Direct observation of a magnetic-field-induced Wigner crystal.

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2-11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

Evidence of the fractional quantum spin Hall effect in moiré MoTe2.

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities1-6. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0 = e2/h (with e and h denoting the electron charge and Planck's constant, respectively)7-14. Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands15,16. At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance 3 2 G 0 with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials17-19.

Fractional quantum anomalous Hall effect in multilayer graphene.

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.

Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene.

Graphene-based, high-quality, two-dimensional electronic systems have emerged as a highly tunable platform for studying superconductivity1-21. Specifically, superconductivity has been observed in both electron- and hole-doped twisted graphene moiré systems1-17, whereas in crystalline graphene systems, superconductivity has so far been observed only in hole-doped rhombohedral trilayer graphene (RTG)18 and hole-doped Bernal bilayer graphene (BBG)19-21. Recently, enhanced superconductivity has been demonstrated20,21 in BBG because of the proximity to a monolayer WSe2. Here we report the observation of superconductivity and a series of flavour-symmetry-breaking phases in electron- and hole-doped BBG/WSe2 devices by electrostatic doping. The strength of the observed superconductivity is tunable by applied vertical electric fields. The maximum Berezinskii-Kosterlitz-Thouless transition temperature for the electron- and hole-doped superconductivity is about 210 mK and 400 mK, respectively. Superconductivities emerge only when the applied electric fields drive the BBG electron or hole wavefunctions towards the WSe2 layer, underscoring the importance of the WSe2 layer in the observed superconductivity. The hole-doped superconductivity violates the Pauli paramagnetic limit, consistent with an Ising-like superconductor. By contrast, the electron-doped superconductivity obeys the Pauli limit, although the proximity-induced Ising spin-orbit coupling is also notable in the conduction band. Our findings highlight the rich physics associated with the conduction band in BBG, paving the way for further studies into the superconducting mechanisms of crystalline graphene and the development of superconductor devices based on BBG.

Terahertz phonon engineering with van der Waals heterostructures.

Phonon engineering at gigahertz frequencies forms the foundation of microwave acoustic filters1, acousto-optic modulators2 and quantum transducers3,4. Terahertz phonon engineering could lead to acoustic filters and modulators at higher bandwidth and speed, as well as quantum circuits operating at higher temperatures. Despite their potential, methods for engineering terahertz phonons have been limited due to the challenges of achieving the required material control at subnanometre precision and efficient phonon coupling at terahertz frequencies. Here we demonstrate the efficient generation, detection and manipulation of terahertz phonons through precise integration of atomically thin layers in van der Waals heterostructures. We used few-layer graphene as an ultrabroadband phonon transducer that converts femtosecond near-infrared pulses to acoustic-phonon pulses with spectral content up to 3 THz. A monolayer WSe2 is used as a sensor. The high-fidelity readout was enabled by the exciton-phonon coupling and strong light-matter interactions. By combining these capabilities in a single heterostructure and detecting responses to incident mechanical waves, we performed terahertz phononic spectroscopy. Using this platform, we demonstrate high-Q terahertz phononic cavities and show that a WSe2 monolayer embedded in hexagonal boron nitride can efficiently block the transmission of terahertz phonons. By comparing our measurements to a nanomechanical model, we obtained the force constants at the heterointerfaces. Our results could enable terahertz phononic metamaterials for ultrabroadband acoustic filters and modulators and could open new routes for thermal engineering.

Imaging tunable Luttinger liquid systems in van der Waals heterostructures.

One-dimensional (1D) interacting electrons are often described as a Luttinger liquid1-4 having properties that are intrinsically different from those of Fermi liquids in higher dimensions5,6. In materials systems, 1D electrons exhibit exotic quantum phenomena that can be tuned by both intra- and inter-1D-chain electronic interactions, but their experimental characterization can be challenging. Here we demonstrate that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays. We have imaged the evolution of DW Luttinger liquids under different interaction regimes tuned by electron density using scanning tunnelling microscopy. Single DWs at low carrier density are highly susceptible to Wigner crystallization consistent with a spin-incoherent Luttinger liquid, whereas at intermediate densities dimerized Wigner crystals form because of an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions that gives rise to new quantum phases. At low electron densities, inter-chain interactions are dominant and induce a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase in which electrons are ordered with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures provides opportunities to explore Luttinger liquid physics.

Van der Waals polarity-engineered 3D integration of 2D complementary logic.

Vertical three-dimensional integration of two-dimensional (2D) semiconductors holds great promise, as it offers the possibility to scale up logic layers in the z axis1-3. Indeed, vertical complementary field-effect transistors (CFETs) built with such mixed-dimensional heterostructures4,5, as well as hetero-2D layers with different carrier types6-8, have been demonstrated recently. However, so far, the lack of a controllable doping scheme (especially p-doped WSe2 (refs. 9-17) and MoS2 (refs. 11,18-28)) in 2D semiconductors, preferably in a stable and non-destructive manner, has greatly impeded the bottom-up scaling of complementary logic circuitries. Here we show that, by bringing transition metal dichalcogenides, such as MoS2, atop a van der Waals (vdW) antiferromagnetic insulator chromium oxychloride (CrOCl), the carrier polarity in MoS2 can be readily reconfigured from n- to p-type via strong vdW interfacial coupling. The consequential band alignment yields transistors with room-temperature hole mobilities up to approximately 425 cm2 V-1 s-1, on/off ratios reaching 106 and air-stable performance for over one year. Based on this approach, vertically constructed complementary logic, including inverters with 6 vdW layers, NANDs with 14 vdW layers and SRAMs with 14 vdW layers, are further demonstrated. Our findings of polarity-engineered p- and n-type 2D semiconductor channels with and without vdW intercalation are robust and universal to various materials and thus may throw light on future three-dimensional vertically integrated circuits based on 2D logic gates.

Reproducible graphene synthesis by oxygen-free chemical vapour deposition.

Chemical vapour deposition (CVD) synthesis of graphene on copper has been broadly adopted since the first demonstration of this process1. However, widespread use of CVD-grown graphene for basic science and applications has been hindered by challenges with reproducibility2 and quality3. Here we identify trace oxygen as a key factor determining the growth trajectory and quality for graphene grown by low-pressure CVD. Oxygen-free chemical vapour deposition (OF-CVD) synthesis is fast and highly reproducible, with kinetics that can be described by a compact model, whereas adding trace oxygen leads to suppressed nucleation and slower/incomplete growth. Oxygen affects graphene quality as assessed by surface contamination, emergence of the Raman D peak and decrease in electrical conductivity. Epitaxial graphene grown in oxygen-free conditions is contamination-free and shows no detectable D peak. After dry transfer and boron nitride encapsulation, it shows room-temperature electrical-transport behaviour close to that of exfoliated graphene. A graphite-gated device shows well-developed integer and fractional quantum Hall effects. By highlighting the importance of eliminating trace oxygen, this work provides guidance for future CVD system design and operation. The increased reproducibility and quality afforded by OF-CVD synthesis will broadly influence basic research and applications of graphene.

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4.

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter1. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order2-8, not possible in quantum Hall and Chern insulator systems. Here we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe4. This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism2-4,9,10.

Graphene nanoribbons grown in hBN stacks for high-performance electronics.

Van der Waals encapsulation of two-dimensional materials in hexagonal boron nitride (hBN) stacks is a promising way to create ultrahigh-performance electronic devices1-4. However, contemporary approaches for achieving van der Waals encapsulation, which involve artificial layer stacking using mechanical transfer techniques, are difficult to control, prone to contamination and unscalable. Here we report the transfer-free direct growth of high-quality graphene nanoribbons (GNRs) in hBN stacks. The as-grown embedded GNRs exhibit highly desirable features being ultralong (up to 0.25 mm), ultranarrow (<5 nm) and homochiral with zigzag edges. Our atomistic simulations show that the mechanism underlying the embedded growth involves ultralow GNR friction when sliding between AA'-stacked hBN layers. Using the grown structures, we demonstrate the transfer-free fabrication of embedded GNR field-effect devices that exhibit excellent performance at room temperature with mobilities of up to 4,600 cm2 V-1 s-1 and on-off ratios of up to 106. This paves the way for the bottom-up fabrication of high-performance electronic devices based on embedded layered materials.

Tuning commensurability in twisted van der Waals bilayers.

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt = 30° and the commensurate moiré crystals at θt = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the K valley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.

Observation of hydrodynamic plasmons and energy waves in graphene.

Thermally excited electrons and holes form a quantum-critical Dirac fluid in ultraclean graphene and their electrodynamic responses are described by a universal hydrodynamic theory. The hydrodynamic Dirac fluid can host intriguing collective excitations distinctively different from those in a Fermi liquid1-4. Here we report the observation of the hydrodynamic plasmon and energy wave in ultraclean graphene. We use the on-chip terahertz (THz) spectroscopy technique to measure the THz absorption spectra of a graphene microribbon as well as the propagation of the energy wave in graphene close to charge neutrality. We observe a prominent high-frequency hydrodynamic bipolar-plasmon resonance and a weaker low-frequency energy-wave resonance of the Dirac fluid in ultraclean graphene. The hydrodynamic bipolar plasmon is characterized by the antiphase oscillation of massless electrons and holes in graphene. The hydrodynamic energy wave is an electron-hole sound mode with both charge carriers oscillating in phase and moving together. The spatial-temporal imaging technique shows that the energy wave propagates at a characteristic speed of [Formula: see text] near the charge neutrality2-4. Our observations open new opportunities to explore collective hydrodynamic excitations in graphene systems.

Mixed-dimensional moiré systems of twisted graphitic thin films.

Moiré patterns formed by stacking atomically thin van der Waals crystals with a relative twist angle can give rise to notable new physical properties1,2. The study of moiré materials has so far been limited to structures comprising no more than a few van der Waals sheets, because a moiré pattern localized to a single two-dimensional interface is generally assumed to be incapable of appreciably modifying the properties of a bulk three-dimensional crystal. Here, we perform transport measurements of dual-gated devices constructed by slightly rotating a monolayer graphene sheet atop a thin bulk graphite crystal. We find that the moiré potential transforms the electronic properties of the entire bulk graphitic thin film. At zero and in small magnetic fields, transport is mediated by a combination of gate-tuneable moiré and graphite surface states, as well as coexisting semimetallic bulk states that do not respond to gating. At high field, the moiré potential hybridizes with the graphitic bulk states due to the unique properties of the two lowest Landau bands of graphite. These Landau bands facilitate the formation of a single quasi-two-dimensional hybrid structure in which the moiré and bulk graphite states are inextricably mixed. Our results establish twisted graphene-graphite as the first in a new class of mixed-dimensional moiré materials.

Thermodynamic evidence of fractional Chern insulator in moiré MoTe2.

Chern insulators, which are the lattice analogues of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices1-3. Until now, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field3-8, whereas fractional Chern insulators have been reported in only graphene-based systems under a finite magnetic field9,10. The emergence of semiconductor moiré materials11, which support tunable topological flat bands12,13, provides an opportunity to realize fractional Chern insulators13-16. Here we report thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor ν = 1 and 2/3, the system is incompressible and spontaneously breaks time-reversal symmetry. We show that they are integer and fractional Chern insulators, respectively, from the dispersion of the state in the filling factor with an applied magnetic field. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for the demonstration of quantized fractional Hall conductance and anyonic excitation and braiding17 in semiconductor moiré materials.

Gate-tunable heavy fermions in a moiré Kondo lattice.

The Kondo lattice-a matrix of local magnetic moments coupled through spin-exchange interactions to itinerant conduction electrons-is a prototype of strongly correlated quantum matter1-4. Usually, Kondo lattices are realized in intermetallic compounds containing lanthanide or actinide1,2. The complex electronic structure and limited tunability of both the electron density and exchange interactions in these bulk materials pose considerable challenges to studying Kondo lattice physics. Here we report the realization of a synthetic Kondo lattice in AB-stacked MoTe2/WSe2 moiré bilayers, in which the MoTe2 layer is tuned to a Mott insulating state, supporting a triangular moiré lattice of local moments, and the WSe2 layer is doped with itinerant conduction carriers. We observe heavy fermions with a large Fermi surface below the Kondo temperature. We also observe the destruction of the heavy fermions by an external magnetic field with an abrupt decrease in the Fermi surface size and quasi-particle mass. We further demonstrate widely and continuously gate-tunable Kondo temperatures through either the itinerant carrier density or the Kondo interaction. Our study opens the possibility of in situ access to the phase diagram of the Kondo lattice with exotic quantum criticalities in a single device based on semiconductor moiré materials2-9.

Tunable electron-flexural phonon interaction in graphene heterostructures.

Peculiar electron-phonon interaction characteristics underpin the ultrahigh mobility1, electron hydrodynamics2-4, superconductivity5 and superfluidity6,7 observed in graphene heterostructures. The Lorenz ratio between the electronic thermal conductivity and the product of the electrical conductivity and temperature provides insight into electron-phonon interactions that is inaccessible to past graphene measurements. Here we show an unusual Lorenz ratio peak in degenerate graphene near 60 kelvin and decreased peak magnitude with increased mobility. When combined with ab initio calculations of the many-body electron-phonon self-energy and analytical models, this experimental observation reveals that broken reflection symmetry in graphene heterostructures can relax a restrictive selection rule8,9 to allow quasielastic electron coupling with an odd number of flexural phonons, contributing to the increase of the Lorenz ratio towards the Sommerfeld limit at an intermediate temperature sandwiched between the low-temperature hydrodynamic regime and the inelastic electron-phonon scattering regime above 120 kelvin. In contrast to past practices of neglecting the contributions of flexural phonons to transport in two-dimensional materials, this work suggests that tunable electron-flexural phonon couping can provide a handle to control quantum matter at the atomic scale, such as in magic-angle twisted bilayer graphene10 where low-energy excitations may mediate Cooper pairing of flat-band electrons11,12.

Coupled ferroelectricity and superconductivity in bilayer Td-MoTe2.

Achieving electrostatic control of quantum phases is at the frontier of condensed matter research. Recent investigations have revealed superconductivity tunable by electrostatic doping in twisted graphene heterostructures and in two-dimensional semimetals such as WTe2 (refs. 1-5). Some of these systems have a polar crystal structure that gives rise to ferroelectricity, in which the interlayer polarization exhibits bistability driven by external electric fields6-8. Here we show that bilayer Td-MoTe2 simultaneously exhibits ferroelectric switching and superconductivity. Notably, a field-driven, first-order superconductor-to-normal transition is observed at its ferroelectric transition. Bilayer Td-MoTe2 also has a maximum in its superconducting transition temperature (Tc) as a function of carrier density and temperature, allowing independent control of the superconducting state as a function of both doping and polarization. We find that the maximum Tc is concomitant with compensated electron and hole carrier densities and vanishes when one of the Fermi pockets disappears with doping. We argue that this unusual polarization-sensitive two-dimensional superconductor is driven by an interband pairing interaction associated with nearly nested electron and hole Fermi pockets.

Evidence for Dirac flat band superconductivity enabled by quantum geometry.

In a flat band superconductor, the charge carriers' group velocity vF is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors1 and heavy-fermion systems2. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small vF in the conventional Bardeen-Cooper-Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene3-7, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system8-13. Using Schwinger-limited non-linear transport studies14,15, we demonstrate an extremely slow normal state drift velocity vn ≈ 1,000 m s-1 for filling fraction ν between -1/2 and -3/4 of the moiré superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid16. Importantly, our measurement of superfluid stiffness, which controls the superconductor's electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution8-12. We find evidence for small Cooper pairs, characteristic of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover17-19, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands.

Enhanced superconductivity in spin-orbit proximitized bilayer graphene.

In the presence of a large perpendicular electric field, Bernal-stacked bilayer graphene (BLG) features several broken-symmetry metallic phases1-3 as well as magnetic-field-induced superconductivity1. The superconducting state is quite fragile, however, appearing only in a narrow window of density and with a maximum critical temperature Tc ≈ 30 mK. Here we show that placing monolayer tungsten diselenide (WSe2) on BLG promotes Cooper pairing to an extraordinary degree: superconductivity appears at zero magnetic field, exhibits an order of magnitude enhancement in Tc and occurs over a density range that is wider by a factor of eight. By mapping quantum oscillations in BLG-WSe2 as a function of electric field and doping, we establish that superconductivity emerges throughout a region for which the normal state is polarized, with two out of four spin-valley flavours predominantly populated. In-plane magnetic field measurements further reveal that superconductivity in BLG-WSe2 can exhibit striking dependence of the critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly obeyed on one end of the superconducting dome, yet sharply violated on the other. Moreover, the superconductivity arises only for perpendicular electric fields that push BLG hole wavefunctions towards WSe2, indicating that proximity-induced (Ising) spin-orbit coupling plays a key role in stabilizing the pairing. Our results pave the way for engineering robust, highly tunable and ultra-clean graphene-based superconductors.

Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene.

The exceptional control of the electronic energy bands in atomically thin quantum materials has led to the discovery of several emergent phenomena1. However, at present there is no versatile method for mapping the local band structure in advanced two-dimensional materials devices in which the active layer is commonly embedded in the insulating layers and metallic gates. Using a scanning superconducting quantum interference device, here we image the de Haas-van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which shows several highly tunable bands2-4. By resolving thermodynamic quantum oscillations spanning more than 100 Landau levels in low magnetic fields, we reconstruct the band structure and its evolution with the displacement field with excellent precision and nanoscale spatial resolution. Moreover, by developing Landau-level interferometry, we show shear-strain-induced pseudomagnetic fields and map their spatial dependence. In contrast to artificially induced large strain, which leads to pseudomagnetic fields of hundreds of tesla5-7, we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by 1 millidegree, two orders of magnitude lower than the typical angle disorder in twisted bilayer graphene8-11. This ability to resolve the local band structure and strain at the nanoscale level enables the characterization and use of tunable band engineering in practical van der Waals devices.