our devices from a nondegenerate charge-neutral Dirac fluid to a compensated two-component e-h Fermi liquid where spatially separated electrons and holes experience strong mutual friction. This friction is revealed through the T^{2} resistivity that accurately follows the e-h drag theory we develop. Our results provide a textbook illustration of a smooth transition between different interaction-limited transport regimes and clarify the conduction mechanisms in charge-neutral SA TBG.

Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Gate voltages applied to top and back gates of a tDBG device tune both the flatness and topology of the electronic bands, enabling an unusual level of experimental control. Metallic states with broken spin and valley symmetries have been observed in tDBG devices with twist angles in the range 1.2–1.3°, but the topologies and order parameters of these states have remained unclear. We report the observation of an anomalous Hall effect in the correlated metal state of tDBG, with hysteresis loops spanning hundreds of mT in out-of-plane magnetic field (B_⊥) that demonstrate spontaneously broken time-reversal symmetry. The B_⊥ hysteresis persists for in-plane fields up to several Tesla, suggesting valley (orbital) ferromagnetism. At the same time, the resistivity is strongly affected by even mT-scale values of in-plane magnetic field, pointing to spin-valley coupling or to a direct orbital coupling between in-plane field and the valley degree of freedom.

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Here, the authors report a strong anomalous Hall effect in the correlated-metal regime of tDBG, indicating time reversal symmetry breaking from orbital ferromagnetism, likely associated with valley polarization.

Intralayer Phonons in Multilayer Graphene Moiré Superlattices

Moiré pattern in twisted multilayers (tMLs) induces many emergent phenomena by subtle variation of atomic registry to modulate quasiparticles and their interactions, such as superconductivity, moiré excitons, and moiré phonons. The periodic superlattice potential introduced by moiré pattern also underlies patterned interlayer coupling at the interface of tMLs. Although this arising patterned interfacial coupling is much weaker than in-plane atomic interactions, it is crucial in moiré systems, as captured by the renormalized interlayer phonons in twisted bilayer transitional metal dichalcogenides. Here, we determine the quantitative relationship between the lattice dynamics of intralayer out-of-plane optical (ZO) phonons and patterned interfacial coupling in multilayer graphene moiré superlattices (MLG-MS) by the proposed perturbation model, which is previously challenging for MLGs due to their out-of-phase displacements of adjacent atoms in one atomic plane. We unveil that patterned interfacial coupling introduces profound modulations on Davydov components of nonfolded ZO phonon that are localized within the AB-stacked constituents, while the coupling results in layer-extended vibrations with symmetry of moiré pattern for moiré ZO phonons. Our work brings further degrees of freedom to engineer moiré physics according to the modulations imprinted on the phonon frequency and wavefunction.

Beginnings of exciton condensation in coronene analog of graphene double layer

Exciton condensation, a Bose-Einstein condensation of excitons into a single quantum state, has recently been achieved in low-dimensional materials including twin layers of graphene and van der Waals heterostructures. Here, we computationally examine the beginnings of exciton condensation in a double layer composed of coronene, a seven-benzene-ring patch of graphene. As a function of interlayer separation, we compute the exciton population in a single coherent quantum state, showing that the population peaks around 1.8 at distances near 2 Å. Visualization reveals interlayer excitons at the separation distance of the condensate. We determine the exciton population as a function of the twist angle between two coronene layers to reveal the magic angles at which the condensation peaks. As with previous recent calculations showing some exciton condensation in hexacene double layers and benzene stacks, the present two-electron reduced-density-matrix calculations with coronene provide computational evidence for the ability to realize exciton condensation in molecular-scale analogs of extended systems such as the graphene double layer.

Additive-Assisted Growth of Scaled and Quality 2D Materials

2D materials are increasingly becoming key components in modern electronics because of their prominent electronic and optoelectronic properties. The central and premise to the entire discipline of 2D materials lie in the high-quality and scaled preparations. The chemical vapor deposition (CVD) method offers compelling benefits in terms of scalability and controllability in shaping large-area and high-quality 2D materials. The past few years have witnessed development of numerous CVD growth strategies, with the use of additives attracting substantial attention in the production of scaled 2D crystals. This review provides an overview of different additives used in CVD growth of 2D materials, as well as a methodical demonstration of their vital roles. In addition, the intrinsic mechanisms of the production of scaled 2D crystals with additives are also discussed. Lastly, reliable guidance on the future design of optimal CVD synthesis routes is provided by analyzing the accessibility, pricing, by-products, controllability, universality, and commercialization of various additives.

2D Heterostructures for Ubiquitous Electronics and Optoelectronics: Principles, Opportunities, and Challenges

A grand family of two-dimensional (2D) materials and their heterostructures have been discovered through the extensive experimental and theoretical efforts of chemists, material scientists, physicists, and technologists. These pioneering works contribute to realizing the fundamental platforms to explore and analyze new physical/chemical properties and technological phenomena at the micro-nano-pico scales. Engineering 2D van der Waals (vdW) materials and their heterostructures via chemical and physical methods with a suitable choice of stacking order, thickness, and interlayer interactions enable exotic carrier dynamics, showing potential in high-frequency electronics, broadband optoelectronics, low-power neuromorphic computing, and ubiquitous electronics. This comprehensive review addresses recent advances in terms of representative 2D materials, the general fabrication methods, and characterization techniques and the vital role of the physical parameters affecting the quality of 2D heterostructures. The main emphasis is on 2D heterostructures and 3D-bulk (3D) hybrid systems exhibiting intrinsic quantum mechanical responses in the optical, valley, and topological states. Finally, we discuss the universality of 2D heterostructures with representative applications and trends for future electronics and optoelectronics (FEO) under the challenges and opportunities from physical, nanotechnological, and material synthesis perspectives.

Scattering between Minivalleys in Twisted Double Bilayer Graphene

A unique feature of the complex band structures of moiré materials is the presence of minivalleys, their hybridization, and scattering between them. Here, we investigate magnetotransport oscillations caused by scattering between minivalleys-a phenomenon analogous to magnetointersubband oscillations-in a twisted double bilayer graphene sample with a twist angle of 1.94°. We study and discuss the potential scattering mechanisms and find an electron-phonon mechanism and valley conserving scattering to be likely. Finally, we discuss the relevance of our findings for different materials and twist angles.

Biomimetic Hierarchically Silver Nanowire Interwoven MXene Mesh for Flexible Transparent Electrodes and Invisible Camouflage Electronics

Flexible transparent electrodes demand high transparency, low sheet resistance, as well as excellent mechanical flexibility simultaneously, however they still remain to be a great challenge due to"trade-off" effect. Herein, inspired by a hollow interconnected leaf vein, we developed robust transparent conductive mesh with biomimetic interwoven structure via hierarchically self-assembles silver nanowires interwoven metal carbide/nitride (MXene) sheets along directional microfibers. Strong interfacial interactions between plant fibers and conductive units facilitate hierarchically interwoven conductive mesh constructed orderly on flexible and lightweight veins while maintaining high transparency, effectively avoiding the trade-off effect between optoelectronic properties. The flexible transparent electrodes exhibit sheet resistance of 0.5 Ω sq^-1 and transparency of 81.6%, with a remarkably high figure of merit of 3523. In addition, invisible camouflage sensors are further successfully developed as a proof of concept that could monitor human body motion signals in an imperceptible state. The flexible transparent conductive mesh holds great potential in high-performance wearable optoelectronics and camouflage electronics.

Tailoring the Band Structure of Twisted Double Bilayer Graphene with Pressure

Twisted two-dimensional structures open new possibilities in band structure engineering. At magic twist angles, flat bands emerge, which gave a new drive to the field of strongly correlated physics. In twisted double bilayer graphene dual gating allows changing of the Fermi level and hence the electron density and also allows tuning of the interlayer potential, giving further control over band gaps. Here, we demonstrate that by application of hydrostatic pressure, an additional control of the band structure becomes possible due to the change of tunnel couplings between the layers. We find that the flat bands and the gaps separating them can be drastically changed by pressures up to 2 GPa, in good agreement with our theoretical simulations. Furthermore, our measurements suggest that in finite magnetic field due to pressure a topologically nontrivial band gap opens at the charge neutrality point at zero displacement field.

Correlated electron-hole state in twisted double-bilayer graphene

[Figure: see text].