Showing papers on "Bilayer graphene published in 2021"

Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene

Abstract: Moire superlattices1,2 have recently emerged as a platform upon which correlated physics and superconductivity can be studied with unprecedented tunability3–6. Although correlated effects have been observed in several other moire systems7–17, magic-angle twisted bilayer graphene remains the only one in which robust superconductivity has been reproducibly measured4–6. Here we realize a moire superconductor in magic-angle twisted trilayer graphene (MATTG)18, which has better tunability of its electronic structure and superconducting properties than magic-angle twisted bilayer graphene. Measurements of the Hall effect and quantum oscillations as a function of density and electric field enable us to determine the tunable phase boundaries of the system in the normal metallic state. Zero-magnetic-field resistivity measurements reveal that the existence of superconductivity is intimately connected to the broken-symmetry phase that emerges from two carriers per moire unit cell. We find that the superconducting phase is suppressed and bounded at the Van Hove singularities that partially surround the broken-symmetry phase, which is difficult to reconcile with weak-coupling Bardeen–Cooper–Schrieffer theory. Moreover, the extensive in situ tunability of our system allows us to reach the ultrastrong-coupling regime, characterized by a Ginzburg–Landau coherence length that reaches the average inter-particle distance, and very large TBKT/TF values, in excess of 0.1 (where TBKT and TF are the Berezinskii–Kosterlitz–Thouless transition and Fermi temperatures, respectively). These observations suggest that MATTG can be electrically tuned close to the crossover to a two-dimensional Bose–Einstein condensate. Our results establish a family of tunable moire superconductors that have the potential to revolutionize our fundamental understanding of and the applications for strongly coupled superconductivity. Highly tunable moire superconductivity is observed in magic-angle twisted trilayer graphene, and observations suggest that this superconductor can be tuned close to the crossover to a two-dimensional Bose–Einstein condensate.

Nematicity and competing orders in superconducting magic-angle graphene.

Abstract: Strongly interacting electrons in solid-state systems often display multiple broken symmetries in the ground state. The interplay between different order parameters can give rise to a rich phase diagram. 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 its crossing with the superconducting dome, a reduction of the critical temperature is observed. Furthermore, the superconducting state exhibits an anisotropic response to a direction-dependent in-plane magnetic field, revealing nematic ordering 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.

Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene

Abstract: Magic-angle twisted bilayer graphene 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, which facilitate the emergence of correlation-induced gaps and topologically non-trivial subbands. In the presence of a magnetic field, well-quantized Hall plateaus at a filling of 1,2,3 carriers per moire cell reveal the subband topology and signal the emergence of Chern insulators with Chern numbers, C = 3,2,1, respectively. Surprisingly, for magnetic fields exceeding 5 T we observe a van Hove singularity at a filling of 3.5, suggesting the possibility of a fractional Chern insulator. This van Hove singularity is accompanied by a crossover from low-temperature metallic, to high-temperature insulating behaviour, characteristic of entropically driven Pomeranchuk-like transitions. A magneto-transport study of twisted bilayer graphene near the magic angle further reveals its rich physics.

Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene

Abstract: When the twist angle between two layers of graphene is approximately 1.1°, interlayer tunnelling and rotational misalignment conspire to create a pair of flat bands1 that are known to host various insulating, superconducting and magnetic states when they are partially filled2–7. Most work has focused on the zero-magnetic-field phase diagram, but here we show that twisted bilayer graphene in a finite magnetic field hosts a cascade of ferromagnetic Chern insulators with Chern number ∣C∣ = 1, 2 and 3. The emergence of the Chern insulators is driven by the interplay of the moire superlattice with the magnetic field, which endows the flat bands with a substructure of topologically non-trivial subbands characteristic of the Hofstadter butterfly8,9. The new phases can be accounted for in a Stoner picture10; in contrast to conventional quantum Hall ferromagnets, electrons polarize into between one and four copies of a single Hofstadter subband1,11,12. Distinct from other moire heterostructures13–15, Coulomb interactions dominate in twisted bilayer graphene, as manifested by the appearance of Chern insulating states with spontaneously broken superlattice symmetry at half filling of a C = −2 subband16,17. Our experiments show that twisted bilayer graphene is an ideal system in which to explore the strong-interaction limit within partially filled Hofstadter bands. In twisted bilayer graphene, the moire potential, strong electron–electron interactions and a magnetic field conspire to split the flat band into topologically non-trivial subbands.

Observation of flat bands in twisted bilayer graphene

Abstract: Transport experiments in twisted bilayer graphene have revealed multiple superconducting domes separated by correlated insulating states1–5. These properties are generally associated with strongly correlated states in a flat mini-band of the hexagonal moire superlattice as was predicted by band structure calculations6–8. Evidence for the existence of a flat band comes from local tunnelling spectroscopy9–13 and electronic compressibility measurements14, which report two or more sharp peaks in the density of states that may be associated with closely spaced Van Hove singularities. However, direct momentum-resolved measurements have proved to be challenging15. Here, we combine different imaging techniques and angle-resolved photoemission with simultaneous real- and momentum-space resolution (nano-ARPES) to directly map the band dispersion in twisted bilayer graphene devices near charge neutrality. Our experiments reveal large areas with a homogeneous twist angle that support a flat band with a spectral weight that is highly localized in momentum space. The flat band is separated from the dispersive Dirac bands, which show multiple moire hybridization gaps. These data establish the salient features of the twisted bilayer graphene band structure. Spectroscopic measurements using nano-ARPES on twisted bilayer graphene directly highlight the presence of the flat bands.

Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene

Abstract: Twisted van der Waals heterostructures with flat electronic bands have recently emerged as a platform for realizing correlated and topological states with a high degree of control and tunability. In graphene-based moire heterostructures, the correlated phase diagram and band topology depend on the number of graphene layers and the details of the external environment from the encapsulating crystals. Here, we report that the system of twisted monolayer–bilayer graphene (tMBG) hosts a variety of correlated metallic and insulating states, as well as topological magnetic states. Because of its low symmetry, the phase diagram of tMBG approximates that of twisted bilayer graphene when an applied perpendicular electric field points from the bilayer towards the monolayer graphene, or twisted double bilayer graphene when the field is reversed. In the former case, we observe correlated states that undergo an orbitally driven insulating transition above a critical perpendicular magnetic field. In the latter case, we observe the emergence of electrically tunable ferromagnetism at one-quarter filling of the conduction band, and an associated anomalous Hall effect. The direction of the magnetization can be switched by electrostatic doping at zero magnetic field. Our results establish tMBG as a tunable platform for investigating correlated and topological states. Stacking a monolayer and bilayer of graphene, with a small twist angle between them, creates a tunable platform where the physics of both twisted bilayer graphene and twisted double bilayer graphene can be realized.

Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening

Abstract: Controlling the strength of interactions is essential for studying quantum phenomena emerging in systems of correlated fermions. We introduce a device geometry whereby magic-angle twisted bilayer graphene is placed in close proximity to a Bernal bilayer graphene, separated by a 3-nanometer-thick barrier. By using charge screening from the Bernal bilayer, the strength of electron-electron Coulomb interaction within the twisted bilayer can be continuously tuned. Transport measurements show that tuning Coulomb screening has opposite effects on the insulating and superconducting states: As Coulomb interaction is weakened by screening, the insulating states become less robust, whereas the stability of superconductivity at the optimal doping is enhanced. The results provide important constraints on theoretical models for understanding the mechanism of superconductivity in magic-angle twisted bilayer graphene.

Symmetry breaking in twisted double bilayer graphene

Abstract: The flat bands that appear in some twisted van der Waals heterostructures provide a setting in which strong interactions between electrons lead to a variety of correlated phases1–20. In particular, heterostructures of twisted double bilayer graphene host correlated insulating states that can be tuned by both the twist angle and an external electric field11–14. Here, we report electrical transport measurements of twisted double bilayer graphene with which we examine the fundamental role of spontaneous symmetry breaking in its phase diagram. The metallic states near each of the correlated insulators exhibit abrupt drops in their resistivity as the temperature is lowered, along with associated nonlinear current–voltage characteristics. Despite qualitative similarities to superconductivity, the simultaneous reversals in the sign of the Hall coefficient point instead to spontaneous symmetry breaking as the origin of the abrupt resistivity drops, whereas Joule heating seems to underlie the nonlinear transport. Our results suggest that similar mechanisms are probably relevant across a broader class of semiconducting flat band van der Waals heterostructures. Transport measurements show that spontaneous symmetry breaking plays a crucial role in the correlated insulating and metallic states in twisted double bilayer graphene.

Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene

Abstract: Based on an all-band moir\'e Hartree-Fock variational method, the authors study theoretically the correlated and topological states in magic-angle twisted bilayer graphene. They construct phase diagrams at various integer fillings. In particular, a so far unknown quantum state of matter, the moir\'e orbital antiferromagnetic state, is identified as the possible ground state at some fillings.

Room-temperature intrinsic ferromagnetism in epitaxial CrTe2 ultrathin films

Abstract: While the discovery of two-dimensional (2D) magnets opens the door for fundamental physics and next-generation spintronics, it is technically challenging to achieve the room-temperature ferromagnetic (FM) order in a way compatible with potential device applications. Here, we report the growth and properties of single- and few-layer CrTe2, a van der Waals (vdW) material, on bilayer graphene by molecular beam epitaxy (MBE). Intrinsic ferromagnetism with a Curie temperature (TC) up to 300 K, an atomic magnetic moment of ~0.21 $${\mu }_{{\rm{B}}}$$ /Cr and perpendicular magnetic anisotropy (PMA) constant (Ku) of 4.89 × 105 erg/cm3 at room temperature in these few-monolayer films have been unambiguously evidenced by superconducting quantum interference device and X-ray magnetic circular dichroism. This intrinsic ferromagnetism has also been identified by the splitting of majority and minority band dispersions with ~0.2 eV at Г point using angle-resolved photoemission spectroscopy. The FM order is preserved with the film thickness down to a monolayer (TC ~ 200 K), benefiting from the strong PMA and weak interlayer coupling. The successful MBE growth of 2D FM CrTe2 films with room-temperature ferromagnetism opens a new avenue for developing large-scale 2D magnet-based spintronics devices. The emergence of two dimensional ferromagnetism suffers from an inherent fragility to thermal fluctuations, which typically restricts the Curie temperature to below room temperature. Here, Zhang et al present CrTe2 thin films grown via molecular beam epitaxy with a Curie temperature exceeding 300 K.

Correlation-driven topological phases in magic-angle twisted bilayer graphene

Abstract: Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron-electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when ±1, ±2 and ±3 electrons occupy each moire unit cell, and lead to the formation of various correlated phases1-4. Although some phases have been shown to have a non-zero Chern number5,6, the local microscopic properties and topological character of many other phases have not yet been determined. Here we introduce a set of techniques that use scanning tunnelling microscopy to map the topological phases that emerge in MATBG in a finite magnetic field. By following the evolution of the local density of states at the Fermi level with electrostatic doping and magnetic field, we create a local Landau fan diagram that enables us to assign Chern numbers directly to all observed phases. We uncover the existence of six topological phases that arise from integer fillings in finite fields and that originate from a cascade of symmetry-breaking transitions driven by correlations7,8. These topological phases can form only for a small range of twist angles around the magic angle, which further differentiates them from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions, exhibits prominent electron-hole asymmetry, and features an unexpectedly large splitting between zero Landau levels (about 3 to 5 millielectronvolts). Our results show how strong electronic interactions affect the MATBG band structure and lead to correlation-enabled topological phases.

Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene

Abstract: Understanding and tuning correlated states is of great interest and importance to modern condensed-matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer graphene presents a unique platform to study correlation phenomena, in which the Coulomb energy dominates over the quenched kinetic energy as a result of hybridized flat bands. Extending this approach to the case of twisted multilayer graphene would allow even higher control over the band structure because of the reduced symmetry of the system. Here we study electronic transport properties of twisted monolayer–bilayer graphene (a bilayer on top of monolayer graphene heterostructure). We observe the formation of van Hove singularities that are highly tunable by changing either the twist angle or external electric field and can cause strong correlation effects under optimum conditions. We provide basic theoretical interpretations of the observed electronic structure. A structure of monolayer and bilayer graphene with a small twist between them shows correlated insulating states that can be tuned by changing the twist angle or applying an electric field.

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 band 1 , 2 . Experiments have shown correlated insulating, superconducting and ferromagnetic states when the flat band is partially filled 3 – 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.

Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene

Abstract: Flat bands in magic-angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations1, superconductivity2–5 and magnetism3,6,7. However, the phases of MATBG in a magnetic field and what they reveal about the zero-field phase diagram remain relatively uncharted. Here we report a rich sequence of wedge-like regions of quantized Hall conductance with Chern numbers C = ±1, ±2, ±3 and ±4, which nucleate from integer fillings of the moire unit cell v = ±3, ±2, ±1 and 0, respectively. We interpret these phases as spin- and valley-polarized many-body Chern insulators. The exact sequence and correspondence of the Chern numbers and filling factors suggest that these states are directly driven by electronic interactions, which specifically break the time-reversal symmetry in the system. We further study the yet unexplored higher-energy dispersive bands with a Rashba-like dispersion. The analysis of Landau-level crossings enables a parameter-free comparison to a newly derived ‘magic series’ of level crossings in a magnetic field and provides constraints on the parameters of the Bistritzer–MacDonald MATBG Hamiltonian. Overall, our data provide direct insights into the complex nature of symmetry breaking in MATBG and allow for the quantitative tests of the proposed microscopic scenarios for its electronic phases. In magic-angle twisted bilayer graphene, topological Chern bands that are driven by electron–electron interactions appear at all the integer fillings of the moire unit cell. The Rashba-like higher-energy bands also show Landau-level crossings.

Localization of lattice dynamics in low-angle twisted bilayer graphene

Abstract: Twisted bilayer graphene is created by slightly rotating the two crystal networks in bilayer graphene with respect to each other. For small twist angles, the material undergoes a self-organized lattice reconstruction, leading to the formation of a periodically repeated domain1-3. The resulting superlattice modulates the vibrational3,4 and electronic5,6 structures within the material, leading to changes in the behaviour of electron-phonon coupling7,8 and to the observation of strong correlations and superconductivity9. However, accessing these modulations and understanding the related effects are challenging, because the modulations are too small for experimental techniques to accurately resolve the relevant energy levels and too large for theoretical models to properly describe the localized effects. Here we report hyperspectral optical images, generated by a nano-Raman spectroscope10, of the crystal superlattice in reconstructed (low-angle) twisted bilayer graphene. Observations of the crystallographic structure with visible light are made possible by the nano-Raman technique, which reveals the localization of lattice dynamics, with the presence of strain solitons and topological points1 causing detectable spectral variations. The results are rationalized by an atomistic model that enables evaluation of the local density of the electronic and vibrational states of the superlattice. This evaluation highlights the relevance of solitons and topological points for the vibrational and electronic properties of the structures, particularly for small twist angles. Our results are an important step towards understanding phonon-related effects at atomic and nanometric scales, such as Jahn-Teller effects11 and electronic Cooper pairing12-14, and may help to improve device characterization15 in the context of the rapidly developing field of twistronics16.

Isospin Pomeranchuk effect in twisted bilayer graphene

Abstract: In condensed-matter systems, higher temperatures typically disfavour ordered phases, leading to an upper critical temperature for magnetism, superconductivity and other phenomena. An exception is the Pomeranchuk effect in 3He, in which the liquid ground state freezes upon increasing the temperature1, owing to the large entropy of the paramagnetic solid phase. Here we show that a similar mechanism describes the finite-temperature dynamics of spin and valley isospins in magic-angle twisted bilayer graphene2. Notably, a resistivity peak appears at high temperatures near a superlattice filling factor of −1, despite no signs of a commensurate correlated phase appearing in the low-temperature limit. Tilted-field magnetotransport and thermodynamic measurements of the in-plane magnetic moment show that the resistivity peak is connected to a finite-field magnetic phase transition3 at which the system develops finite isospin polarization. These data are suggestive of a Pomeranchuk-type mechanism, in which the entropy of disordered isospin moments in the ferromagnetic phase stabilizes the phase relative to an isospin-unpolarized Fermi liquid phase at higher temperatures. We find the entropy, in units of Boltzmann’s constant, to be of the order of unity per unit cell area, with a measurable fraction that is suppressed by an in-plane magnetic field consistent with a contribution from disordered spins. In contrast to 3He, however, no discontinuities are observed in the thermodynamic quantities across this transition. Our findings imply a small isospin stiffness4,5, with implications for the nature of finite-temperature electron transport6–8, as well as for the mechanisms underlying isospin ordering and superconductivity9,10 in twisted bilayer graphene and related systems. An electronic analogue of the Pomeranchuk effect is present in twisted bilayer graphene, shown by the stability of entropy in a ferromagnetic phase compared to an unpolarized Fermi liquid phase at certain high temperatures.

Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene

Abstract: Twisted van der Waals heterostructures with flat electronic bands have recently emerged as a platform for realizing correlated and topological states with a high degree of control and tunability. In graphene-based moire heterostructures, the correlated phase diagram and band topology depend on the number of graphene layers and the details of the external environment from the encapsulating crystals. Here, we report that the system of twisted monolayer–bilayer graphene (tMBG) hosts a variety of correlated metallic and insulating states, as well as topological magnetic states. Because of its low symmetry, the phase diagram of tMBG approximates that of twisted bilayer graphene when an applied perpendicular electric field points from the bilayer towards the monolayer graphene, or twisted double bilayer graphene when the field is reversed. In the former case, we observe correlated states that undergo an orbitally driven insulating transition above a critical perpendicular magnetic field. In the latter case, we observe the emergence of electrically tunable ferromagnetism at one-quarter filling of the conduction band, and an associated anomalous Hall effect. The direction of the magnetization can be switched by electrostatic doping at zero magnetic field. Our results establish tMBG as a tunable platform for investigating correlated and topological states. Stacking a monolayer and bilayer of graphene, with a small twist angle between them, creates a tunable platform where the physics of both twisted bilayer graphene and twisted double bilayer graphene can be realized.

Nematic topological semimetal and insulator in magic-angle bilayer graphene at charge neutrality

Abstract: This work explores the possible interacting ground states of magic angle twisted bilayer graphene at charge neutrality, emphasizing the role of three-fold lattice rotation symmetry.

Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist

Abstract: Bilayer graphene has been predicted to host a moire miniband with flat dispersion if the layers are stacked at specific twist angles known as the ’magic angles’1,2. Recently, twisted bilayer graphene (tBLG) with a magic angle twist was reported to exhibit a correlated insulating state and superconductivity3,4, where the presence of the flat miniband in the system is thought to be essential for the emergence of these ordered phases in the transport measurements. Although tunnelling spectroscopy5–9 and electronic compressibility measurements10 in tBLG have found a van Hove singularity that is consistent with the presence of the flat miniband, a direct observation of the flat dispersion in the momentum space of such a moire miniband in tBLG is still lacking. Here, we report the visualization of this flat moire miniband by using angle-resolved photoemission spectroscopy with nanoscale resolution. The high spatial resolution of this technique enabled the measurement of the local electronic structure of the tBLG. The measurements demonstrate the existence of the flat moire band near the charge neutrality for tBLG close to the magic angle at room temperature. The flat electronic bands that are associated with ordered phases in twisted bilayer graphene at a magic twist angle have been imaged using angle-resolved photoemission spectroscopy.

Fractional Chern insulators in magic-angle twisted bilayer graphene

Abstract: Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue toward manipulating non-abelian excitations. Early theoretical studies have predicted their existence in systems with energetically flat Chern bands and highlighted the critical role of a particular quantum band geometry. Thus far, however, FCI states have only been observed in Bernal-stacked bilayer graphene aligned with hexagonal boron nitride (BLG/hBN), in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field and limiting its potential for applications. By contrast, magic angle twisted bilayer graphene (MATBG) supports flat Chern bands at zero magnetic field, and therefore offers a promising route toward stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in MATBG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically-trivial charge density wave states. Unlike the BLG/hBN platform, we demonstrate that the principal role of the weak magnetic field here is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum band geometry favorable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in moire systems with native flat Chern bands.

Strain fields in twisted bilayer graphene

Abstract: Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles <2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moire heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moire materials.

Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing

Abstract: We find exact analytic expressions for the energies and wave functions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of projected Coulomb Hamiltonians in twisted bilayer graphene. Our exact expressions are valid for any form of the Coulomb interaction and any form of $AA$ and $AB/BA$ tunneling. The single charge excitation energy is a convolution of the Coulomb potential with a quantum geometric tensor of the TBG bands. The neutral excitations are (high-symmetry group) magnons, and their dispersion is analytically calculated in terms of the form factors of the active bands in TBG. The two-charge excitation energy and wave functions are also obtained, and a sufficient condition on the graphene eigenstates for obtaining a Cooper pair from Coulomb interactions is obtained. For the actual TBG bands at the first magic angle, we can analytically show that the Cooper pair binding energy is zero in all such projected Coulomb models, implying that either phonons and/or nonzero kinetic energy are needed for superconductivity. Since Vafek and Kang [Phys. Rev. Lett. 125, 257602 (2020)] showed that the kinetic energy bounds on the superexchange energy are less ${10}^{\ensuremath{-}3}$ in Coulomb units, the phonon mechanism becomes then very likely. If nonetheless the superconductivity is due to kinetic terms which render the bands nonflat, one prediction of our theory is that the highest ${T}_{c}$ would not occur at the highest DOS.

Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene

Abstract: Quantum Monte Carlo simulations of so-called ``magic angle'' twisted bilayer graphene reveal three novel insulating phases that may help elucidate the origin of unusual electronic behaviors in this material.

Evidence for unconventional superconductivity in twisted bilayer graphene.

Abstract: The emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors1–4, as described by the Bardeen-Cooper-Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened5,6. This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states (DOS) of its flat bands. Here we combine tunnelling and Andreev reflection spectroscopy with the scanning tunnelling microscope (STM) to observe several key experimental signatures for unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature Tc are inconsistent with those of a conventional s-wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap ΔT, which far exceeds the mean-field BCS ratio (with 2ΔT/kBTc ~ 25), and the gap ΔAR extracted from Andreev reflection spectroscopy (2ΔAR/kBTc ~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride (hBN). These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.

Hetero-site nucleation for growing twisted bilayer graphene with a wide range of twist angles.

Abstract: Twisted bilayer graphene (tBLG) has recently attracted growing interest due to its unique twist-angle-dependent electronic properties. The preparation of high-quality large-area bilayer graphene with rich rotation angles would be important for the investigation of angle-dependent physics and applications, which, however, is still challenging. Here, we demonstrate a chemical vapor deposition (CVD) approach for growing high-quality tBLG using a hetero-site nucleation strategy, which enables the nucleation of the second layer at a different site from that of the first layer. The fraction of tBLGs in bilayer graphene domains with twist angles ranging from 0° to 30° was found to be improved to 88%, which is significantly higher than those reported previously. The hetero-site nucleation behavior was carefully investigated using an isotope-labeling technique. Furthermore, the clear Moire patterns and ultrahigh room-temperature carrier mobility of 68,000 cm2 V−1 s−1 confirmed the high crystalline quality of our tBLG. Our study opens an avenue for the controllable growth of tBLGs for both fundamental research and practical applications. The synthesis of twisted bilayer graphene with controllable angles is challenging. Here, the authors devise a chemical vapor deposition approach using a hetero-site nucleation strategy that affords twist angles ranging from 0° to 30°.

Twisted bilayer graphene. I. Matrix elements, approximations, perturbation theory, and a k .p two-band model

Abstract: The physics of twisted bilayer graphene (TBG) is a complicated m\'elange of topology and interactions. A unified understanding of the correlated insulators in TBG emerges in this series of six papers (TBG1--TBG6). Starting from the physics of single-particle bands, TBG1 simplifies the physics of the infinite dimensional Bistritzer-Macdonald Hamiltonian to that of a 12-site model. TBG2 challenges the well-accepted thought that the active bands in TBG are fragile topological, and proves their stable topology. TBG3 and TBG4 analytically obtain the many-body interacting Hamiltonian, its symmetries, and the exact correlated insulator ground states at integer filling. TBG5 then obtains charge 0,+- 1,+-2 exact excitations above these ground states and their Goldstone modes, and proves the impossibility of pairing with repulsive projected interactions. Finally, TBG6 performs large-scale exact diagonalization studies, confirming the validity of the analytic results.

Strain-Induced Quantum Phase Transitions in Magic-Angle Graphene.

Abstract: We investigate the effect of uniaxial heterostrain on the interacting phase diagram of magic-angle twisted bilayer graphene. Using both self-consistent Hartree-Fock and density-matrix renormalization group calculations, we find that small strain values (e∼0.1%-0.2%) drive a zero-temperature phase transition between the symmetry-broken "Kramers intervalley-coherent" insulator and a nematic semimetal. The critical strain lies within the range of experimentally observed strain values, and we therefore predict that strain is at least partly responsible for the sample-dependent experimental observations.

Moiré metrology of energy landscapes in van der Waals heterostructures.

Abstract: The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moire superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moire metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moire domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moire metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moire metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers. Here, a combined experiment-theory framework based on different nano-imaging techniques and first-principle calculations is used to analyse the shapes of moire patterns in twisted van der Waals structures, enabling an accurate description of the coupling between the atomically thin layers.

Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene

Abstract: The interplay between strong electron–electron interactions and band topology can produce electronic states that spontaneously break symmetries. The discovery of flat bands in magic-angle twisted bilayer graphene (MATBG)1–3 with non-trivial topology4–7 has provided a compelling platform in which to search for new symmetry-broken phases. Recent scanning tunnelling microscopy8,9 and transport experiments10–13 have revealed a sequence of topological insulating phases in MATBG near integer filling of the electronic bands produced by the moire pattern. These correspond to a simple pattern of flavour-symmetry-breaking Chern insulators that fill bands of different flavours one after the other. Here we report the high-resolution local compressibility measurements of MATBG with a scanning single-electron transistor, which reveal an additional sequence of incompressible states with unexpected Chern numbers observed down to zero magnetic field. We find that the Chern numbers for eight of the observed incompressible states are incompatible with the simple picture in which the bands are sequentially filled. We show that the emergence of these unusual incompressible phases can be understood as a consequence of broken translation symmetry that doubles the moire unit cell and splits each flavour band in two. Our findings expand the known phase diagram of MATBG, and shed light on the origin of the close competition between different correlated phases in the system. In addition to the broken time-reversal symmetry that typifies Chern insulators, twisted bilayer graphene hosts a set of topological states with broken translational symmetry.

Quad-band polarization-insensitive metamaterial perfect absorber based on bilayer graphene metasurface

Abstract: In this paper a quad-band, polarization-insensitive metamaterial perfect absorber (MPA) based on bi-layer graphene in the terahertz regime is presented. Initially, four models of the desired structure by using a single-layer graphene metasurface were examined. The results of the proposed four models show that two absorption peaks were finally achieved at frequencies of 3.19 THz and 4.66 THz with the absorption of 99.61% and 99.95%, respectively. Then, by stacking the double layer graphene metasurface, a quad-band perfect absorber with an average absorption of 99.43% at the frequencies of 2.7 THz, 3.19 THz, 3.99 THz and 4.46 THz is obtained for 0.9 eV Fermi energy. Also, physical mechanisms of MPA have been studied by impedance matching theory. The study of the proposed structure with graphene metasurface has the advantage that the resonant frequency can be tunably adjusted without manufacturing again of the proposed structure. Furthermore, the proposed perfect absorber of metamaterial is polarization-insensitive and is more tolerant than the incident angle. The proposed absorber in this paper has potential in filtering, detection, imaging and other applications photodetectors, and other applications.