Superconductivity in rhombohedral trilayer graphene

Ephemeral superconductivity atop the false vacuum

A many-body system in the vicinity of a first-order phase transition may get trapped in a local minimum of the free energy landscape. These so-called false-vacuum states may survive for exceedingly long times if the barrier for their decay is high enough. The rich phase diagram obtained in graphene multilayer devices presents a unique opportunity to explore transient superconductivity on top of a correlated false vacuum. Specifically, we consider superconductors which are terminated by an apparent first-order phase transition to a correlated phase with different symmetry. We propose that quenching across this transition leads to a non-equilibrium ephemeral superconductor, readily detectable using straightforward transport measurements. Moreover, the transient superconductor also generically enhances the false vacuum lifetime, potentially by orders of magnitude. In several scenarios, the complimentary effect takes place as well: superconductivity is temporarily emboldened in the false vacuum, albeit ultimately decaying. We demonstrate the applicability of these claims for different instances of superconductivity terminated by a first order transition in rhombohedral graphene. The obtained decay timescales position this class of materials as a promising playground to unambiguously realize and measure non-equilibrium superconductivity.

How does goldene stack?

The recent synthesis of goldene, a 2D atomic monolayer of gold, has opened new avenues in exploring novel materials. However, the question of when multilayer goldene transitions into bulk gold remains unresolved. This study used density functional theory calculations to address this fundamental question. Our findings reveal that multilayer goldene retains an AA-like stacking configuration of up to six layers, with no observation of Bernal-like stacking as seen in graphene. Goldene spontaneously transitions to a bulk-like gold structure at seven layers, adopting a rhombohedral (ABC-like) stacking characteristic of bulk face-centered cubic (FCC) gold. The atomic arrangement converges entirely to the bulk gold lattice for more than ten layers. Quantum confinement significantly impacts the electronic properties, with monolayer and bulk goldene exhibiting levels with linear dispersion at the X-point of the Brillouin zone. In contrast, multilayer goldene shows levels with linear dispersions at the X- and Y-points. Monolayer goldene exhibits anisotropic optical absorption, which is absent in bulk gold. This study provides a deeper understanding of multilayer goldene's structural and electronic properties and stacked 2D materials in general.

Theory of correlated insulators and superconductor at ν = 1 in twisted WSe2

The observation of a superconducting phase, an intertwined insulating phase, and a continuous transition between the two at a commensurate filling of ν = 1 in bilayers of twisted WSe2 at θ = 3.650 raises a number of intriguing questions about the origin of this phenomenology. Here we report the possibility of a displacement-field induced continuous transition between a superconductor and a quantum spin-liquid Mott insulator at ν = 1, starting with a simplified three-orbital model of twisted WSe2, including on-site, nearest-neighbor density-density interactions, and a chiral-exchange interaction, respectively. By employing parton mean-field theory, we discuss the nature of these correlated insulators, their expected evolution with the displacement-field, and their phenomenological properties.

Electric Field-Tunable Superconductivity with Competing Orders in Twisted Bilayer Graphene near the Magic Angle

Superconductivity (SC) in twisted bilayer graphene (tBLG) has been explored by varying carrier concentrations, twist angles, and screening strength, with the aim of uncovering its origin and possible connections to strong electronic correlations in narrow bands and various resulting broken symmetries. However, the link between the tBLG band structure and the onset of SC and other orders largely remains unclear. In this study, we address this crucial gap by examining in situ band structure tuning of a near magic-angle (θ ≈ 0.95°) tBLG device with a displacement field (D) and reveal competition between SC and other broken symmetries. At zero D, the device exhibits superconducting signatures without the resistance peak at half-filling, a characteristic signature with a strong electronic correlation. As D increases, the SC is suppressed, accompanied by the appearance of a resistance peak at half-filling. Hall density measurements reveal that at zero D, SC arises around the van Hove singularity (vHs) from an isospin or spin-valley unpolarized band. At higher D, the suppression of SC coincides with broken isospin symmetry near half-filling with lifted degeneracy (gd ∼ 2). Additionally, as the SC phase becomes weaker with D, vHs shifts to higher fillings, highlighting the modification of the underlying band structure with the applied electric field. These findings, with recent theoretical study on SC in tBLG, highlight the competition, rather than being connected concomitantly, between SC and other orders promoted by broken symmetries.

Proximity-Induced Superconductivity in Ferromagnetic Fe3GeTe2 and Josephson Tunneling through a van der Waals Heterojunction

Synergy between superconductivity and ferromagnetism may offer great opportunities in nondissipative spintronics and topological quantum computing. Yet at the microscopic level, the exchange splitting of the electronic states responsible for ferromagnetism is inherently incompatible with the spin-singlet nature of conventional superconducting Cooper pairs. Here, we exploit the recently discovered van der Waals ferromagnets as enabling platforms with marvelous controllability to unravel the myth between ferromagnetism and superconductivity. We report unambiguous experimental evidence of superconductivity in few-layer ferromagnetic Fe3GeTe2 (FGT) proximity coupled to a superconducting NbSe2 overlayer through an insulating spacer, demonstrating coexistence of these two seemingly antagonistic orderings. Our transport measurements reveal a sudden resistance drop to zero in FGT below the superconducting critical temperature of NbSe2 and detect a Josephson supercurrent through the NbSe2/insulator/FGT van der Waals junction. Furthermore, using anomalous Hall effect and magnetic force microscopy characterizations, we confirm that FGT preserves its ferromagnetism in the superconducting regime. Our central findings reveal the microscopic harmony between ferromagnetism and superconductivity and render these systems immense technological potentials.

Quasiperiodic Pairing in Graphene Quasicrystals

We investigate the superconducting instabilities of twisted bilayer graphene quasicrystals (TBGQCs) obtained by stacking two monolayer graphene sheets with 30° relative twisting. The electronic energy spectrum of the TBGQC contains periodic energy ranges (PERs) and quasiperiodic energy ranges (QERs), where the underlying local density of states (LDOS) exhibits periodic and quasiperiodic distribution, respectively. We found that superconductivity in the PER is a simple superposition of two monolayer superconductors. This is because, particularly near the charge neutrality point of the TBGQC, the two layers are weekly coupled, leading to pairing instabilities with a uniform distribution in real space. On the other hand, within the QER, the inhomogeneous distribution of the LDOS enhances the superconducting instability with a nonuniform distribution of pairing amplitudes, leading to quasiperiodic superconductivity. Our study can qualitatively explain the superconductivity in recently discovered moiré quasicrystals, which show superconductivity in their QER.

Nanoscale Structure and Interfacial Electrochemical Reactivity of Moiré-Engineered Atomic Layers

ConspectusThe electronic properties of atomically thin van der Waals (vdW) materials can be precisely manipulated by vertically stacking them with a controlled offset (for example, a rotational offset─i.e., twist─between the layers, or a small difference in lattice constant) to generate moiré superlattices. In recent years, the application of this "twistronics" concept to interfacial electrochemistry has unveiled unique pathways for tailoring the electrochemical reactivity. This Account provides an overview of our work that leveraged a suite of structural characterization methods, such as interferometric four-dimensional scanning transmission electron microscopy, dark-field transmission electron microscopy, and scanning tunneling microscopy, along with nanoscale electrochemical measurement techniques, namely, scanning electrochemical cell microscopy (SECCM), to uncover and dissect the profound impact of electrode electronic structure, controlled by interlayer twist, on interfacial electron transfer kinetics. At the heart of our findings is the discovery that moiré engineering enables the isolation of thermodynamically unfavorable stacking configurations, or topological defects, that substantially increase the standard electron transfer rate constant at the solid-liquid interface beyond what has been measured on conventional, nontwisted two-dimensional (2D) materials. This enhancement in interfacial reactivity can be attributed to the localization of a high density of electronic states within these particular sites in the superlattice, a similar effect to that which occurs upon incorporation of physical defects or vacancies in an electrode material but instead using an atomically pristine surface with a highly tunable structure. Throughout our studies, understanding the nuances of the relationship between the preimposed moiré twist angle and the observed electron transfer kinetics has heavily relied on the interrogation of additional factors such as spontaneous superlattice reconstruction and three-dimensional localization of electronic states, illustrating the importance of combining electrochemical measurements with both nanoscale structural probes and theoretical modeling for designing and optimizing moiré-engineered electrodes. The insight afforded by our efforts in this space continues to deepen our understanding of the fundamental mechanisms governing electron transfer at electrochemical interfaces at large and also points to the revolutionary prospect of twistronics for advancing electrochemical technologies. While our electrochemical studies have, so far, focused largely on graphene-based moiré materials, we also offer a perspective on the promise of transition metal dichalcogenide (TMD)-based moirés as candidates for highly versatile (photo)electrode surfaces. Accordingly, we provide a discussion of our studies on the structural relaxation observed in moiré superlattices of TMDs, and we summarize our work combining SECCM with field-effect electrostatic gating of TMDs to deconvolute the influences of material conductivity and intrinsic electron transfer kinetics from the overall electrochemical response of a semiconducting 2D material. Overall, this body of work establishes a distinctive foundation for the design of a wide range of materials with tailored properties that can provide crucial insights into interfacial charge transfer chemistry─potentially serving as platforms for sensing, energy conversion, and electrocatalysis─in addition to the emergent exotic correlated electron physics that originally ignited intense interest in moiré twistronics.

Layer-dependent evolution of electronic structures and correlations in rhombohedral multilayer graphene

The recent discovery of superconductivity and magnetism in trilayer rhombohedral graphene (RG) establishes an ideal, untwisted platform to study strong correlation electronic phenomena. However, the correlated effects in multilayer RG have received limited attention, and, particularly, the evolution of the correlations with increasing layer number remains an unresolved question. Here we show the observation of layer-dependent electronic structures and correlations-under surprising liquid nitrogen temperature-in RG multilayers from 3 to 9 layers by using scanning tunnelling microscopy and spectroscopy. We explicitly determine layer-enhanced low-energy flat bands and interlayer coupling strengths. The former directly demonstrates the further flattening of low-energy bands in thicker RG, and the latter indicates the presence of varying interlayer interactions in RG multilayers. Moreover, we find significant splittings of the flat bands, ranging from ~50 meV to 80 meV, at 77 K when they are partially filled, indicating the emergence of interaction-induced strongly correlated states. Particularly, the strength of the correlated states is notably enhanced in thicker RG and reaches its maximum in the six-layer, validating directly theoretical predictions and establishing abundant new candidates for strongly correlated systems. Our results provide valuable insights into the layer dependence of the electronic properties in RG and demonstrate it as a suitable system for investigating robust and highly accessible correlated phases.

Polytype switching by super-lubricant van der Waals cavity arrays

Expanding the performance of field-effect devices is a key challenge of the ever-growing chip industry at the core of current technologies1. Non-volatile multiferroic transistors that control atomic movements rather than purely electronic distribution are highly desired2. Recently, a field-effect control over structural transitions was achieved in commensurate stacking configurations of honeycomb van der Waals (vdW) polytypes by sliding boundary strips between oppositely polarized domains3-6. This ferroelectric hysteretic response, however, relied on pre-existing dislocation strips between relatively large micron-scale domains, severely limiting practical implementations3,7,8. Here we report the robust electric switching of single-domain polytypes in nanometre-scale islands embedded in super-lubricant vdW arrays. We etch cavities into a thin layered spacer and then encapsulate it with functional flakes. The flakes above/under the lattice-mismatched spacer sag and touch at each cavity to form islands of commensurate and metastable polytype configurations. By imaging the polarization of the polytypes, we observe nucleation and annihilation of boundary strips and geometry-adaptable ferroelectric hysteresis loops. Using mechanical stress, we further control the position of boundary strips, modify marginal twist angles and nucleate patterns of polar domain. This super-lubricant arrays of polytype (SLAP) concept suggests 'slidetronics' device applications such as elastic-coupled neuromorphic memory cells and non-volatile multiferroic tunnelling transistors and programmable response by designing the size, shape and symmetry of the islands and of the arrays9.

Electrically Switching Ferroelectric Order in 3R-MoS2 Layers

Transition metal dichalcogenides (TMDs) with rhombohedral (3R) stacking order are excellent platforms to realize multiferroelectricity. In this work, we demonstrate the electrical switching of ferroelectric orders in bilayer, trilayer, and tetralayer 3R-MoS2 dual-gate devices by examining their reflection and photoluminescence (PL) responses under sweeping out-of-plane electric fields. We observe sharp shifts in excitonic spectra at different critical fields with pronounced hysteresis. These phenomena are attributed to distinct interlayer polarizations resulting from specific lateral displacements between the layers, with each configuration yielding a unique ferroelectric state. Our findings indicate two, three, and four ferroelectric regimes for bilayer, trilayer, and tetralayer structures, respectively, in agreement with theoretical prediction. Moreover, each polarization state can be stabilized at zero applied electric field. The tunable ferroelectric phases of these multilayers pave the way for innovative applications in non-volatile memory, logic circuits, and optoelectronic devices.

Nonlinear optics of graphitic carbon allotropes: from 0D to 3D

The dimensionality of materials fundamentally influences their electronic and optical properties, presenting a complex interplay with nonlinear optical (NLO) characteristics that remains largely unexplored. In this review, we focus on the influence of dimensionality on the NLO properties of graphitic allotropes, ranging from 0D fullerenes, 1D carbon nanotubes, and 2D graphene, to 3D graphite, all of which share a consistent sp2 hybridized chemical bonding structure. We examine the distinct physical and NLO properties across these dimensions, underscoring the profound impact of dimensionality. Notably, dimension-specific physical phenomena, such as Luttinger liquid in 1D and Landau quantization in 2D, play a significant role in shaping NLO phenomena. Finally, we explore the promising potential of NLO properties in systems with mixed dimensionalities, setting the stage for future breakthroughs and innovative applications.

Anomalous photovoltaics in Janus MoSSe monolayers

The anomalous photovoltaic effect (APE) in polar crystals is a promising avenue for overcoming the energy conversion efficiency limits of conventional photoelectric devices utilizing p-n junction architectures. To facilitate effective photocarrier separation and enhance the APE, polar materials need to be thinned down to maximize the depolarization field. Here, we demonstrate Janus MoSSe monolayers (~0.67 nm thick) with strong spontaneous photocurrent generation. A photoresponsivity up to 3 mA/W, with ~ 1% external quantum efficiency and ultrafast photoresponse (~50 ps) were observed in the MoSSe device. Moreover, unlike conventional 2D materials that require careful twist alignment, the photovoltage can be further scaled up by simply stacking the MoSSe layers without the need for specific control on interlayer twist angles. Our work paves the way for the development of high-performance, flexible, and compact photovoltaics and optoelectronics with atomically engineered Janus polar materials.

Superconductivity in twisted bilayer WSe2

Moiré materials have enabled the realization of flat electron bands and quantum phases that are driven by the strong correlations associated with flat bands1-4. Superconductivity has been observed, but only in graphene moiré materials5-9. The absence of robust superconductivity in moiré materials beyond graphene, such as semiconductor moiré materials4, has remained a mystery and challenged our current understanding of superconductivity in flat bands. Here we report the observation of robust superconductivity in both 3.5° and 3.65° twisted bilayer tungsten diselenide (WSe2), which hosts a hexagonal moiré lattice10,11. Superconductivity emerges near half-band filling and zero external displacement fields. The optimal superconducting transition temperature is about 200 mK in both cases and constitutes about 1-2% of the effective Fermi temperature; the latter is comparable to the value in high-temperature cuprate superconductors12 and suggests strong pairing. The superconductor borders on two distinct metals below and above half-band filling; it undergoes a continuous transition to a correlated insulator by tuning the external displacement field. The observed superconductivity on the verge of Coulomb-induced charge localization suggests roots in strong electron correlations12,13.

3D Crystal Construction by Single-Crystal 2D Material Supercell Multiplying

2D stacking presents a promising avenue for creating periodic superstructures that unveil novel physical phenomena. While extensive research has focused on lateral 2D material superstructures formed through composition modulation and twisted moiré structures, the exploration of vertical periodicity in 2D material superstructures remains limited. Although weak van der Waals interfaces enable layer-by-layer vertical stacking, traditional methods struggle to control in-plane crystal orientation over large areas, and the vertical dimension is constrained by unscalable, low-throughput processes, preventing the achievement of global order structures. In this study, a supercell multiplying approach is introduced that enables high-throughput construction of 3D superstructures on a macroscopic scale, utilizing artificially stacked single-crystalline 2D multilayers as foundational repeating units. By employing wafer-scale single-crystalline 2D materials and referencing the crystal orientation of substrates, the method ensures precise alignment of crystal orientation within and across each supercell, thereby achieving controllable periodicity along all three axes. A centimeter-scale 3R-MoS₂ crystal is successfully constructed, comprising over 200 monolayers of single-crystalline MoS₂, through a bottom-up stacking process. Additionally, the approach accommodates the integration of amorphous oxide, enabling the assembly of 3D non-linear optical crystals with quasi-phase matching. This method paves the way for the bottom-up construction of macroscopic artificial 3D crystals with atomic plane precision, enabling tailored optical, electrical, and thermal properties and advancing the development of novel artificial materials and high-performance applications.

Superconductivity in 5.0° twisted bilayer WSe2

The discovery of superconductivity in twisted bilayer and trilayer graphene1-5 has generated tremendous interest. The key feature of these systems is an interplay between interlayer coupling and a moiré superlattice that gives rise to low-energy flat bands with strong correlations6. Flat bands can also be induced by moiré patterns in lattice-mismatched and/or twisted heterostructures of other two-dimensional materials, such as transition metal dichalcogenides (TMDs)7,8. Although a wide range of correlated phenomena have indeed been observed in moiré TMDs9-19, robust demonstration of superconductivity has remained absent9. Here we report superconductivity in 5.0° twisted bilayer WSe2 with a maximum critical temperature of 426 mK. The superconducting state appears in a limited region of displacement field and density that is adjacent to a metallic state with a Fermi surface reconstruction believed to arise from AFM order20. A sharp boundary is observed between the superconducting and magnetic phases at low temperature, reminiscent of spin fluctuation-mediated superconductivity21. Our results establish that moiré flat-band superconductivity extends beyond graphene structures. Material properties that are absent in graphene but intrinsic among TMDs, such as a native band gap, large spin-orbit coupling, spin-valley locking and magnetism, offer the possibility of accessing a broader superconducting parameter space than graphene-only structures.

Extended quantum anomalous Hall states in graphene/hBN moiré superlattices

Electrons in topological flat bands can form new topological states driven by correlation effects. The pentalayer rhombohedral graphene/hexagonal boron nitride (hBN) moiré superlattice was shown to host fractional quantum anomalous Hall effect (FQAHE) at approximately 400 mK (ref. 1), triggering discussions around the underlying mechanism and role of moiré effects2-6. In particular, new electron crystal states with non-trivial topology have been proposed3,4,7-15. Here we report electrical transport measurements in rhombohedral pentalayer and tetralayer graphene/hBN moiré superlattices at electronic temperatures down to below 40 mK. We observed two more fractional quantum anomalous Hall (FQAH) states and smaller Rxx values in pentalayer devices than those previously reported. In the new tetralayer device, we observed FQAHE at moiré filling factors v = 3/5 and 2/3. With a small current at the base temperature, we observed a new extended quantum anomalous Hall (EQAH) state and magnetic hysteresis, where Rxy = h/e2 and vanishing Rxx spans a wide range of v from 0.5 to 1.3. At increased temperature or current, EQAH states disappear and partially transition into the FQAH liquid16-18. Furthermore, we observed displacement field-induced quantum phase transitions from the EQAH states to the Fermi liquid, FQAH liquid and the likely composite Fermi liquid. Our observations established a new topological phase of electrons with quantized Hall resistance at zero magnetic field and enriched the emergent quantum phenomena in materials with topological flat bands.

Twisted Bilayer MoS2 under Electric Fields: A System with Tunable Symmetry

Gate voltages take full advantage of 2D systems, making it possible to explore novel states of matter by controlling their electron concentration or applying perpendicular electric fields. Here, we study the electronic properties of small-angle twisted bilayer MoS2 under a strong electric field. We show that transport across one of its constituent layers can be effectively regarded as a two-dimensional electron gas under a nanoscale potential. We find that the band structure of such a system is reconstructed following two fundamentally different symmetries depending on the orientation of the external electric field, namely, hexagonal or honeycomb. By studying this system under magnetic fields, we demonstrate that this duality not only translates into two different transport responses but also results in having two different Hofstadter's spectra. Our work opens up a new route for the creation of controllable artificial superlattices in van der Waals heterostructures.

Topological Superconductivity in Heavily Doped Single-Layer Graphene

The existence of superconductivity (SC) appears to be established in both twisted and nontwisted graphene multilayers. However, whether their building block, single-layer graphene (SLG), can also host SC remains an open question. Earlier theoretical works predicted that SLG could become a chiral d-wave superconductor driven by electronic interactions when doped to its van Hove singularity, but questions such as whether the d-wave SC survives the strong band renormalizations seen in experiments, its robustness against the source of doping, or if it will occur at any reasonable critical temperature (Tc) have remained difficult to answer, in part due to uncertainties in model parameters. Furthermore, doping of graphene beyond its van Hove singularity remained experimentally challenging and was not demonstrated until recently. In this study, we n dope SLG past the van Hove singularity by employing Tb intercalation and derive structural models from angle-resolved photoemission spectroscopy measurements. We adopt a reliable numerical framework based on a random-phase approximation technique to investigate the emergence of unconventional SC in the heavily doped monolayer. We predict that robust d + id topological SC could arise in SLG doped by Tb, with a Tc up to 600 mK. We also employ first-principles calculations to investigate the possibility of realizing d-wave SC with other dopants, such as Li or Cs. We find that dopants that change the lattice symmetry of SLG are detrimental to the d-wave state. The stability of the d-wave SC predicted here in Tb-doped SLG could provide a valuable insight for guiding future experimental efforts aimed at exploring topological superconductivity in monolayer graphene.

Topological flat bands in a family of multilayer graphene moiré lattices

Moiré materials host a wealth of intertwined correlated and topological states of matter, all arising from flat electronic bands with nontrivial quantum geometry. A prominent example is the family of alternating-twist magic-angle graphene stacks, which exhibit symmetry-broken states at rational fillings of the moiré band and superconductivity close to half filling. Here, we introduce a second family of twisted graphene multilayers made up of twisted sheets of M- and N-layer Bernal-stacked graphene flakes. Calculations indicate that applying an electric displacement field isolates a flat and topological moiré conduction band that is primarily localized to a single graphene sheet below the moiré interface. Phenomenologically, the result is a striking similarity in the hierarchies of symmetry-broken phases across this family of twisted graphene multilayers. Our results show that this family of structures offers promising new opportunities for the discovery of exotic new correlated and topological phenomena, enabled by using the layer number to fine tune the flat moiré band and its screening environment.

Magnonic superconductivity

We uncover a superconducting state with partial spin polarization induced by a magnetic field. This state, which we call "magnonic superconductor," lacks a conventional pairing order parameter but is characterized instead by a composite order parameter that represents the binding of electron pairs and magnons. We rigorously demonstrate the existence of magnonic superconductivity with high transition temperature in one-dimensional and two-dimensional Hubbard models with repulsive interaction. We further show that magnonic Cooper pairs can attract to form higher-charge bound states, which can give rise to charge-6e superconductivity.

On-Chip Terahertz Spectroscopy for Dual-Gated van der Waals Heterostructures at Cryogenic Temperatures

Van der Waals heterostructures have emerged as a versatile platform to study correlated and topological electron physics. Spectroscopy experiments in the THz regime are crucial since the energy of THz photons matches that of relevant excitations and charge dynamics. However, their micrometer size and complex (dual-)gated structures have challenged such measurements. Here, we demonstrate on-chip THz spectroscopy on a dual-gated bilayer graphene device at liquid helium temperature. To avoid unwanted THz absorption by metallic gates, we developed a scheme of operation by combining semiconducting gates and optically controlled gating. This allows us to measure the clean THz response of graphene without being affected by the gates. We observed the THz signatures of electric-field-induced bandgap opening at the charge neutrality. We measured Drude conductivities at varied charge densities and extracted key parameters including effective masses and scattering rates. This work paves the way for studying novel emergent phenomena in dual-gated two-dimensional materials.

Suppression of symmetry-breaking correlated insulators in a rhombohedral trilayer graphene superlattice

Counterintuitive temperature dependence of isospin flavor polarization has recently been found in twisted bilayer graphene, where unpolarized electrons in a Fermi liquid become a spin-valley polarized insulator upon heating. So far, the effect has been limited to v = +/-1 (one electron/hole per superlattice cell), leaving open questions such as whether it is a general property of symmetry-breaking electronic phases. Here, by studying a rhombohedral trilayer graphene/boron nitride moiré superlattice, we report that at v = -3 a resistive peak emerges at elevated temperatures or in parallel magnetic fields. Concomitantly, the Hall carrier density tends to reset at the integer filling, signaling spin-valley flavor symmetry breaking. These phenomena can also be observed at v = -1 and -2 when the displacement field is large enough to suppress correlated insulators at low temperatures. Our results greatly expand the scope for observing the counterintuitive temperature dependence of flavor polarization, i.e., the regimes proximal to symmetry-breaking phases where the flavor polarization order strongly fluctuates, encouraging more experimental and theoretical exploration of isospin flavor polarization dynamics in flat-band moiré systems.

Correlated topological flat bands in rhombohedral graphite

Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here, we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon in situ electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states.

Designing Moiré Patterns by Shearing

We analyze the elastic properties, structural effects, and low-energy physics of a sheared nanoribbon placed on top of graphene, which creates a gradually changing moiré pattern. By means of a classical elastic model we derive the strains in the ribbon and we obtain its electronic energy spectrum with a scaled tight-binding model. The size of the sheared region is determined by the balance between elastic and van der Waals energy, and different regimes are identified. Near the clamped edge, moderate strains and small twist angles lead to one-dimensional channels. Near the sheared edge, a long region behaves like magic angle twisted bilayer graphene (TBG), showing a sharp peak in the density of states, mostly isolated from the rest of the spectrum. We also calculate the band topology along the ribbon and we find that it is stable for large intervals of strains and twist angles. Together with the experimental observations, these results show that the sheared nanoribbon geometry is ideal for exploring superconductivity and correlated phases in TBG in the very sought-after regime of ultralow twist angle disorder.

Engineering band structures of two-dimensional materials with remote moiré ferroelectricity

The stacking order and twist angle provide abundant opportunities for engineering band structures of two-dimensional materials, including the formation of moiré bands, flat bands, and topologically nontrivial bands. The inversion symmetry breaking in rhombohedral-stacked transitional metal dichalcogenides endows them with an interfacial ferroelectricity associated with an out-of-plane electric polarization. By utilizing twist angle as a knob to construct rhombohedral-stacked transitional metal dichalcogenides, antiferroelectric domain networks with alternating out-of-plane polarization can be generated. Here, we demonstrate that such spatially periodic ferroelectric polarizations in parallel-stacked twisted WSe2 can imprint their moiré potential onto a remote bilayer graphene. This remote moiré potential gives rise to pronounced satellite resistance peaks besides the charge-neutrality point in graphene, which are tunable by the twist angle of WSe2. Our observations of ferroelectric hysteresis at finite displacement fields suggest the moiré is delivered by a long-range electrostatic potential. The constructed superlattices by moiré ferroelectricity represent a highly flexible approach, as they involve the separation of the moiré construction layer from the electronic transport layer. This remote moiré is identified as a weak potential and can coexist with conventional moiré. Our results offer a comprehensive strategy for engineering band structures and properties of two-dimensional materials by utilizing moiré ferroelectricity.

Antiscreening and Nonequilibrium Layer Electric Phases in Graphene Multilayers

Screening is a ubiquitous phenomenon through which the polarization of bound or mobile charges tends to reduce the strengths of electric fields inside materials. Here, we show how photoexcitation can be used as a knob to transform conventional out-of-plane screening into antiscreening-the amplification of electric fields-in multilayer graphene. We find that, by varying the photoexcitation intensity, multiple nonequilibrium screening regimes can be accessed, including near-zero screening, antiscreening, and overscreening (reversing electric fields). Strikingly, at modest continuous wave photoexcitation intensities, the nonequilibrium polarization states become multistable, hosting light-induced ferroelectriclike steady states with nonvanishing out-of-plane polarization (and band gaps) even in the absence of an externally applied displacement field in nominally inversion symmetric stacks. This rich phenomenology reveals a novel paradigm of dynamical quantum matter that we expect will enable a variety of nonequilibrium broken symmetry phases.

Infrared single-photon detection with superconducting magic-angle twisted bilayer graphene

The moiré superconductor magic-angle twisted bilayer graphene (MATBG) shows exceptional properties, with an electron (hole) ensemble of only ~1011 carriers per square centimeter, which is five orders of magnitude lower than traditional superconductors (SCs). This results in an ultralow electronic heat capacity and a large kinetic inductance of this truly two-dimensional SC, providing record-breaking parameters for quantum sensing applications, specifically thermal sensing and single-photon detection. To fully exploit these unique superconducting properties for quantum sensing, here, we demonstrate a proof-of-principle experiment to detect single near-infrared photons by voltage biasing an MATBG device near its superconducting phase transition. We observe complete destruction of the SC state upon absorption of a single infrared photon even in a 16-square micrometer device, showcasing exceptional sensitivity. Our work offers insights into the MATBG-photon interaction and demonstrates pathways to use moiré superconductors as an exciting platform for revolutionary quantum devices and sensors.

Van Hove Singularity-Enhanced Raman Scattering and Photocurrent Generation in Twisted Monolayer-Bilayer Graphene

Twisted monolayer-bilayer graphene (TMBG) has recently emerged as an exciting platform for exploring correlated physics and topological states with rich tunability. Strong light-matter interaction was realized in twisted bilayer graphene, boosting the development of broadband graphene photodetectors from the visible to infrared spectrum with high responsivity. Extending this approach to the case of TMBG will help design advanced quantum nano-optoelectronic devices because of the reduced symmetry of the system. Here, we observe the formation of van Hove singularities (VHSs) in TMBG by monitoring the significant enhancement of the Raman intensity of the G peak and the intensity ratio of G and 2D peaks. The strong interlayer coupling also leads to the appearance of twist-angle-dependent Raman R and R' peaks in TMBG. Furthermore, the constructed graphene photodetectors from 13.5°-TMBG show significantly enhanced photoresponsivity (∼31 folds of monolayer graphene and ∼15 folds of trilayer graphene) when the energy of incident photons matches the interval energy between the two VHSs in the conduction and valence bands. Our findings establish TMBG as a tunable platform for investigating the light-matter interaction and designing high-performance graphene photodetectors with combined high responsivity and high selectivity.

Geometric Inhibition of Superflow in Single-Layer Graphene Suggests a Staggered-Flux Superconductivity in Bilayer and Trilayer Graphene

In great contrast to the numerous discoveries of superconductivity in layer-stacked graphene systems, the absence of superconductivity in the simplest monolayer graphene remains quite puzzling. Here, through realistic computation of the electronic structure, we identify a systematic trend that superconductivity emerges only upon alteration of the low-energy electronic lattice from the underlying honeycomb atomic structure. We then demonstrate that this inhibition can result from geometric frustration of the bond lattice that disables the quantum phase coherence of the order parameter residing on it. In comparison, upon deviation from the honeycomb lattice, relief of geometric frustration allows robust superfluidity with nontrivial spatial structures. For the specific examples of bilayer and trilayer graphene under an external electric field, such a bond-centered order parameter would develop superfluidity with staggered flux that breaks the time-reversal symmetry. Our study also suggests the possible realization of the long-sought superconductivity in single-layer graphene via the application of unidirectional strain.

Interaction-Driven Quasi-Insulating Ground States of Gapped Electron-Doped Bilayer Graphene

Bernal bilayer graphene has recently been discovered to exhibit a wide range of unique ordered phases resulting from interaction-driven effects and encompassing spin and valley magnetism, correlated insulators, correlated metals, and superconductivity. This Letter reports on a novel family of correlated phases characterized by spin and valley ordering, distinct from those reported previously. These phases emerge in electron-doped bilayer graphene where the energy bands are exceptionally flat, manifested through an intriguing nonlinear current-bias behavior that occurs at the onset of the phases and is accompanied by an insulating temperature dependence. These characteristics align with the presence of charge- or spin-density-wave states that open a gap on a portion of the Fermi surface or fully gapped Wigner crystals, resulting in an exceptionally intricate phase diagram.

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.

Evolution of superconductivity in twisted graphene multilayers

The group of moiré graphene superconductors keeps growing, and by now it contains twisted graphene multilayers as well as untwisted stacks. We analyze here the contribution of long-range charge fluctuations in the superconductivity of twisted double bilayers and helical trilayers, and compare the results to twisted bilayer graphene. A diagrammatic approach which depends on a few, well-known parameters is used. We find that the critical temperature and the order parameter differ significantly between twisted double bilayers and helical trilayers on one hand, and twisted bilayer graphene on the other. This trend, consistent with experiments, can be associated with the role played by moiré Umklapp processes in the different systems.

Fast and broadband spatial-photoresistance modulation in graphene-silicon heterojunctions

Different types of devices with modulable resistance are attractive for the significant potential applications such as sensors, information storage, computation, etc. Although extensive research has been reported on resistance effects, there is still a need for exploring new mechanisms that offer advantages of low power consumption, high sensitivity, and long-term stability. Here, we report a graphene-Si based spatial-dependence photo-rheostat (SDPR), which enables bipolar resistance modulation in the range of 5 mm with a resistance sensitivity exceeding 1,000 Ω/mm at operating wavelengths from visible to near infrared band (1,550 nm). Especially, at ultra-low energy consumption, the device can achieve modulation of even 5 orders of magnitude of resistance and response speed up to 10 kHz. A theoretical model based on carrier dynamics is established to reveal the diffusion and drift of carriers as a mechanism explaining such experimental phenomenon. This work provides a new avenue to modulate resistance at low power consumption as novel opto-potentiometers in various photoelectric applications.

Enhanced Quantum Metric due to Vacancies in Graphene

Random vacancies in a graphene monolayer induce defect states that are known to form a narrow impurity band centered around zero energy at half filling. We use a space-resolved formulation of the quantum metric and establish a strong enhancement of the electronic correlations in this impurity band. The enhancement is primarily due to strong correlations between pairs of vacancies situated on different sublattices at anomalously large spatial distances. We trace the strong enhancement to both the multifractal vacancy wave functions, which ties the system exactly at the Anderson insulator transition for all defect concentrations, and preserving the chiral symmetry.

Inversion Symmetry-Broken Tetralayer Graphene Probed by Second-Harmonic Generation

Stacking orders provide a unique way to tune the properties of two-dimensional materials. Recently, ABCB-stacked tetralayer graphene has been predicted to possess atypical elemental ferroelectricity arising from its symmetry breaking but has been experimentally explored very little. Here, we observe pronounced nonlinear optical second-harmonic generation (SHG) in ABCB-stacked tetralayer graphene while absent in both ABAB- and ABCA-stacked allotropes. Our results provide direct evidence of symmetry breaking in ABCB-stacked tetralayer graphene. The remarkable contrast in the SHG spectra of tetralayer graphene allows straightforward identification of ABCB domains from the other two kinds of stacking order and facilitates the characterization of their crystalline orientation. The employed SHG technique serves as a convenient tool for exploring the intriguing physics and novel nonlinear optics in ABCB-stacked graphene, where spontaneous polarization and intrinsically gapped flat bands coexist. Our results establish ABCB-stacked graphene as a unique platform for studying the rare ferroelectricity in noncentrosymmetric elemental structures.

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.

Nematic Metal in a Multivalley Electron Gas: Variational Monte Carlo Analysis and Application to AlAs

The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with C_{4} (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Electrons in our model interact via Coulomb repulsion, screened by distant metallic gates. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground state. Our results are of direct relevance to the recently discovered "nematic" state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, m_{x}/m_{y}≈5.2, we obtain a transition from an anisotropic metal to a valley-polarized metal at r_{s}≈12 (where r_{s} is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.

Van Hove Singularity and Enhanced Superconductivity in Ca-Intercalated Bilayer Graphene Induced by Confinement Epitaxy

We demonstrate the impact of high-density calcium introduction into Ca-intercalated bilayer graphene on a SiC substrate, wherein a metallic layer of Ca has been identified at the interface. We have discerned that the additional Ca layer engenders a free-electron-like band, which subsequently hybridizes with a Dirac band, leading to the emergence of a van Hove singularity. Coinciding with this, there is an increase in the critical temperature for superconductivity. These findings allude to the manifestation of Ca-driven confinement epitaxy, augmenting superconductivity through the enhancement of attractive interactions in a pair of electron and hole bands with flat dispersion around the Fermi level.

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.

Probing the tunable multi-cone band structure in Bernal bilayer graphene

Bernal bilayer graphene (BLG) offers a highly flexible platform for tuning the band structure, featuring two distinct regimes. One is a tunable band gap induced by large displacement fields. Another is a gapless metallic band occurring at low fields, featuring rich fine structure consisting of four linearly dispersing Dirac cones and van Hove singularities. Even though BLG has been extensively studied experimentally, the evidence of this band structure is still elusive, likely due to insufficient energy resolution. Here, we use Landau levels as markers of the energy dispersion and analyze the Landau level spectrum in a regime where the cyclotron orbits of electrons or holes in momentum space are small enough to resolve the distinct mini Dirac cones. We identify the presence of four Dirac cones and map out topological transitions induced by displacement field. By clarifying the low-energy properties of BLG bands, these findings provide a valuable addition to the toolkit for graphene electronics.

Layer-polarized ferromagnetism in rhombohedral multilayer graphene

Flat-band systems with strongly correlated electrons can exhibit a variety of phenomena, such as correlated insulating and topological states, unconventional superconductivity, and ferromagnetism. Rhombohedral multilayer graphene has recently emerged as a promising platform for investigating exotic quantum states due to its hosting of topologically protected surface flat bands at low energy, which have a layer-dependent energy dispersion. However, the complex relationship between the surface flat bands and the highly dispersive high-energy bands makes it difficult to study correlated surface states. In this study, we introduce moiré superlattices as a method to isolate the surface flat bands of rhombohedral multilayer graphene. The observed pronounced screening effects in the moiré potential-modulated rhombohedral multilayer graphene indicate that the two surface states are electronically decoupled. The flat bands that are isolated promote correlated surface states in areas that are distant from the charge neutrality points. Notably, we observe tunable layer-polarized ferromagnetism, which is evidenced by a hysteretic anomalous Hall effect. This is achieved by polarizing the surface states with finite displacement fields.

Electrical Control of Spin and Valley in Spin-Orbit Coupled Graphene Multilayers

Electrical control of magnetism has been a major technological pursuit of the spintronics community, owing to its far-reaching implications for data storage and transmission. Here, we propose and analyze a new mechanism for electrical switching of isospin, using chiral-stacked graphene multilayers, such as Bernal bilayer graphene or rhombohedral trilayer graphene, encapsulated by transition metal dichalcogenide (TMD) substrates. Leveraging the proximity-induced spin-orbit coupling from the TMD, we demonstrate electrical switching of correlation-induced spin and/or valley polarization, by reversing a perpendicular displacement field or the chemical potential. We substantiate our proposal with both analytical arguments and self-consistent Hartree-Fock numerics. Finally, we illustrate how the relative alignment of the TMDs, together with the top and bottom gate voltages, can be used to selectively switch distinct isospin flavors, putting forward correlated Van der Waals heterostructures as a promising platform for spintronics and valleytronics.

Local atomic stacking and symmetry in twisted graphene trilayers

Moiré superlattices formed by twisting trilayers of graphene are a useful model for studying correlated electron behaviour and offer several advantages over their formative bilayer analogues, including a more diverse collection of correlated phases and more robust superconductivity. Spontaneous structural relaxation alters the behaviour of moiré superlattices considerably and has been suggested to play an important role in the relative stability of superconductivity in trilayers. Here we use an interferometric four-dimensional scanning transmission electron microscopy approach to directly probe the local graphene layer alignment over a wide range of trilayer graphene structures. Our results inform a thorough understanding of how reconstruction modulates the local lattice symmetries crucial for establishing correlated phases in twisted graphene trilayers, evincing a relaxed structure that is markedly different from that proposed previously.

Electric-Field-Tunable Edge Transport in Bernal-Stacked Trilayer Graphene

This Letter presents a nonlocal study on the electric-field-tunable edge transport in h-BN-encapsulated dual-gated Bernal-stacked (ABA) trilayer graphene across various displacement fields (D) and temperatures (T). Our measurements revealed that the nonlocal resistance (R_{NL}) surpassed the expected classical Ohmic contribution by a factor of at least 2 orders of magnitude. Through scaling analysis, we found that the nonlocal resistance scales linearly with the local resistance (R_{L}) only when the D exceeds a critical value of ∼0.2  V/nm. Additionally, we observed that the scaling exponent remains constant at unity for temperatures below the bulk-band gap energy threshold (T<25  K). Further, the value of R_{NL} decreases in a linear fashion as the channel length (L) increases. These experimental findings provide evidence for edge-mediated charge transport in ABA trilayer graphene under the influence of a finite displacement field. Furthermore, our theoretical calculations support these results by demonstrating the emergence of dispersive edge modes within the bulk-band gap energy range when a sufficient displacement field is applied.

Electron/infrared-phonon coupling in ABC trilayer graphene

Stacking order plays a crucial role in determining the crystal symmetry and has significant impacts on electronic, optical, magnetic, and topological properties. Electron-phonon coupling, which is central to a wide range of intriguing quantum phenomena, is expected to be intricately connected with stacking order. Understanding the stacking order-dependent electron-phonon coupling is essential for understanding peculiar physical phenomena associated with electron-phonon coupling, such as superconductivity and charge density waves. In this study, we investigate the effect of stacking order on electron-infrared phonon coupling in graphene trilayers. By using gate-tunable Raman spectroscopy and excitation frequency-dependent near-field infrared nanoscopy, we show that rhombohedral ABC-stacked trilayer graphene has a significant electron-infrared phonon coupling strength. Our findings provide novel insights into the superconductivity and other fundamental physical properties of rhombohedral ABC-stacked trilayer graphene, and can enable nondestructive and high-throughput imaging of trilayer graphene stacking order using Raman scattering.

Stoner Ferromagnetism in a Momentum-Confined Interacting 2D Electron Gas

In this work we investigate the ground state of a momentum-confined interacting 2D electron gas, a momentum-space analog of an infinite quantum well. The study is performed by combining analytical results with a numerical exact diagonalization procedure. We find a ferromagnetic ground state near a particular electron density and for a range of effective electron (or hole) masses. We argue that this observation may be relevant to the generalized Stoner ferromagnetism recently observed in multilayer graphene systems. The collective magnon excitations exhibit a linear dispersion, which originates from a diverging spin stiffness.

Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene

Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n = 0 and displacement field D = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a magnetic field of around 1 T. At high D and n, we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering.

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.

Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene

Interactions among charge carriers in graphene can lead to the spontaneous breaking of multiple degeneracies. When increasing the number of graphene layers following rhombohedral stacking, the dominant role of Coulomb interactions becomes pronounced due to the significant reduction in kinetic energy. In this study, we employ phonon-polariton-assisted near-field infrared imaging to determine the stacking orders of tetralayer graphene devices. Through quantum transport measurements, we observe a range of spontaneous broken-symmetry states and their transitions, which can be finely tuned by carrier density n and electric displacement field D. Specifically, we observe a layer-antiferromagnetic insulator at n = D = 0 with a gap of approximately 15 meV. Increasing D allows for a continuous phase transition from a layer-antiferromagnetic insulator to a layer-polarized insulator. By simultaneously tuning n and D, we observe isospin-polarized metals, including spin-valley-polarized and spin-polarized metals. These transitions are associated with changes in the Fermi surface topology and are consistent with the Stoner criteria. Our findings highlight the efficient fabrication of specially stacked multilayer graphene devices and demonstrate that crystalline multilayer graphene is an ideal platform for investigating a wide range of broken symmetries driven by Coulomb interactions.