Unusual magnetotransport in twisted bilayer graphene.

SignificanceWhen two sheets of graphene are twisted to the magic angle of 1.1∘, the resulting flat moiré bands can host exotic correlated electronic states such as superconductivity and ferromagnetism. Here, we show transport properties of a twisted bilayer graphene device at 1.38∘, far enough above the magic angle that we do not expect exotic correlated states. Instead, we see several unusual behaviors in the device's resistivity upon tuning both charge carrier density and perpendicular magnetic field. We can reproduce these behaviors with a surprisingly simple model based on Hofstadter's butterfly. These results shed light on the underlying properties of twisted bilayer graphene.

Chirality Probe of Twisted Bilayer Graphene in the Linear Transport Regime.

We propose minimal transport experiments in the coherent regime that can probe the chirality of twisted moiré structures. We show that only with a third contact and in the presence of an in-plane magnetic field (or another time-reversal symmetry breaking effect) a chiral system may display nonreciprocal transport in the linear regime. We then propose to use the third lead as a voltage probe and show that opposite enantiomers give rise to different voltage drops on the third lead. Additionally, in the scenario of layer-discriminating contacts, the third lead can serve as a current probe capable of detecting different handedness even in the absence of a magnetic field. In a complementary configuration, applying opposite voltages on the two layers of the third lead gives rise to a chiral (super)current in the absence of a source-drain voltage whose direction is determined by its chirality.

Electron Collimation in Twisted Bilayer Graphene via Gate-Defined Moiré Barriers.

Electron collimation via a graphene p-n junction allows electrostatic control of ballistic electron trajectories akin to that of an optical circuit. Similar manipulation of novel correlated electronic phases in twisted-bilayer graphene (tBLG) can provide additional probes to the underlying physics and device components toward advanced quantum electronics. In this work, we demonstrate collimation of the electron flow via gate-defined moiré barriers in a tBLG device, utilizing the band-insulator gap of the moiré superlattice. A single junction can be tuned to host a chosen combination of conventional pseudo barrier and moiré tunnel barriers, from which we demonstrate improved collimation efficiency. By measuring transport through two consecutive moiré collimators separated by 1 µm, we demonstrate evidence of electron collimation in tBLG in the presence of realistic twist-angle inhomogeneity.

Nonlinear Electrical Transport Unveils Fermi Surface Malleability in a Moiré Heterostructure.

Van Hove singularities enhance many-body interactions and induce collective states of matter ranging from superconductivity to magnetism. In magic-angle twisted bilayer graphene, van Hove singularities appear at low energies and are malleable with density, leading to a sequence of Lifshitz transitions and resets observable in Hall measurements. However, without a magnetic field, linear transport measurements have limited sensitivity to the band's topology. Here, we utilize nonlinear longitudinal and transverse transport measurements to probe these unique features in twisted bilayer graphene at zero magnetic field. We demonstrate that the nonlinear responses, induced by the Berry curvature dipole and extrinsic scattering processes, intricately map the Fermi surface reconstructions at various fillings. Importantly, our experiments highlight the intrinsic connection of these features with the moiré bands. Beyond corroborating the insights from linear Hall measurements, our findings establish nonlinear transport as a pivotal tool for probing band topology and correlated phenomena.

A Resonance-Sensitive Ultralow-Frequency Raman Mode in Twisted Bilayer Graphene.

Twisted bilayer graphene (tBLG) possesses intriguing physical properties including unconventional superconductivity, enhanced light-matter interaction due to the formation of van Hove singularities (vHS), and a divergence of density of states in the electronic band structures. The vHS energy band gap provides optical resonant transition channels that can be tuned by the twist angle and interlayer coupling. Raman spectroscopy provides rich information on the vHS structure of tBLG. Here, we report the discovery of an ultralow-frequency Raman mode at ∼49 cm-1 in tBLG. This mode is assigned to the combination of ZA (an out-of-plane acoustic phonon) and TA (a transverse acoustic phonon) phonons, and the Raman scattering is proposed to occur at the so-called mini-valley. This mode is found to be particularly sensitive to the change in vHS in tBLG. Our findings may deepen the understanding of Raman scattering in tBLG and help to reveal vHS-related electron-phonon interactions in tBLG.

Emergent phases in graphene flat bands.

Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.

Strain Engineering of Twisted Bilayer Graphene: The Rise of Strain-Twistronics.

The layer-by-layer stacked van der Waals structures (termed vdW hetero/homostructures) offer a new paradigm for materials design-their physical properties can be tuned by the vertical stacking sequence as well as by adding a mechanical twist, stretch, and hydrostatic pressure to the atomic structure. In particular, simple twisting and stacking of two layers of graphene can form a uniform and ordered Moiré superlattice, which can effectively modulate the electrons of graphene layers and lead to the discovery of unconventional superconductivity and strong correlations. However, the twist angle of twisted bilayer graphene (tBLG) is almost unchangeable once the interlayer stacking is determined, while applying mechanical elastic strain provides an alternative way to deeply regulate the electronic structure by controlling the lattice spacing and symmetry. In this review, diverse experimental advances are introduced in straining tBLG by in-plane and out-of-plane modes, followed by the characterizations and calculations toward quantitatively tuning the strain-engineered electronic structures. It is further discussed that the structural relaxation in strained Moiré superlattice and its influence on electronic structures. Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook on the intriguing emerging field, namely "strain-twistronics".

Fast Twist Angle Mapping of Bilayer Graphene Using Spectroscopic Ellipsometric Contrast Microscopy.

Twisted bilayer graphene provides an ideal solid-state model to explore correlated material properties and opportunities for a variety of optoelectronic applications, but reliable, fast characterization of the twist angle remains a challenge. Here we introduce spectroscopic ellipsometric contrast microscopy (SECM) as a tool for mapping twist angle disorder in optically resonant twisted bilayer graphene. We optimize the ellipsometric angles to enhance the image contrast based on measured and calculated reflection coefficients of incident light. The optical resonances associated with van Hove singularities correlate well to Raman and angle-resolved photoelectron emission spectroscopy, confirming the accuracy of SECM. The results highlight the advantages of SECM, which proves to be a fast, nondestructive method for characterization of twisted bilayer graphene over large areas, unlocking process, material, and device screening and cross-correlative measurement potential for bilayer and multilayer materials.

Kinetics of Nanobubbles in Tiny-Angle Twisted Bilayer Graphene.

Realization of high-quality van der Waals (vdWs) heterostructures by stacking two-dimensional (2D) layers requires atomically clean interfaces. Because of strong adhesion between the constituent layers, the vdWs forces could drive trapped contaminants together into submicron-size "bubbles", which leaves large interfacial areas atomically clean. Here, we study the kinetics of nanobubbles in tiny-angle twisted bilayer graphene (TBG) and our results reveal a substantial influence of the moiré superlattice on the motion of nanoscale interfacial substances. Our experiments indicate that the bubbles will mainly move along the triangular network of domain boundaries in the tiny-angle TBG when the sizes of the bubbles are comparable to that of an AA-stacking region. When the size of the bubble is smaller than that of an AA-stacking region, the bubble becomes motionless and is fixed in the AA-stacking region, because of its large out-of-plane corrugation.

Layer-Dependent Interaction Effects in the Electronic Structure of Twisted Bilayer Graphene Devices.

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the K points that is qualitatively consistent with moiré models of the Hartree-Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

Twisted Bilayer Graphene Induced by Intercalation.

Twisted bilayer graphene (tBLG) has gained significant attention due to its unique physical and electronic properties. However, efficient fabrication of high-quality tBLG with diverse twist angles is crucial to expedite research on angle-dependent physics and potential applications. In this study, an intercalation strategy utilizing organic molecules, such as 1,2-dichloroethane, is developed to weaken the interlayer interaction and induce slide or rotation of the topmost graphene layer for tBLG fabrication. The proportion of tBLGs in the resulting 1,2-dichloroethane-treated BLG (dtBLG) reaches up to 84.4% for twist angles ranging from 0° to 30°, surpassing previously reported methods using chemical vapor deposition (CVD). Moreover, the twist angle distribution is not uniform and tends to concentrate in the ranges of 0-10° and 20-30°. This facile and rapid intercalation-based methodology provides a practical solution for studying angle-dependent physics and advancing the utilization of twisted two-dimensional materials.

Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene.

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.

Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices.

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.

Real-Space Mapping of Local Subdegree Lattice Rotations in Low-Angle Twisted Bilayer Graphene.

In two-dimensional small-angle twisted bilayers, van der Waals (vdW) interlayer interaction introduces an atomic-scale reconstruction, which consists of a moiré-periodic network of local subdegree lattice rotations. However, real-space measurement of the subdegree lattice rotation requires extremely high spatial resolution, which is an outstanding challenge in an experiment. Here, a topmost small-period graphene moiré pattern is introduced as a magnifying lens to magnify sub-Angstrom lattice distortions in small-angle twisted bilayer graphene (TBG) by about 2 orders of magnitude. Local moiré periods of the topmost graphene moiré patterns and low-energy van Hove singularities of the system are spatially modified by the atomic-scale reconstruction of the underlying TBG, thus enabling real-space mapping of the networks of the subdegree lattice rotations both in structure and in electronic properties. Our results indicate that it is quite facile to study subdegree lattice rotation in vdW systems by measuring the periods of the topmost moiré superlattice.

Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene.

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry; superconductivity and correlated insulators emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess-Zumino-Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a "mechanism" for superconductivity. We present a comprehensive listing of plausible low-temperature orders and the parent flavor symmetry-breaking orders. The previously characterized topological nature of the band structure of twisted bilayer graphene plays an important role in this analysis.

Uncovering Topological Edge States in Twisted Bilayer Graphene.

Twisted bilayer graphene (t-BLG) has recently been introduced as a rich physical platform displaying flat electronic bands, strongly correlated states, and unconventional superconductivity. Studies have hinted at an unusual Z2 topology of the moiré Dirac bands of t-BLG. However, direct experimental evidence of this moiré band topology and associated edge states is still lacking. Herein, using superconducting quantum interferometry, we reconstructed the spatial supercurrent distribution in t-BLG Josephson junctions and revealed the presence of edge states located in the superlattice band gaps. The absence of edge conduction in high resistance regions just outside the superlattice band gap confirms that the edge transport originates from the filling of electronic states located inside the band gap and further allows us to exclude several other edge conduction mechanisms. These results confirm the unusual moiré band topology of twisted bilayer graphene and will stimulate further research to explore its consequences.

Moiré-Induced Transport in CVD-Based Small-Angle Twisted Bilayer Graphene.

To realize the applicative potential of 2D twistronic devices, scalable synthesis and assembly techniques need to meet stringent requirements in terms of interface cleanness and twist-angle homogeneity. Here, we show that small-angle twisted bilayer graphene assembled from separated CVD-grown graphene single-crystals can ensure high-quality transport properties, determined by a device-scale-uniform moiré potential. Via low-temperature dual-gated magnetotransport, we demonstrate the hallmarks of a 2.4°-twisted superlattice, including tunable regimes of interlayer coupling, reduced Fermi velocity, large interlayer capacitance, and density-independent Brown-Zak oscillations. The observation of these moiré-induced electrical transport features establishes CVD-based twisted bilayer graphene as an alternative to "tear-and-stack" exfoliated flakes for fundamental studies, while serving as a proof-of-concept for future large-scale assembly.

Pressure Tunable van Hove Singularities of Twisted Bilayer Graphene.

The giant light-matter interaction induced by van Hove singularities (vHSs) of twisted bilayer graphene (tBLG) is responsible for enhanced optical absorption and strong photoresponse. Here, we investigated the evolution of vHSs in tBLG under pressure by using Raman spectroscopy. Pressure not only induces a blue shift of the G/R band but also tunes the intensity of the G/R band. The blue shift of the G/R band is due to the reduction of the in-plane lattice constant, and the variation of the G/R band intensity is due to the vHSs' shift of tBLG. Moreover, the main band in the absorption spectrum of tBLG is attributed to multiple transitions from valence to conduction bands. Because the ratio of R to G band intensity increases under pressure and the origins of R and G bands are different, we claim that pressure enhances intervalley electron scattering. This study paves the way for pressure engineering of vHS and the corresponding photon-electron-phonon interaction in tBLG.

Correlated States in Strained Twisted Bilayer Graphenes Away from the Magic Angle.

Graphene moiré superlattice formed by rotating two graphene sheets can host strongly correlated and topological states when flat bands form at so-called magic angles. Here, we report that, for a twisting angle far away from the magic angle, the heterostrain induced during stacking heterostructures can also create flat bands. Combining a direct visualization of strain effect in twisted bilayer graphene moiré superlattices and transport measurements, features of correlated states appear at "non-magic" angles in twisted bilayer graphene under the heterostrain. Observing correlated states in these "non-standard" conditions can enrich the understanding of the possible origins of the correlated states and widen the freedom in tuning the moiré heterostructures and the scope of exploring the correlated physics in moiré superlattices.

Quantum Plasmonic Nonreciprocity in Parity-Violating Magnets.

The optical responses of metals are often dominated by plasmonic resonances, that is, the collective oscillations of interacting electron liquids. Here we unveil a new class of plasmons─quantum metric plasmons (QMPs)─that arise in a wide range of parity-violating magnetic metals. In these materials, a dipolar distribution of the quantum metric (a fundamental characteristic of Bloch wave functions) produces intrinsic nonreciprocal bulk plasmons. Strikingly, QMP nonreciprocity manifests even when the single-particle dispersion is symmetric: QMPs are sensitive to time-reversal and parity violations hidden in the Bloch wave function. In materials with asymmetric single-particle dispersions, quantum metric dipole induced nonreciprocity can continue to dominate at large frequencies. We anticipate that QMPs can be realized in a wide range of parity-violating magnets, including twisted bilayer graphene heterostructures, where quantum geometric quantities can achieve large values.