Magic-angle Graphene Research Articles

Effective model for superconductivity in magic-angle graphene

We carry out large-scale quantum Monte Carlo simulations of a candidate field theory for the onset of superconductivity in magic-angle twisted bilayer graphene. The correlated insulating state at charge neutrality spontaneously breaks U(1) Moiré valley symmetry. Owing to the topological nature of the bands, skyrmion defects of the order parameter carry charge 2e and condense upon doping. In our calculations we encode the U(1) symmetry by an internal degree of freedom such that it is not broken upon lattice regularization. Furthermore, the skyrmion carries the same charge. The nature of the doping-induced phase transitions depends on the strength of the easy-plane anisotropy that reduces the SU(2) valley symmetry to U(1)×Z2. For large anisotropy, we observe two distinct transitions separated by phase coexistence. While the insulator to superconducting transition is of mean-field character, the U(1) transition is consistent with three-dimensional XY criticality. Hence, the coupling between the gapless charge excitations of the superconducting phase and the XY order parameter is irrelevant. At small anisotropy, we observe a first-order transition characterized by phase separation. Published by the American Physical Society 2024

Atomistic theory of the moiré Hofstadter butterfly in magic-angle graphene

Atomistic theory of the moiré Hofstadter butterfly in magic-angle graphene

Research on the electronic structure of the interface between the LiNbO3 and the magic angle graphene electrode: first principle calculation

In this paper, the interfacial electronic structures of the monolayer, bilayer, and magic-angle graphene/LiNbO3 heterostructures are calculated. The density, energy band, differential charge density, effective mass are calculated and analyzed for the model of structure. The results show that the interface material can adjust the state density, band width, electron concentration and effective mass of the electrons around the Fermi energy level. Therefore, we predict that this structure is feasible in principle for experimental preparation, and can improve the transfer efficiency of carrier, which can provide a high-speed carrier basis for the solar cells.

Quantum textures of the many-body wavefunctions in magic-angle graphene.

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that reflect electronic correlation effects, broken symmetries and collective excitations. Many quantum phases have been discovered in magic-angle twisted bilayer graphene (MATBG), including correlatedinsulating1, unconventional superconducting2-5 and magnetic topological6-9 phases. The lack of microscopic information10,11 of possible broken symmetries has hampered our understanding of these phases12-17. Here we use high-resolution scanning tunnelling microscopy to study the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlatedinsulating, pseudogap and superconducting phases, show distinct broken-symmetry patterns with a √3 × √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré scale. We introduce a symmetry-based analysis using a set of complex-valued local order parameters, which show intricate textures that distinguish the various correlated phases. We compare the observed quantum textures of the correlated insulators at fillings of ±2 electrons per moiré unit cell to those expected for proposed theoretical ground states. In typical MATBG devices, these textures closely match those of the proposed incommensurate Kekulé spiral order15, whereas in ultralow-strain samples, our data have local symmetries like those of a time-reversal symmetric intervalley coherent phase12. Moreover, the superconducting state of MATBG shows strong signatures of intervalley coherence, only distinguishable from those of the insulator with our phase-sensitive measurements.

Five years of superconductivity in magic-angle graphene

Five years of superconductivity in magic-angle graphene

Modulations in Superconductors: Probes of Underlying Physics.

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors

Recent studies point to an exotic spin-triplet valley-singlet (STVS) superconducting phase in certain two-valley electron liquids, including rhombohedral trilayer graphene, Bernal bilayer graphene and ZrNCl, which nevertheless admits only trivial topology. Here, we predict that upon twisting two layers of STVS superconductors, a chiral fpm {{{{{{{rm{i}}}}}}}}{f}^{{prime} }-wave superconducting phase emerges near the ‘maximal’ twist angle of 30∘ where the system becomes an extrinsic quasi-crystal with 12-fold tiling. The resulting composite hosts an odd number of chiral Majorana edge modes and a single non-Abelian Majorana zero mode (MZM) in the vortex core. Through detailed symmetry analysis and microscopic modelling, we demonstrate that the non-Abelian topological superconductivity (TSC) forms robustly near the maximal twist when the isolated Fermi pockets coalesce into a single connected Fermi surface in the moiré Brillouin zone. Our results establish the large-twist-angle engineering, with distinct underlying moiré physics from magic-angle graphene, as a viable route toward non-Abelian TSC.

Spin-triplet superconductivity from intervalley Goldstone modes in magic-angle graphene

We consider magic-angle graphene in the doping regime around charge neutrality and study the connection between a recently proposed inter-valley coherent insulator at zero doping and the neighboring superconducting domes. The magic-angle graphene continuum model has an emergent U(1) valley-charge conservation symmetry, and an emergent SU(2) symmetry corresponding to opposite spin rotations in the two valleys. The inter-valley coherent insulator spontaneously breaks both these emergent symmetries, and as a result has four Goldstone modes which couple to doped charge carriers. We derive the effective interaction mediated by the Goldstone modes, and study its role in electron pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction, which is attractive in spin-triplet pairing channels and repulsive in spin-singlet channels. From a weak-coupling BCS calculation, we find the leading superconducting instability in the p-wave channel.

Moiré Superlattice MXene Nanosheets Constructed from Twisted Hexagon-Ti3AlC2 by Microwave-Assisted Lewis Molten Salt Etching: Implications for Structural Stability in Electrochemical Energy Storage

In order to solve the problem of instability of MXene nanosheet structure in electrochemical energy storage processes, inspired by the moiré superlattice effect of magic angle graphene, a twisted hexagon-Ti3AlC2 precursor was synthesized by an in situ reaction method using the molten pool effect of Lewis acid molten salt. In addition, moiré superlattice MXene Ti3C2 nanosheets with rotating moiré pattern lattice structure were innovatively constructed by the substitution reaction etching of the twisted hexagon-Ti3AlC2 precursor with different ionic Lewis acid salts and microwave-assisted etching. The microstructure evolution of moiré superlattice Ti3C2 nanosheets was characterized by a simple and intuitive method. The atomic arrangement and the rotating moiré pattern were modeled. The formation mechanism and relationship between the rotation angle and rotating moiré pattern were also analyzed. This contributes to the enrichment of the moiré superlattice material family. It is expected to further promote the research progress of MXene nanomaterials in the field of electrochemical energy storage.

Progress in Graphene and Magic-angle Graphene Superlattice in the Aspect of Superconductivity

Graphene, a relevant new material first defined in 1986, is gathering more and more interest in the circle of science and engineering especially material and electrical fields. It exhibit excellent mechanical features, extraordinary electrical and thermal properties due to its single atomic layer thickness and honeycomb bonding structure. Graphene is used as an advanced alternative to many traditional materials in a wide range of applications. There are two main synthesis methods, the top-down and the bottom-up, with many branches. The current research state cannot fulfill the urgent demands from the application. Therefore, sub-subjects of graphene are created by splitting or restructuring such as graphene quantum dot and graphene nanotube. In 2018, Yuan Cao et al. have reported a newest research about twisted multilayer graphene. This derivative of graphene showed tunable superconductivity, which also inherited the mechanical structure and thermodynamic properties of graphene. The twisted graphene holds great promise and is likely to be a milestone in superconductivity. Therefore, in this work, the progress in graphene and magic-angle graphene superlattice in the aspect of superconductivity were introduced.

Promotion of superconductivity in magic-angle graphene multilayers.

Graphene moiré superlattices show an abundance of correlated insulating, topological, and superconducting phases. Whereas the origins of strong correlations and nontrivial topology can be directly linked to flat bands, the nature of superconductivity remains enigmatic. We demonstrate that magic-angle devices made of twisted tri-, quadri-, and pentalayer graphene placed on monolayer tungsten diselenide exhibit flavor polarization and superconductivity. We also observe insulating states in the tril- and quadrilayer arising at finite electric displacement fields. As the number of layers increases, superconductivity emerges over an enhanced filling-factor range, and in the pentalayer it extends well beyond the filling of four electrons per moiré unit cell. Our results highlight the role of the interplay between flat and more dispersive bands in extending superconducting regions in graphene moiré superlattices.

Detecting Symmetry Breaking in Magic Angle Graphene Using Scanning Tunneling Microscopy.

A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry-breaking transitions, sparking interest in the potential relationship between symmetry breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here, we show how atomically resolved scanning tunneling microscopy can be used as a fingerprint of symmetry-breaking order. By analyzing the pattern of sublattice polarization and "Kekulé" distortions in small magnetic fields, order parameters for each of the most competitive symmetry-breaking states can be identified. In particular, we show that the "Kramers intervalley coherent state," which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field.

Fast proton and water transport in ceramic membrane-based magic-angle graphene

Ceramic membranes for energy conversion and storage devices are essential for becoming carbon neutral due to low cost and high stability, but limited by slow proton and water transport. Meanwhile magic-angle graphene with unconventional superconductivity ushers in a new era, properties research of which are in infant stage, urgently longing for specific applications. Herein, we investigate the ionic-conductivity and water-transport properties of ceramic membrane-based magic-angle graphene by choosing proton and water as a proof-of-concept for the first time, discover the twist-angle tuned proton conduction and water transport in ceramic membrane-based magic-angle graphene, demonstrate the faster proton and water transport in magic-angle graphene than that in graphene, and construct an efficient device of protonic ceramic membrane fuel cell based upon the new fast proton-conducting materials of magic-angle graphene. The proton conduction and water transport in magic-angle graphene can be easily tuned by the twist angle, explained by the corresponding potential energy surface. The smaller the twist angle is, and the faster the proton transport is. The protonic migration energy barrier in magic-angle graphene is lower by about 50% than that in graphene. Additionally, the water transport properties in magic-angle graphene can be improved by tuning twist angles. The electrode with magic-angle graphene can provide higher performance of protonic ceramic membrane fuel cells. The present work opens the specific application of ceramic membrane-based magic-angle graphene as new proton-conducting and water-transport materials in energy and environment.

Chern mosaic and Berry-curvature magnetism in magic-angle graphene

Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number, leading to the quantum anomalous Hall and Chern insulator states at integer fillings $\nu$ of the bands. It has been recently predicted, however, that depending on the local atomic-scale arrangements of the graphene and the encapsulating hBN lattices, rather than being a global topological invariant, the Chern number C may become position dependent, altering transport and magnetic properties of the itinerant electrons. Using a SQUID-on-tip, we directly image the nanoscale Berry-curvature-induced equilibrium orbital magnetism, the polarity of which is governed by the local Chern number, and detect its two constituent components associated with the drift and the self-rotation of the electronic wave packets. At $\nu=1$, we observe local zero-field valley-polarized Chern insulators forming a mosaic of microscopic patches of C=-1, 0, or 1, governed by the local sublattice polarization, consistent with predictions. Upon further filling, we find a first-order phase transition due to recondensation of electrons from valley K to K', which leads to irreversible flips of the local Chern number and the magnetization, and to the formation of valley domain walls giving rise to hysteretic global anomalous Hall resistance. The findings shed new light on the structure and dynamics of topological phases and call for exploration of the controllable formation of flavor domain walls and their utilization in twistronic devices.

Twisted graphene stabilized by organic linkers pillaring

Twisted graphene, including magic angle graphene, has attracted extensive attentions for its novel properties recently. However, twisted graphene is intrinsically unstable and this will obstruct their application in practice, especially for twisted nano graphene. The twist angles between adjacent layers will change spontaneously. This relaxation process will be accelerated under heat and strain. To solve this problem, we propose a strategy of pillaring twisted graphene by organic linkers in theory. The necessity and feasibility of this strategy is proved by numerical calculation.

Fermionic Monte Carlo Study of a Realistic Model of Twisted Bilayer Graphene

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight binding models and the long-ranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here we present for the first time unbiased Monte Carlo simulations of realistic models of magic angle TBG at charge-neutrality. We establish the absence of a sign problem for this model in a momentum space approach, and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion. Our results include (i) the emergence of an insulating Kramers inter-valley coherent ground state in competition with a correlated semi-metal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions which reveal a `pseudogap' regime, in which gap features are established at a higher temperature than the onset of order and (iii) predictions for electronic tunneling spectra and their evolution with temperature. Our results pave the way towards uncovering the physics of magic angle graphene through exact simulations of over a hundred electrons across a wide temperature range.

Moiré Physics of One-Dimensional Related Systems and Their Measurement

Currently, the magic-angle graphene has given a tremendous boost to the study of unconventional superconductors. On the other hand, there were still limited experimental studies on superconductivity in one-dimensional (1D) carbon nanotube systems. The study of experimental systems in demonstrating superconductivity was therefore scientifically important. In this review, we have shown strategies toward demonstrating the superconductivity for the single double-wall carbon nanotube (DWCNT). In general, there have been two directions to analyse superconducting properties of one-dimensional materials: (i) strong correlated states (ii) anomalous electron transport operations. We introduced the transmission electron microscope (TEM) and Rayleigh scattering spectroscopy to describe the strong correlation. The theoretical foundations of moiré physics have also been described. Given all the methods, we concluded that the most intuitive way to demonstrate the superconductivity of single double-walled carbon nanotubes is the critical temperature. The sharp drop of the resistance could be directly observed, and the Tc could be obtained from the electrical transport data. In the last section, we also summarized the challenges that need to be addressed in future superconductivity studies of 1D carbon nanotubes.

Growing twisted bilayer graphene at small angles

Growing twisted bilayer graphene at small angles

Strong coupling theory of magic-angle graphene: A pedagogical introduction

We give a self contained review of a recently developed strong coupling theory of magic-angle graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. We begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. We highlight how similarities between the flat bands and the lowest Landau level give insight into the effect of interactions. For example, at certain fractional fillings, we note the promise for realizing fractional Chern states. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Unexpectedly, topological textures of the sigma model carry electric charge which allows us to extend the same theory to describe the doped phases away from integer filling. We show how this approach can lead to superconductivity through the proliferation of charged topological textures, and estimate the Tc for the superconductor. We highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. Seeking to enhance this coupling helps predict new superconducting platforms, including the recently discovered alternating twist trilayer platform. We also contrast our proposal from strong coupling theories for other superconductors.

Frank-van der Merwe growth in bilayer graphene

Frank-van der Merwe growth in bilayer graphene