The ability to control the strength of interaction is essential for studying quantum phenomena emerging from a system of correlated fermions. For example, the isotope effect illustrates the effect of electron-phonon coupling on superconductivity, providing an important experimental support for the BCS theory. In this work, we report a new device geometry where the magic-angle twisted bilayer graphene (tBLG) is placed in close proximity to a Bernal bilayer graphene (BLG) separated by a 3 nm thick barrier. 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 effect on the insulating and superconducting states: as Coulomb interaction is weakened by screening, the insulating states become less robust, whereas the stability of superconductivity is enhanced. Out results demonstrate the ability to directly probe the role of Coulomb interaction in magic-angle twisted bilayer graphene. Most importantly, the effect of Coulomb screening points toward electron-phonon coupling as the dominant mechanism for Cooper pair formation, and therefore superconductivity, in magic-angle twisted bilayer graphene.
In this work we address the re-entrance of magic-angle phenomena (band flatness and quantum-geometric transport) in twisted bilayer graphene (TBG) subjected to strong magnetic fluxes $\pm Φ_0$, $\pm 2 Φ_0$, $\pm 3 Φ_0$... ($Φ_0 = h/e$ is the flux quantum per moiré cell). The moiré translation invariance is restored at the integer fluxes, for which we calculate the TBG band structure using accurate atomistic models with lattice relaxations. Similarly to the zero-flux physics outside the magic angle condition, the reported effect breaks down rapidly with the twist. We conclude that the magic-ang…
In the past two years, magic-angle twisted bilayer graphene has emerged as a uniquely versatile experimental platform that combines metallic, superconducting, magnetic and insulating phases in a single crystal. In particular the ability to tune the superconducting state with a gate voltage opened up intriguing prospects for novel device functionality. Here we present the first demonstration of a device based on the interplay between two distinct phases in adjustable regions of a single magic-angle twisted bilayer graphene crystal. We electrostatically define the superconducting and insulating …
Twisted bilayered graphenes at magic angles are systems housing long ranged periodicity of Moiré pattern together with short ranged periodicity associated with the individual graphenes. Such materials are a fertile ground for novel states largely driven by electronic correlations. Here we find that the ubiquitous Casimir force can serve as a platform for macroscopic manifestations of the quantum effects stemming from the magic angle bilayered graphenes properties and their phases determined by electronic correlations. By utilizing comprehensive calculations for the electronic and optical respo…
Moiré systems displaying flat bands have emerged as novel platforms to study correlated electron phenomena. Insulating and superconducting states appear upon doping magic angle twisted bilayer graphene (TBG), and there is evidence of correlation induced effects at the charge neutrality point (CNP) which could originate from spontaneous symmetry breaking. Our theoretical calculations show how optical conductivity measurements can distinguish different symmetry breaking states, and reveal the nature of the correlated states. In the specific case of nematic order, which breaks the discrete rotati…
Twisted bilayer graphene (TBG) has been experimentally observed to exhibit almost flat bands when the twisting occurs at certain magic angles. In this letter, we report new results on the continuum model of twisted bilayer graphene and its electronic band structure. Under we show that in the approximation of vanishing AA-coupling, the magic angles (at which there exist entirely flat bands) are given as the eigenvalues of a non-hermitian operator, and that all bands start squeezing exponentially fast as the angle $θ$ tends to $0$. In particular, as the interaction potential changes, the dynamic…
Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. In this paper 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. We also extract a transport "scattering rate", which satisfies a near Planckian form that is universally related to the ratio of $(k_BT/\hbar)$. Our…
We present a theory of superconductivity in twisted bilayer graphene in which attraction is generated between electrons on the same honeycomb sublattice when the system is close to a sublattice polarization instability. The resulting Cooper pairs are spin-polarized valley-singlets. Because the sublattice polarizability is mainly contributed by interband fluctuations, superconductivity occurs over a wide range of filling fraction. It is suppressed by i) applying a sublattice polarizing field (generated by an aligned BN substrate) or ii) changing moiré band filling to favor valley polarization. …
Studies of twisted moiré systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature stable quadratic-band-touching points and find exotic physics different from previously studied twisted moiré systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number ($C=\pm 2$). We further consider the effect of Coulomb interactions in such magic-angle twisted systems an…
Kitaev quantum spin liquids have been the focus of intense research effort thanks to the discovery of various materials (e.g., RuCl3) that approximate their intriguing physics. In this paper we construct a mean-field approximation for a moir`e superlattice emerging in twisted Kitaev bilayers in terms of solutions of commensurate bilayers. We show that the band structure of deconfined spinons, defined on the mini-Brillouin zone of the superlattice, is greatly modified. The system exhibits a hyper-magic manifold: a series of nearly perfectly-flat bands appear at energies above the lowest gap, ex…
Near a magic twist angle, the lowest energy conduction and valence bands of bilayer graphene moiré superlattices become extremely narrow. The band dispersion that remains is sensitive to the moiré's strain pattern, nonlocal tunneling between layers, and filling-factor dependent Hartree and exchange band renormalizations. In this article we analyze the influence of these band-structure details on the pattern of flavor-symmetry-breaking observed in this narrow band system, and on the associated pattern of Fermi surface reconstructions revealed by weak-field-Hall and Schubnikov-de Haas magneto-tr…
We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat…
Coulomb screening of superconductivity in magic-angle twisted bilayer graphene
School of Physics & Astronomy, University of Manchester（曼彻斯特大学物理与天文学学院）；National Graphene Institute, University of Manchester（曼彻斯特大学国家石墨烯研究所）；Department of Physics, Washington University in St. Louis（华盛顿大学圣路易斯分校物理系）；Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学物理与天文学系）；Department of Physics, University of Antwerp（安特卫普大学物理系）；Henry Royce Institute for Advanced Materials, The University of Manchester（曼彻斯特大学亨利·罗伊斯先进材料研究所）；National Institute for Materials Science（国立材料研究所）；Department of Materials Science and Engineering, National University of Singapore（新加坡国立大学材料科学与工程系）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions, that are Wannier-like in one direction and Bloch-like in the other. We focus on the active bands as given by the continuum model proposed by Bistritzer and MacDonald, and discuss the properties of corresponding hybrid Wannier functions. We then employ the method for a study of the fillings of $\pm 3$ electrons per moiré cell using the Hartree-Fock method. We discuss at length different regimes under which a quantized anomalous Hall effect is seen in these two fillings.
Magic-angle twisted bilayer graphene (MA-tBLG) has appeared as a tunable testing ground to investigate the conspiracy of electronic interactions, band structure, and lattice degrees of freedom to yield exotic quantum many-body ground states in a two-dimensional Dirac material framework. While the impact of external parameters such as doping or magnetic field can be conveniently modified and analyzed, the all-surface nature of the quasi-2D electron gas combined with its intricate internal properties pose a challenging task to characterize the quintessential nature of the different insulating an…
Twisted Bilayer graphene (TBG) is known to feature isolated and relatively flat bands near charge neutrality, when tuned to special magic angles. However, different criteria for the magic angle such as the vanishing of Dirac speed, minimal bandwidth or maximal band gap to higher bands typically give different results. Here we study a modified continuum model for TBG which has an infinite sequence of magic angles $θ$ at which, we simultaneously find that (i) the Dirac speed vanishes (ii) absolutely flat bands appear at neutrality and (iii) bandgaps to the excited bands are maximized. When param…
At a discrete set of magic angles, twisted bilayer graphene has been shown to host extraordinarily flat bands, correlated insulating states, unconventional superconductivity, and distinct Landau level degeneracies. In this work, we design a highly efficient quantum Otto engine using a twisted bilayer graphene sample. Flat bands, which occur at magic angles, make the prospect of extracting useful work from our Otto engine lucrative. We use an eight-band continuum model of twisted bilayer graphene to compute efficiencies and work outputs for magic and non-magic angle twists, and compare the resu…
The importance of phonons in the strong correlation phenomena observed in twisted bilayer graphene (TBG) at the so-called magic-angle is under debate. Here we apply gate-dependent micro-Raman spectroscopy to monitor the G band linewidth in TBG devices of twist angles $θ=0^{\circ}$, $\sim 1.1^{\circ}$ (magic-angle) and $\sim 7^{\circ}$ (large angle). The results show a broad and p/n-asymmetric doping behavior at the magic-angle, in clear contrast to the behavior observed in twist angles above and below. Atomistic modeling reproduces the experimental observations, revealing how the unique electr…
Thanks to the recent discovery on the magic-angle bilayer graphene, twistronics is quickly becom11 ing a burgeoning field in condensed matter physics. This letter expands the realm of twistronics to acoustics by introducing twisted bilayer phononic graphene, which remarkably also harbors the magic angle, evidenced by the associated ultra-flat bands. Beyond mimicking quantum mechanical behaviors of twisted bilayer graphene, we show that their acoustic counterpart offers a considerably more straightforward and robust way to alter the interlayer hopping strength, enabling us to unlock magic angle…
Twist bilayer graphenes with magical angle have nearly flat band, which become strongly correlated electron systems. Herein, we propose another system based on strained bilayer graphene that have flat band at the intrinsic Fermi level. The top and bottom layers are uniaxially stretched along different directions. When the strength and directions of the strain satisfy certain condition, the periodical lattices of the two layers are commensurate to each other. The regions with AA, AB and BA stacking arrange in a triangular lattice. With magical strain, the bands around the intrinsic Fermi level …
Twisted bilayer graphene with tiny rotation angles have drawn significant attention due to the observation of the unconventional superconducting and correlated insulating behaviors. In this paper, we employ a full tight-binding model to investigate collective excitations in twisted bilayer graphene near magic angle. The polarization function is obtained from the tight-binding propagation method without diagonalization of the Hamiltonian matrix. With the atomic relaxation considered in the simulation, damped and undamped interband plasmon modes are discovered near magic angle under both room te…
We show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle flat bands. When the system is insulating at moiré band filling $ν=-3$, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moiré Brillouin zone, one of which couples strongly to THz photons. The low-energy collective modes are faithfully described by a model with a local $SU…
The correlated insulator (CI) states and the recently discovered density wave (DW) states in magic-angle twisted bilayer graphene (TBG) have stimulated intense research interest. However, up to date, the nature of these "featureless" correlated states with zero Chern numbers are still elusive, and are lack of characteristic experimental signature. Thus, an experimental probe to identify the characters of these featureless CI and DW states are urgently needed. In this work, we theoretically study the correlated insulators and density-wave states at different integer and fractional fillings of t…
Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings
We derive a simple formula for the real-space chirality of twisted bilayer graphene that can be related to the cross-product of its sheet currents. This quantity shows well-defined plateaus for the first remote band as function of the gate voltage which are approximately quantized for commensurate twist angles. The zeroth plateau corresponds to the first magic angle where a sign change occurs due to an emergent $C_6$-symmetry. Our observation offers a new definition of the magic angle based on a macroscopic observable which is accessible in typical transport experiments.
This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor compo…
The simultaneous co-existence and gate-tuneability of the superconducting (SC), magnetic and topological orders in magic angle twisted bilayer graphene (MATBG) open up entirely new possibilities for the creation of complex hybrid Josephson junctions (JJ). Here we report on the creation of gate-defined, magnetic Josephson junctions in MATBG, where the weak link is gate-tuned close to the correlated state at a moiré filling factor of ν=-2. A highly unconventional Fraunhofer pattern emerges, which is phase-shifted and asymmetric with respect to the current and magnetic field directions, and shows…
Twisted bilayer graphene with a twist angle of around 1.1° features a pair of isolated flat electronic bands and forms a strongly correlated electronic platform. Here, we use scanning tunneling microscopy to probe local properties of highly tunable twisted bilayer graphene devices and show that the flat bands strongly deform when aligned with the Fermi level. At half filling of the bands, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring a substantially enhanced flat band split…
We have investigated the Coulomb screening properties and collective excitations in a graphene bilayer. The static screening effect is anisotropic and is much stronger in the undoped graphene bilayer than in a monolayer graphene [1]. The dynamic screening shows the properties of a Dirac gas in the low frequency and that of a Fermi gas in the high frequency. The transition from the Dirac to the Fermi gas is also observed in the plasmon spectrum. Finally, we find that an electron gas in a doped graphene bilayer has quite similar properties as those of a Fermi gas in materials containing two ener…
We revisit the localized Wannier state description of the twisted bilayer graphene, focusing on the chiral limit. We provide a simple method for constructing such 2D exponentially localized -- yet valley polarized -- Wannier states, centered on the sites of the honeycomb lattice, paying particular attention to maintaining all the unobstructed symmetries. This includes the unitary particle-hole symmetry, and the combination of $C_2\mathcal{T}$ and the chiral particle-hole symmetry. The $C_2\mathcal{T}$ symmetry alone remains topologically obstructed and is not represented in a simple site-to-si…
We study theoretically the magnetic screening properties of thin, diffusive superconductor/ferromagnet bilayers subject to a perpendicular magnetic field. We find that the effective penetration depth characterizing the magnetic response oscillates with the thickness of the ferromagnetic layer on the scale of the ferromagnetic coherence length.
Moiré superlattices in two-dimensional (2D) van der Waals (vdW) heterostructures provide 20 an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has built this moiré system one of the most renowned condensed matter platforms (1-10). So far the studies of tBLG has been mostly focused on the lowest two flat moiré bands at the first magic angle θm1 ~ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report 25 an observation of multiple well-isolated flat moiré ban…
At certain angles of rotation called `magic angles' twisted bilayer graphene features almost flat bands. The resulting strong correlations drive the system to novel phases which have been observed in experiments recently. A complete understanding of the `magic' angle physics---both at the single-particle as well as the many-particle level---is still missing, and the search is ongoing. Here, we identify a new set of `magic' angles, where locally flat bands with a variety of possible many-body instabilities arise, but where the single-particle problem admits an exact solution. This occurs in the…
We combine state-of-the-art large-scale first principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $θ=1.08^\circ$. We show that the energy width of the flat band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes.
This comment pertains the recent manuscript by Morissette {\it et al.} [arXiv:2206.08354v1]. The authors claim to have found signatures of collective excitations in electron spin resonance experiments that would be linked to the correlated structure of magic angle bilayer graphene. However, identical resonance features have already been reported in previous works on mono- and few-layer graphene, voiding their theoretical framework. A straight forward theoretical picture within the single-particle topologically non-trivial band structure of graphene delivers satisfactory explanations for the ob…
We theoretically study the band structure and optical conductivity of twisted bilayer graphene (TBG) near the magic angle considering the effects of lattice relaxation. We show that the optical conductivity spectrum is characterized by a series of peaks associated with the van Hove singularities in the band structure, and the peak energies evolve systematically with the twist angle. Lattice relaxation effects in TBG modify its band structure, especially the flat bands, which lead to significant shifts of the peaks in optical conductivity. These results demonstrate that spectroscopic features i…
When two monolayers of graphene are stacked with a small relative twist angle, the resulting band structure exhibits a remarkably flat pair of bands at a sequence of 'magic angles' where correlation effects can induce a host of exotic phases. Here, we study a class of related models of $n$-layered graphene with alternating relative twist angle $\pm θ$ which exhibit magic angle flat bands coexisting with several Dirac dispersing bands at the Moiré K point. Remarkably, we find that the Hamiltonian for the multilayer system can be mapped exactly to a set of decoupled bilayers at {\it different} a…
The long wavelength moiré superlattices in twisted 2D structures have emerged as a highly tunable platform for strongly correlated electron physics. We study the moiré bands in twisted transition metal dichalcogenide homobilayers, focusing on WSe$_2$, at small twist angles using a combination of first principles density functional theory, continuum modeling, and Hartree-Fock approximation. We reveal the rich physics at small twist angles $θ<4^\circ$, and identify a particular magic angle at which the top valence moiré band achieves almost perfect flatness. In the vicinity of this magic angle, …
In this work, we study the Raman spectra of twisted bilayer graphene samples as a function of their twist-angles ($θ$), ranging from 0.03$^\circ$ to 3.40$^\circ$, where local $θ$ are determined by analysis of their associated moire superlattices, as imaged by scanning microwave impedance microscopy. Three standard excitation laser lines are used (457, 532, and 633 nm wavelengths), and the main Raman active graphene bands (G and 2D) are considered. Our results reveal that electron-phonon interaction influences the G band's linewidth close to the magic angle regardless of laser excitation wavele…
In the magic-angle twisted bilayer graphene (MA-TBG), strong electron-electron (e-e) correlations caused by the band-flattening lead to many exotic quantum phases such as superconductivity, correlated insulator, ferromagnetism, and quantum anomalous Hall effects, when its low-energy van Hove singularities (VHSs) are partially filled. Here our high-resolution scanning tunneling microscope and spectroscopy measurements demonstrate that the e-e correlation in a non-magic-angle TBG with a twist angle θ = 1.49 still plays an important role in determining its electronic properties. Our most interest…
We introduce a new approach that allows one complete control over the modulation of the effective twist angle change in few-layer van der Waals heterostructures by irradiating them with longitudinal waves of light at the end of a waveguide. As a specific application, we consider twisted bilayer graphene and show that one can tune the magic angles to be either larger or smaller, allowing in-situ experimental control of the phase diagram of this and other related materials. A waveguide allows one to circumvent the free-space constraints on the absence of longitudinal electric field components of…
Graphene, a one-layer honeycomb lattice of carbon atoms, exhibits unconventional phenomena and attracts much interest since its discovery. Recently, an unexpected Mott-like insulator state induced by moiré pattern and a superconducting state are observed in magic-angle-twisted bilayer graphene, especially, without correlations between electrons, which gives more hints for the understanding and investigation of strongly correlated phenomena. The photon as boson, behaving differently with fermion, can also retrieve the unconventional phenomena of graphene, such as the bearded edge state which is…
Flat band electronic modes are responsible for superconductivity in twisted bilayer graphene (TBG) rotated at magic angles. From there other magic angles can be found for any multilayered twisted graphene systems. Eventually, this lead to the discovery of the highest ever known electron-electron correlated material. Moreover, the quantum phase diagram of TBG is akin to those observed among high-$T_{c}$ superconductors and thus there is a huge research effort to understand TBG in the hope of clarifying the physics behind such strong correlations. A particularity of the TBG is the coexistence of…
In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed11-16. Heterostrain, which is almost unavoidable in the TBG, can modify its single-particle band structure and lead to novel properties of the TBG that have never been considered so far. Here, we show that heterostrain in a TBG near the magic angle generates a new zero-energy flat band between the two VHSs. Doping the TBG to partially …
Very recently, twisted graphene bilayer (TGB) around the first magic angle 1.1° has attracted much attention for the realization of exotic quantum states, such as correlated insulator behavior and unconventional superconductivity. Here we elaborately studied a series of TGBs around the first magic angle engineered by heterostrain, where each layer is strained independently. Our experiment indicated that a moderate heterostrain enables the structural evolution from the small-angle TGB ( ~ 1.5°) to the strained magic-angle TGB (θ ~ 1.1°), exhibiting the characteristic low-energy flat bands. The …
