Showing papers on "Bilayer graphene published in 2020"

Tunable correlated states and spin-polarized phases in twisted bilayer-bilayer graphene.

Abstract: The recent discovery of correlated insulator states and superconductivity in magic-angle twisted bilayer graphene1,2 has enabled the experimental investigation of electronic correlations in tunable flat-band systems realized in twisted van der Waals heterostructures3-6. This novel twist angle degree of freedom and control should be generalizable to other two-dimensional systems, which may exhibit similar correlated physics behaviour, and could enable techniques to tune and control the strength of electron-electron interactions. Here we report a highly tunable correlated system based on small-angle twisted bilayer-bilayer graphene (TBBG), consisting of two rotated sheets of Bernal-stacked bilayer graphene. We find that TBBG exhibits a rich phase diagram, with tunable correlated insulator states that are highly sensitive to both the twist angle and the application of an electric displacement field, the latter reflecting the inherent polarizability of Bernal-stacked bilayer graphene7,8. The correlated insulator states can be switched on and off by the displacement field at all integer electron fillings of the moire unit cell. The response of these correlated states to magnetic fields suggests evidence of spin-polarized ground states, in stark contrast to magic-angle twisted bilayer graphene. Furthermore, in the regime of lower twist angles, TBBG shows multiple sets of flat bands near charge neutrality, resulting in numerous correlated states corresponding to half-filling of each of these flat bands, all of which are tunable by the displacement field as well. Our results could enable the exploration of twist-angle- and electric-field-controlled correlated phases of matter in multi-flat-band twisted superlattices.

Tunable spin-polarized correlated states in twisted double bilayer graphene

Abstract: Reducing the energy bandwidth of electrons in a lattice below the long-range Coulomb interaction energy promotes correlation effects. Moire superlattices—which are created by stacking van der Waals heterostructures with a controlled twist angle1–3—enable the engineering of electron band structure. Exotic quantum phases can emerge in an engineered moire flat band. The recent discovery of correlated insulator states, superconductivity and the quantum anomalous Hall effect in the flat band of magic-angle twisted bilayer graphene4–8 has sparked the exploration of correlated electron states in other moire systems9–11. The electronic properties of van der Waals moire superlattices can further be tuned by adjusting the interlayer coupling6 or the band structure of constituent layers9. Here, using van der Waals heterostructures of twisted double bilayer graphene (TDBG), we demonstrate a flat electron band that is tunable by perpendicular electric fields in a range of twist angles. Similarly to magic-angle twisted bilayer graphene, TDBG shows energy gaps at the half- and quarter-filled flat bands, indicating the emergence of correlated insulator states. We find that the gaps of these insulator states increase with in-plane magnetic field, suggesting a ferromagnetic order. On doping the half-filled insulator, a sudden drop in resistivity is observed with decreasing temperature. This critical behaviour is confined to a small area in the density–electric-field plane, and is attributed to a phase transition from a normal metal to a spin-polarized correlated state. The discovery of spin-polarized correlated states in electric-field-tunable TDBG provides a new route to engineering interaction-driven quantum phases. Twisted double bilayer graphene devices show tunable spin-polarized correlated states that are sensitive to electric and magnetic fields, providing further insights into correlated states in two-dimensional moire materials.

Intrinsic quantized anomalous Hall effect in a moiré heterostructure

Abstract: The quantum anomalous Hall (QAH) effect combines topology and magnetism to produce precisely quantized Hall resistance at zero magnetic field. We report the observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride. The effect is driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moire miniband with Chern number C = 1. In contrast to magnetically doped systems, the measured transport energy gap is larger than the Curie temperature for magnetic ordering, and quantization to within 0.1% of the von Klitzing constant persists to temperatures of several kelvin at zero magnetic field. Electrical currents as small as 1 nanoampere controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory.

Graphene bilayers with a twist

Abstract: Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive to carrier density and to controllable environmental factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena, magic-angle twisted bilayer graphene hosts superconductivity, interaction-induced insulating states, magnetism, electronic nematicity, linear-in-temperature low-temperature resistivity and quantized anomalous Hall states. We highlight some key research results in this field, point to important questions that remain open and comment on the place of magic-angle twisted bilayer graphene in the strongly correlated quantum matter world.

Bandgap engineering of two-dimensional semiconductor materials

Abstract: Semiconductors are the basis of many vital technologies such as electronics, computing, communications, optoelectronics, and sensing. Modern semiconductor technology can trace its origins to the invention of the point contact transistor in 1947. This demonstration paved the way for the development of discrete and integrated semiconductor devices and circuits that has helped to build a modern society where semiconductors are ubiquitous components of everyday life. A key property that determines the semiconductor electrical and optical properties is the bandgap. Beyond graphene, recently discovered two-dimensional (2D) materials possess semiconducting bandgaps ranging from the terahertz and mid-infrared in bilayer graphene and black phosphorus, visible in transition metal dichalcogenides, to the ultraviolet in hexagonal boron nitride. In particular, these 2D materials were demonstrated to exhibit highly tunable bandgaps, achieved via the control of layers number, heterostructuring, strain engineering, chemical doping, alloying, intercalation, substrate engineering, as well as an external electric field. We provide a review of the basic physical principles of these various techniques on the engineering of quasi-particle and optical bandgaps, their bandgap tunability, potentials and limitations in practical realization in future 2D device technologies.

Strange metal in magic-angle graphene with near Planckian dissipation

Abstract: Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. Here we show that magic-angle bilayer graphene exhibits another hallmark of strongly correlated systems-a broad regime of T-linear resistivity above a small density-dependent crossover temperature-for a range of fillings near the correlated insulator. This behavior is reminiscent of similar behavior in other strongly correlated systems, often denoted "strange metals," such as cuprates, iron pnictides, ruthenates, and cobaltates, where the observations are at odds with expectations in a weakly interacting Fermi liquid. We also extract a transport "scattering rate," which satisfies a near Planckian form that is universally related to the ratio of (k_{B}T/ℏ). Our results establish magic-angle bilayer graphene as a highly tunable platform to investigate strange metal behavior, which could shed light on this mysterious ubiquitous phase of correlated matter.

Mapping the twist-angle disorder and Landau levels in magic-angle graphene

Abstract: The recently discovered flat electronic bands and strongly correlated and superconducting phases in magic-angle twisted bilayer graphene (MATBG)1,2 crucially depend on the interlayer twist angle, θ. Although control of the global θ with a precision of about 0.1 degrees has been demonstrated1-7, little information is available on the distribution of the local twist angles. Here we use a nanoscale on-tip scanning superconducting quantum interference device (SQUID-on-tip)8 to obtain tomographic images of the Landau levels in the quantum Hall state9 and to map the local θ variations in hexagonal boron nitride (hBN)-encapsulated MATBG devices with relative precision better than 0.002 degrees and a spatial resolution of a few moire periods. We find a correlation between the degree of θ disorder and the quality of the MATBG transport characteristics and show that even state-of-the-art devices-which exhibit correlated states, Landau fans and superconductivity-display considerable local variation in θ of up to 0.1 degrees, exhibiting substantial gradients and networks of jumps, and may contain areas with no local MATBG behaviour. We observe that the correlated states in MATBG are particularly fragile with respect to the twist-angle disorder. We also show that the gradients of θ generate large gate-tunable in-plane electric fields, unscreened even in the metallic regions, which profoundly alter the quantum Hall state by forming edge channels in the bulk of the sample and may affect the phase diagram of the correlated and superconducting states. We thus establish the importance of θ disorder as an unconventional type of disorder enabling the use of twist-angle gradients for bandstructure engineering, for realization of correlated phenomena and for gate-tunable built-in planar electric fields for device applications.

Cascade of phase transitions and Dirac revivals in magic-angle graphene.

Abstract: Twisted bilayer graphene near the magic angle1–4 exhibits rich electron-correlation physics, displaying insulating3–6, magnetic7,8 and superconducting phases4–6. The electronic bands of this system were predicted1,2 to narrow markedly9,10 near the magic angle, leading to a variety of possible symmetry-breaking ground states11–17. Here, using measurements of the local electronic compressibility, we show that these correlated phases originate from a high-energy state with an unusual sequence of band population. As carriers are added to the system, the four electronic ‘flavours’, which correspond to the spin and valley degrees of freedom, are not filled equally. Rather, they are populated through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moire lattice. At each transition, a single spin/valley flavour takes all the carriers from its partially filled peers, ‘resetting’ them to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breaking. The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state that we report here, with its strongly broken electronic flavour symmetry and revived Dirac-like electronic character, is important in the physics of magic-angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge. Local electronic compressibility measurements of magic-angle twisted bilayer graphene show that the insulating and superconducting phases of this system are both derived from a high-energy symmetry-broken state.

Cascade of electronic transitions in magic-angle twisted bilayer graphene

Abstract: Magic-angle twisted bilayer graphene exhibits a variety of electronic states, including correlated insulators1–3, superconductors2–4 and topological phases3,5,6. Understanding the microscopic mechanisms responsible for these phases requires determination of the interplay between electron–electron interactions and quantum degeneracy (the latter is due to spin and valley degrees of freedom). Signatures of strong electron–electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements7–10, and transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moire unit cell2–4. However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Here we report a cascade of transitions in the spectroscopic properties of magic-angle twisted bilayer graphene as a function of electron filling, determined using high-resolution scanning tunnelling microscopy. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moire flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions that we report here characterizes the correlated high-temperature parent phase11,12 from which various insulating and superconducting ground-state phases emerge at low temperatures in magic-angle twisted bilayer graphene. Electron–electron interactions in magic-angle twisted bilayer graphene can split usually degenerate electronic bands, giving rise to a cascade of electronic transitions revealed by spectroscopy.

Untying the insulating and superconducting orders in magic-angle graphene

Abstract: The coexistence of superconducting and correlated insulating states in magic-angle twisted bilayer graphene1–11 prompts fascinating questions about their relationship. Independent control of the microscopic mechanisms that govern these phases could help uncover their individual roles and shed light on their intricate interplay. Here we report on direct tuning of electronic interactions in this system by changing the separation distance between the graphene and a metallic screening layer12,13. We observe quenching of correlated insulators in devices with screening layer separations that are smaller than the typical Wannier orbital size of 15 nanometres and with twist angles that deviate slightly from the magic angle of 1.10 ± 0.05 degrees. Upon extinction of the insulating orders, the vacated phase space is taken over by superconducting domes that feature critical temperatures comparable to those in devices with strong insulators. In addition, we find that insulators at half-filling can reappear in small out-of-plane magnetic fields of 0.4 tesla, giving rise to quantized Hall states with a Chern number of 2. Our study suggests re-examination of the often-assumed ‘parent-and-child’ relation between the insulating and superconducting phases in moire graphene, and suggests a way of directly probing the microscopic mechanisms of superconductivity in strongly correlated systems. Tuning the electronic interactions by changing the dielectric environment of twisted bilayer graphene reveals the disappearance of the insulating states and their replacement by superconducting phases, suggesting a competition between the two phases.

Independent superconductors and correlated insulators in twisted bilayer graphene

Abstract: When two sheets of graphene are stacked on top of each other with a small twist of angle θ ≈ 1.1° between them, theory predicts the formation of a flat electronic band1,2. Experiments have shown correlated insulating, superconducting and ferromagnetic states when the flat band is partially filled3–8. The proximity of superconductivity to correlated insulators suggested a close relationship between these states, reminiscent of the cuprates where superconductivity arises by doping a Mott insulator. Here, we show that superconductivity can appear far away from the correlated insulating states. Although both superconductivity and correlated insulating behaviour are strongest near the flat-band condition, superconductivity survives to larger detuning of the angle. Our observations are consistent with a ‘competing phases’ picture in which insulators and superconductivity arise from different mechanisms. Here, it is shown that superconductivity can exist without correlated insulating states in twisted bilayer graphene devices a little away from the magic angle. This indicates the two phases compete with each other, in contrast to previous claims.

Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling

Abstract: An usual insulating behavior in twisted bilayer graphene can be explained by a symmetry breaking that arises when cells in the superlattice are filled with an even number of electrons.

Strongly correlated Chern insulators in magic-angle twisted bilayer graphene.

Abstract: Interactions between electrons and the topology of their energy bands can create unusual quantum phases of matter. Most topological electronic phases appear in systems with weak electron–electron interactions. The instances in which topological phases emerge only as a result of strong interactions are rare and mostly limited to those realized in intense magnetic fields1. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for strongly correlated topological phases2–9. Here we introduce a local spectroscopic technique using a scanning tunnelling microscope to detect a sequence of topological insulators in MATBG with Chern numbers C = ±1, ±2 and ±3, which form near filling factors of ±3, ±2 and ±1 electrons per moire unit cell, respectively, and are stabilized by modest magnetic fields. One of the phases detected here (C = +1) was previously observed when the sublattice symmetry of MATBG was intentionally broken by a hexagonal boron nitride substrate, with interactions having a secondary role9. We demonstrate that strong electron–electron interactions alone can produce not only the previously observed phase, but also other unexpected Chern insulating phases in MATBG. The full sequence of phases that we observe can be understood by postulating that strong correlations favour breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moire systems beyond those anticipated from weakly interacting models. Strong electron–electron interactions in magic-angle twisted bilayer graphene can fundamentally change the topology of the system’s flat bands, producing a hierarchy of strongly correlated topological insulators in modest magnetic fields.

Correlated states in twisted double bilayer graphene

Abstract: Electron–electron interactions play an important role in graphene and related systems and can induce exotic quantum states, especially in a stacked bilayer with a small twist angle1–7. For bilayer graphene where the two layers are twisted by the ‘magic angle’, flat band and strong many-body effects lead to correlated insulating states and superconductivity4–7. In contrast to monolayer graphene, the band structure of untwisted bilayer graphene can be further tuned by a displacement field8–10, providing an extra degree of freedom to control the flat band that should appear when two bilayers are stacked on top of each other. Here, we report the discovery and characterization of displacement field-tunable electronic phases in twisted double bilayer graphene. We observe insulating states at a half-filled conduction band in an intermediate range of displacement fields. Furthermore, the resistance gap in the correlated insulator increases with respect to the in-plane magnetic fields and we find that the g factor, according to the spin Zeeman effect, is ~2, indicating spin polarization at half-filling. These results establish twisted double bilayer graphene as an easily tunable platform for exploring quantum many-body states. Placing two Bernal-stacked graphene bilayers on top of each other with a small twist angle gives correlated states. As the band structure can be tuned by an electric field, this platform is a more varied setting to study correlated electrons.

Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene.

Abstract: Motivated by the recent observation of an anomalous Hall effect in twisted bilayer graphene, we use a lowest Landau level model to understand the origin of the underlying symmetry-broken correlated state. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an intervalley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.

Superconductivity in metallic twisted bilayer graphene stabilized by WSe2.

Abstract: Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1 degrees, features isolated flat electronic bands that host a rich phase diagram of correlated insulating, superconducting, ferromagnetic and topological phases1–6. Correlated insulators and superconductivity have been previously observed only for angles within 0.1 degree of the magic angle and occur in adjacent or overlapping electron-density ranges; nevertheless, the origins of these states and the relation between them remain unclear, owing to their sensitivity to microscopic details. Beyond twist angle and strain, the dependence of the TBG phase diagram on the alignment4,6 and thickness of the insulating hexagonal boron nitride (hBN)7,8 used to encapsulate the graphene sheets indicates the importance of the microscopic dielectric environment. Here we show that adding an insulating tungsten diselenide (WSe2) monolayer between the hBN and the TBG stabilizes superconductivity at twist angles much smaller than the magic angle. For the smallest twist angle of 0.79 degrees, superconductivity is still observed despite the TBG exhibiting metallic behaviour across the whole range of electron densities. Finite-magnetic-field measurements further reveal weak antilocalization signatures as well as breaking of fourfold spin–valley symmetry, consistent with spin–orbit coupling induced in the TBG via its proximity to WSe2. Our results constrain theoretical explanations for the emergence of superconductivity in TBG and open up avenues towards engineering quantum phases in moire systems. Placing a single layer of tungsten diselenide in contact with twisted bilayer graphene enables superconductivity even for non-magic twist angles where insulating behavior is absent.

Nematicity and Competing Orders in Superconducting Magic-Angle Graphene

Abstract: Strongly interacting electrons in solid-state systems often display tendency towards multiple broken symmetries in the ground state. The complex interplay between different order parameters can give rise to a rich phase diagram. Here, we report on the identification of intertwined phases with broken rotational symmetry in magic-angle twisted bilayer graphene (TBG). Using transverse resistance measurements, we find a strongly anisotropic phase located in a 'wedge' above the underdoped region of the superconducting dome. Upon crossing the superconducting dome, a reduction of the critical temperature is observed, similar to the behavior of certain cuprate superconductors. Furthermore, the superconducting state exhibits a anisotropic response to an directional-dependent in-plane magnetic field, revealing a nematic pairing state across the entire superconducting dome. These results indicate that nematic fluctuations might play an important role in the low-temperature phases of magic-angle TBG, and pave the way for using highly-tunable moire superlattices to investigate intertwined phases in quantum materials.

Flat bands in twisted bilayer transition metal dichalcogenides

Abstract: The crystal structure of a material creates a periodic potential that electrons move through giving rise to its electronic band structure. When two-dimensional materials are stacked, the resulting moire pattern introduces an additional periodicity so that the twist angle between the layers becomes an extra degree of freedom for the resulting heterostructure. As this angle changes, the electronic band structure is modified leading to the possibility of flat bands with localized states and enhanced electronic correlations1–6. In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moire wavelengths over a range of twist angles around 0° and 60° (ref. 4) giving much wider versatility than magic-angle twisted bilayer graphene. Here, we show the existence of a flat band in the electronic structure of 3° and 57.5° twisted bilayer WSe2 samples using scanning tunnelling spectroscopy. Our direct spatial mapping of wavefunctions at the flat-band energy show that the localization of the flat bands is different for 3° and 57.5°, in agreement with first-principles density functional theory calculations4. Using scanning tunnelling spectroscopy, the flat bands in twisted bilayer WSe2 are shown near both 0° and 60° twist angles.

Chemically induced transformation of chemical vapour deposition grown bilayer graphene into fluorinated single-layer diamond

Abstract: Notwithstanding the numerous density functional studies on the chemically induced transformation of multilayer graphene into a diamond-like film carried out to date, a comprehensive convincing experimental proof of such a conversion is still lacking. We show that the fluorination of graphene sheets in Bernal (AB)-stacked bilayer graphene grown by chemical vapour deposition on a single-crystal CuNi(111) surface triggers the formation of interlayer carbon-carbon bonds, resulting in a fluorinated diamond monolayer ('F-diamane'). Induced by fluorine chemisorption, the phase transition from (AB)-stacked bilayer graphene to single-layer diamond was studied and verified by X-ray photoelectron, UV photoelectron, Raman, UV-Vis and electron energy loss spectroscopies, transmission electron microscopy and density functional theory calculations.

Chern Insulators and Topological Flat-bands in Magic-angle Twisted Bilayer Graphene

Abstract: Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum phase transitions triggered by enhanced electron-electron interactions when its flat-bands are partially filled. However, the phases themselves and their connection to the putative non-trivial topology of the flat bands are largely unexplored. Here we report transport measurements revealing a succession of doping-induced Lifshitz transitions that are accompanied by van Hove singularities (VHS) which facilitate the emergence of correlation-induced gaps and topologically non-trivial sub-bands. In the presence of a magnetic field, well quantized Hall plateaus at filling of 1, 2, 3 carriers per moire-cell reveal the sub-band topology and signal the emergence of Chern insulators with Chern-numbers, ! = !, !, !, respectively. Surprisingly, for magnetic fields exceeding 5T we observe a VHS at a filling of 3.5, suggesting the possibility of a fractional Chern insulator. This VHS is accompanied by a crossover from low-temperature metallic, to high-temperature insulating behavior, characteristic of entropically driven Pomeranchuk-like transitions,

Moiré Hyperbolic Metasurfaces.

Abstract: Recent advances in twistronics of low-dimensional materials, such as bilayer graphene and transition-metal dichalcogenides, have enabled a plethora of unusual phenomena associated with moire physic...

Unconventional ferroelectricity in moiré heterostructures

Abstract: The constituent particles of matter can arrange themselves in various ways, giving rise to emergent phenomena that can be surprisingly rich and often cannot be understood by studying only the individual constituents. Discovering and understanding the emergence of such phenomena in quantum materials-especially those in which multiple degrees of freedom or energy scales are delicately balanced-is of fundamental interest to condensed-matter research1,2. Here we report on the surprising observation of emergent ferroelectricity in graphene-based moire heterostructures. Ferroelectric materials show electrically switchable electric dipoles, which are usually formed by spatial separation between the average centres of positive and negative charge within the unit cell. On this basis, it is difficult to imagine graphene-a material composed of only carbon atoms-exhibiting ferroelectricity3. However, in this work we realize switchable ferroelectricity in Bernal-stacked bilayer graphene sandwiched between two hexagonal boron nitride layers. By introducing a moire superlattice potential (via aligning bilayer graphene with the top and/or bottom boron nitride crystals), we observe prominent and robust hysteretic behaviour of the graphene resistance with an externally applied out-of-plane displacement field. Our systematic transport measurements reveal a rich and striking response as a function of displacement field and electron filling, and beyond the framework of conventional ferroelectrics. We further directly probe the ferroelectric polarization through a non-local monolayer graphene sensor. Our results suggest an unconventional, odd-parity electronic ordering in the bilayer graphene/boron nitride moire system. This emergent moire ferroelectricity may enable ultrafast, programmable and atomically thin carbon-based memory devices.

Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe$_2$

Abstract: Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1$^\circ$, features isolated flat electronic bands that host a rich phase diagram of correlated insulating, superconducting, ferromagnetic, and topological phases. The origins of the correlated insulators and superconductivity, and the interplay between them, are particularly elusive. Both states have been previously observed only for angles within $\pm0.1^\circ$ from the magic-angle value and occur in adjacent or overlapping electron density ranges; nevertheless, it is still unclear how the two states are related. Beyond the twist angle and strain, the dependence of the TBG phase diagram on the alignment and thickness of insulating hexagonal boron nitride (hBN) used to encapsulate the graphene sheets indicates the importance of the microscopic dielectric environment. Here we show that adding an insulating tungsten-diselenide (WSe$_2$) monolayer between hBN and TBG stabilizes superconductivity at twist angles much smaller than the established magic-angle value. For the smallest angle of $\theta$ = 0.79$^\circ$, we still observe clear superconducting signatures, despite the complete absence of the correlated insulating states and vanishing gaps between the dispersive and flat bands. These observations demonstrate that, even though electron correlations may be important, superconductivity in TBG can exist even when TBG exhibits metallic behaviour across the whole range of electron density. Finite-magnetic-field measurements further reveal breaking of the four-fold spin-valley symmetry in the system, consistent with large spin-orbit coupling induced in TBG via proximity to WSe$_2$. Our results highlight the importance of symmetry breaking effects in stabilizing electronic states in TBG and open new avenues for engineering quantum phases in moire systems.

Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene

Abstract: Bilayer graphene can be modified by rotating (twisting) one layer with respect to the other. The interlayer twist gives rise to a moiré superlattice that affects the electronic motion and alters the band structure1–4. Near a ‘magic angle’ of twist2,4, where the emergence of a flat band causes the charge carriers to slow down3, correlated electronic phases including Mott-like insulators and superconductors were recently discovered5–8 by using electronic transport. These measurements revealed an intriguing similarity between magic-angle twisted bilayer graphene and high-temperature superconductors, which spurred intensive research into the underlying physical mechanism9–14. Essential clues to this puzzle, such as the symmetry and spatial distribution of the spectral function, can be accessed through scanning tunnelling spectroscopy. Here we use scanning tunnelling microscopy and spectroscopy to visualize the local density of states and charge distribution in magic-angle twisted bilayer graphene. Doping the sample to partially fill the flat band, we observe a pseudogap phase accompanied by a global stripe charge order that breaks the rotational symmetry of the moiré superlattice. Both the pseudogap and the stripe charge order disappear when the band is either empty or full. The close resemblance to similar observations in high-temperature superconductors15–21 provides new evidence of a deeper link underlying the phenomenology of these systems.When scanning tunnelling spectroscopy is used to map the electronic structure of magic-angle twisted bilayer graphene, a pseudogap phase is found, accompanied by a global charge-ordered stripe phase.

Ferromagnetism in Narrow Bands of Moiré Superlattices.

Abstract: Many graphene moir\'e superlattices host narrow bands with nonzero valley Chern numbers. We provide analytical and numerical evidence for a robust spin and/or valley polarized insulator at total integer band filling in nearly flat bands of several different moir\'e materials. In the limit of a perfectly flat band, we present analytical arguments in favor of the ferromagnetic state substantiated by numerical calculations. Further, we numerically evaluate its stability for a finite bandwidth. We provide exact diagonalization results for models appropriate for ABC trilayer graphene aligned with hBN, twisted double bilayer graphene, and twisted bilayer graphene aligned with hBN. We also provide DMRG results for a honeycomb lattice with a quasiflat band and nonzero Chern number, which extend our results to larger system sizes. We find a maximally spin and valley polarized insulator at all integer fillings when the band is sufficiently flat. We also show that interactions may induce effective dispersive terms strong enough to destabilize this state. These results still hold in the case of zero valley Chern number (for example, trivial side of TLG/hBN). We give an intuitive picture based on extended Wannier orbitals, and emphasize the role of the quantum geometry of the band, whose microscopic details may enhance or weaken ferromagnetism in moir\'e materials.

Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene

Abstract: Interactions among electrons and the topology of their energy bands can create novel quantum phases of matter. Most topological electronic phases appear in systems with weak electron-electron interactions. The instances where topological phases emerge only as a result of strong interactions are rare, and mostly limited to those realized in the presence of intense magnetic fields. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for new strongly correlated topological phases. Here we introduce a novel local spectroscopic technique using a scanning tunneling microscope (STM) to detect a sequence of topological insulators in MATBG with Chern numbers C = $\pm$ 1, $\pm$ 2, $\pm$ 3, which form near $ u$ = $\pm$ 3, $\pm$ 2, $\pm$ 1 electrons per moire unit cell respectively, and are stabilized by the application of modest magnetic fields. One of the phases detected here (C = +1) has been previously observed when the sublattice symmetry of MATBG was intentionally broken by hexagonal boron nitride (hBN) substrates, with interactions playing a secondary role. We demonstrate that strong electron-electron interactions alone can produce not only the previously observed phase, but also new and unexpected Chern insulating phases in MATBG. The full sequence of phases we observed can be understood by postulating that strong correlations favor breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moire systems beyond those anticipated from weakly interacting models.

Fractional Chern insulator states in twisted bilayer graphene: An analytical approach

Abstract: This work shows that the character of the narrow band wave functions in twisted bilayer graphene favor the formation of fractional Quantum Hall states even in the absence of a magnetic field. The authors trace the features of magic angle bands to a holomorphic property of the tractable chiral limit which also allows for mapping to a Dirac particle in an inhomogeneous magnetic field and the explicit construction of Laughlin like ground states.

Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: A Hartree-Fock study

Abstract: Motivated by the recently observed insulating states in twisted bilayer graphene, we study the nature of the correlated insulating phases of the twisted bilayer graphene at commensurate filling fractions. We use the continuum model and project the Coulomb interaction onto the flat bands to study the ground states by using a Hartree-Fock approximation. In the absence of the hexagonal boron nitride substrate, the ground states are the intervalley coherence states at charge neutrality (filling $\ensuremath{ u}=0$, or four electrons per moir\'e cell) and at $\ensuremath{ u}=\ensuremath{-}1/4$ and $\ensuremath{-}1/2$ (three and two electrons per cell, respectively) and the ${C}_{2}\mathcal{T}$ symmetry-broken state at $\ensuremath{ u}=\ensuremath{-}3/4$ (one electron per cell). The hexagonal boron nitride substrate drives the ground states at all $\ensuremath{ u}$ into ${C}_{2}\mathcal{T}$ symmetry broken-states. Our results provide good reference points for further study of the rich correlated physics in the twisted bilayer graphene.

Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene.

Abstract: We present a microscopic theory for collective excitations of quantum anomalous Hall ferromagnets (QAHF) in twisted bilayer graphene. We calculate the spin magnon and valley magnon spectra by solving Bethe-Salpeter equations and verify the stability of QAHF. We extract the spin stiffness from the gapless spin wave dispersion and estimate the energy cost of a skyrmion-antiskyrmion pair, which is found to be comparable in energy with the Hartree-Fock gap. The valley wave mode is gapped, implying that the valley polarized state is more favorable compared to the valley coherent state. Using a nonlinear sigma model, we estimate the valley ordering temperature, which is considerably reduced from the mean-field transition temperature due to thermal excitations of valley waves.