The electronic properties of bilayer graphene

Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene

Graphene-based, high-quality, two-dimensional electronic systems have emerged as a highly tunable platform for studying superconductivity1-21. Specifically, superconductivity has been observed in both electron- and hole-doped twisted graphene moiré systems1-17, whereas in crystalline graphene systems, superconductivity has so far been observed only in hole-doped rhombohedral trilayer graphene (RTG)18 and hole-doped Bernal bilayer graphene (BBG)19-21. Recently, enhanced superconductivity has been demonstrated20,21 in BBG because of the proximity to a monolayer WSe2. Here we report the observation of superconductivity and a series of flavour-symmetry-breaking phases in electron- and hole-doped BBG/WSe2 devices by electrostatic doping. The strength of the observed superconductivity is tunable by applied vertical electric fields. The maximum Berezinskii-Kosterlitz-Thouless transition temperature for the electron- and hole-doped superconductivity is about 210 mK and 400 mK, respectively. Superconductivities emerge only when the applied electric fields drive the BBG electron or hole wavefunctions towards the WSe2 layer, underscoring the importance of the WSe2 layer in the observed superconductivity. The hole-doped superconductivity violates the Pauli paramagnetic limit, consistent with an Ising-like superconductor. By contrast, the electron-doped superconductivity obeys the Pauli limit, although the proximity-induced Ising spin-orbit coupling is also notable in the conduction band. Our findings highlight the rich physics associated with the conduction band in BBG, paving the way for further studies into the superconducting mechanisms of crystalline graphene and the development of superconductor devices based on BBG.

Swelling of Thin Graphene Oxide Film in Water Vapor Studied by In Situ Spectroscopic Ellipsometry

Graphene oxide (GO) is obtained by the chemical treatment of graphene sheets, resulting in decoration with oxygen-containing functional groups. In the work presented here, we examined marked changes that occur in a thin film of parallel aligned GO sheets when exposed to water vapor at various pressures. It was found that exceptionally fast and substantial water uptake and release occur that is accompanied by major changes in GO interlayer spacing. These characteristics were obtained in situ with spectroscopic ellipsometry. At 99% relative humidity (RH) and 25 °C, the interlayer spacing became 1.41 nm, which recovers to ∼0.8 nm within 30 s when exposed to 10% RH. Besides layer thickness values, uniaxial optical constants for the GO vs RH were derived from the ellipsometry data. Molar refraction theory was applied that indicated monolayer water formation at ∼91% RH at 25 °C upon water adsorption. Our findings contribute to the understanding of the interaction between GO and its environment. The very outspoken effect of external water vapor pressure on GO water content, interlayer spacing, and optical properties can be utilized in sensing and separation devices, subnanometer positioning, chemical switches, and environmentally aware materials.

Toward Fully Multiferroic van der Waals SpinFETs: Basic Design and Quantum Calculations

Manipulating spin transport enhances the functionality of electronic devices, allowing them to surpass physical constraints related to speed and power. For this reason, the use of van der Waals multiferroics at the interface of heterostructures offers promising prospects for developing high-performance devices, enabling the electrical control of spin information. Our work focuses primarily on a mechanism for multiferroicity in two-dimensional van der Waals materials that stems from an interplay between antiferromagnetism and the breaking of inversion symmetry in certain bilayers. We provide evidence for spin-electrical couplings that include manipulating van der Waals multiferroic edges via external voltages and the subsequent control of spin transport including for fully multiferroic spin field-effect transistors.

Probing the Anisotropic Fermi Surface in Tetralayer Graphene via Transverse Magnetic Focusing

Bernal-stacked tetralayer graphene (4LG) exhibits intriguing low-energy properties, featuring two massive sub-bands and showcasing diverse features of topologically distinct, anisotropic Fermi surfaces, including Lifshitz transitions and trigonal warping. Here, we study the influence of the band structure on electron dynamics within 4LG using transverse magnetic focusing. Our analysis reveals two distinct focusing peaks corresponding to the two sub-bands. Furthermore, we uncover a pronounced dependence of the focusing spectra on crystal orientations, indicative of an anisotropic Fermi surface. Utilizing the semiclassical model, we attribute this orientation-dependent behavior to the trigonal warping of the band structure. This phenomenon leads to variations in electron trajectories based on crystal orientation. Our findings not only enhance our understanding of the dynamics of electrons in 4LG but also offer a promising method for probing anisotropic Fermi surfaces in other materials.

Width effects on bilayer graphene nanoribbon polarons

Recent progress in nanoelectronics suggests that stacking armchair graphene nanoribbons (AGNRs) into bilayer systems can generate materials with emergent quasiparticle properties. In this context, the impact of width changes is especially relevant. However, its effect on charged carriers remains elusive. In this work, we investigate the effect of width and interlayer interaction changes on polaron states via a hybrid Hamiltonian that couples the electronic and lattice interactions. Results show the rising of two interlayer polarons: the non-symmetric and the symmetric. The coupling strength needed to induce the transition between states depends on the nanoribbon width, being at the most extreme case of ≈174 meV. Electronic properties such as the coupling strength threshold, carrier size, and gap are shown to respect the AGNR width family 3p, 3p + 1, and 3p + 2 rule. The findings demonstrate that strong interlayer interaction simultaneously delocalizes the carriers and reduces the gap up to 0.6 eV. Additionally, it is found that some layers are more prone to share charge, indicating a potential heterogeneous stacking where a particular electronic pathway is favored. The results present an encouraging prospect for integrating AGNR bilayers in future flexible electronics.

Effective Manipulation of a Colossal Second-Order Transverse Response in an Electric-Field-Tunable Graphene Moiré System

The second-order nonlinear transport illuminates a frequency-doubling response emerging in quantum materials with a broken inversion symmetry. The two principal driving mechanisms, the Berry curvature dipole and the skew scattering, reflect various information including ground-state symmetries, band dispersions, and topology of electronic wave functions. However, effective manipulation of them in a single system has been lacking, hindering the pursuit of strong responses. Here, we report on the effective manipulation of the two mechanisms in a single graphene moiré superlattice, AB-BA stacked twisted double bilayer graphene. Most saliently, by virtue of the high tunability of moiré band structures and scattering rates, a record-high second-order transverse conductivity ∼ 510 μm S V-1 is observed, which is orders of magnitude higher than any reported values in the literature. Our findings establish the potential of electrically tunable graphene moiré systems for nonlinear transport manipulations and applications.

Quantum-Geometric Origin of Out-of-Plane Stacking Ferroelectricity

Stacking ferroelectricity (SFE) has been discovered in a wide range of van der Waals materials and holds promise for applications, including photovoltaics and high-density memory devices. We show that the microscopic origin of out-of-plane stacking ferroelectric polarization can be generally understood as a consequence of a nontrivial Berry phase borne out of an effective Su-Schrieffer-Heeger model description with broken sublattice symmetry, thus elucidating the quantum-geometric origin of polarization in the extremely nonperiodic bilayer limit. Our theory applies to known stacking ferroelectrics such as bilayer transition-metal dichalcogenides in 3R and T_{d} phases, as well as general AB-stacked honeycomb bilayers with staggered sublattice potential. Our explanatory and self-consistent framework based on the quantum-geometric perspective establishes quantitative understanding of out-of-plane SFE materials beyond symmetry principles.

Toward the Production of Super Graphene

The quality requirements of graphene depend on the applications. Some have a high tolerance for graphene quality and even require some defects, while others require graphene as perfect as possible to achieve good performance. So far, synthesis of large-area graphene films by chemical vapor deposition of carbon precursors on metal substrates, especially on Cu, remains the main way to produce high-quality graphene, which has been significantly developed in the past 15 years. However, although many prototypes are demonstrated, their performance is still more or less far from the theoretical property limit of graphene. This review focuses on how to make super graphene, namely graphene with a perfect structure and free of contaminations. More specially, this study focuses on graphene synthesis on Cu substrates. Typical defects in graphene are first discussed together with the formation mechanisms and how they are characterized normally, followed with a brief review of graphene properties and the effects of defects. Then, the synthesis progress of super graphene from the aspects of substrate, grain size, wrinkles, contamination, adlayers, and point defects are reviewed. Graphene transfer is briefly discussed as well. Finally, the challenges to make super graphene are discussed and a strategy is proposed.

Superconducting Cavity-Based Sensing of Band Gaps in 2D Materials

The superconducting coplanar waveguide (SCPW) cavity plays an essential role in various areas like superconducting qubits, parametric amplifiers, radiation detectors, and studying magnon-photon and photon-phonon coupling. Despite its wide-ranging applications, the use of SCPW cavities to study various van der Waals 2D materials has been relatively unexplored. The resonant modes of the SCPW cavity exquisitely sense the dielectric environment. In this work, we measure the charge compressibility of bilayer graphene coupled to a half-wavelength SCPW cavity. Our approach provides a means to detect subtle changes in the capacitance of the bilayer graphene heterostructure, which depends on the compressibility of bilayer graphene, manifesting as shifts in the resonant frequency of the cavity. This method holds promise for exploring a wide class of van der Waals 2D materials, including transition metal dichalcogenides (TMDs) and their moiré, where DC transport measurement is challenging.

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

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

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

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

Infrared Resonance Raman of Bilayer Graphene: Signatures of Massive Fermions and Band Structure on the 2D Peak

Few-layer graphene possesses low-energy carriers that behave as massive Fermions, exhibiting intriguing properties in both transport and light scattering experiments. Lowering the excitation energy of resonance Raman spectroscopy down to 1.17 eV, we target these massive quasiparticles in the split bands close to the K point. The low excitation energy weakens some of the Raman processes that are resonant in the visible, and induces a clearer frequency-separation of the substructures of the resonance 2D peak in bi- and trilayer samples. We follow the excitation-energy dependence of the intensity of each substructure, and comparing experimental measurements on bilayer graphene with ab initio theoretical calculations, we trace back such modifications on the joint effects of probing the electronic dispersion close to the band splitting and enhancement of electron-phonon matrix elements.

De Haas-van Alphen spectroscopy and magnetic breakdown in moiré graphene

Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas-van Alphen effect in moiré graphene. Scanning by means of superconducting quantum interference device (SQUID)-on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moiré bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.

Coherent charge oscillations in a bilayer graphene double quantum dot

The coherent dynamics of a quantum mechanical two-level system passing through an anti-crossing of two energy levels can give rise to Landau-Zener-Stückelberg-Majorana (LZSM) interference. LZSM interference spectroscopy has proven to be a fruitful tool to investigate charge noise and charge decoherence in semiconductor quantum dots (QDs). Recently, bilayer graphene has developed as a promising platform to host highly tunable QDs potentially useful for hosting spin and valley qubits. So far, in this system no coherent oscillations have been observed and little is known about charge noise in this material. Here, we report coherent charge oscillations and [Formula: see text] charge decoherence times in a bilayer graphene double QD. The charge decoherence times are measured independently using LZSM interference and photon assisted tunneling. Both techniques yield [Formula: see text] average values in the range of 400-500 ps. The observation of charge coherence allows to study the origin and spectral distribution of charge noise in future experiments.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Intra-Zero-Energy Landau Level Crossings in Bilayer Graphene at High Electric Fields

The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.

Gapless edge states localized to odd/even layers of AA'-stacked honeycomb multilayers with staggered AB-sublattice potentials

In honeycomb multilayers with staggered AB-sublattice potentials, we predict gapless edge states localized to either of the odd and the even layers for the AA[Formula: see text] stacking order in which the sublattice-pseudospin polarizations of adjacent layers are antiparallel. Gaps in the projected layer-pseudospin spectrum suppress interlayer hopping between odd and even layers. The layer-valley Chern number corresponding to the edge states was obtained by decomposing the occupied state into two layer-pseudospin sectors by using a projected layer-pseudospin operator. For the AB[Formula: see text] stacking, the sublattice-pseudospin polarizations of adjacent layers are antiparallel, but the layer-pseudospin spectrum gap closes at the interface of the topologically different states, leading to gapped edge states. For the AA and AB stackings where the sublattice-pseudospin polarizations of the adjacent layers are parallel, the gapless edge states corresponding to quantum valley Hall states are evenly distributed across the layers.

Signatures of Cooper pair dynamics and quantum-critical superconductivity in tunable carrier bands

Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Quantum-critical soft modes drive pairing interactions in which the pair scattering processes are highly collinear and can be classified into two categories: forward scattering and backscattering. Conversely, in conventional phonon mechanisms, Cooper pair scattering is of a generic noncollinear character. In this study, we present a method to discern the kinematic type by observing the evolution of superconductivity while adjusting the Fermi surface geometry. To demonstrate our approach, we utilize the recently reported phase diagrams of untwisted graphene multilayers. Our analysis connects the emergence of superconductivity at "ghost crossings" of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed nonmonotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it lends strong support to a particular quantum-critical superconductivity scenario in which pairing is driven by intervalley coherence fluctuations. These findings offer direct insights into the genesis of pairing in these systems, providing compelling evidence for the electron-electron interactions driving superconductivity. More broadly, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.

Coexistence of large-area topological pseudospin and valley states in a tri-band heterostructure system

The rapid development of topological photonics has significantly revolutionized our comprehension of electromagnetic wave manipulation in recent decades. Recent research exploiting large-area topological states inserts an additional gapless PC structure between topologically trivial and nontrivial PCs, effectively introducing the mode width degree of freedom. Nevertheless, these heterostructures mainly support only single-type waveguide states operating within a single frequency band. To address these limitations, we propose a novel, to the best of our knowledge, tri-band three-layer heterostructure system, supporting both large-area pseudospin- and valley-locked states. The system showcases tunable mode widths with different operational bandwidths. Moreover, the heterostructures exhibit inherent topological characteristics and reflection-free interfacing, which are verified in the well-designed Z-shaped channels. The proposed heterostructure system can be used to design multi-band multi-functional high-flexibility topological devices, providing great advantages for enlarging the on-chip integrated communication systems.

Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot

We predict the existence of spontaneous spin and valley symmetry-broken states of interacting massive Dirac Fermions in a gated bilayer graphene quantum dot based on the exact diagonalization of the many-body Hamiltonian. The dot is defined by a vertical electric field and lateral gates, and its single-particle (SP) energies, wave functions, and Coulomb matrix elements are computed by using the atomistic tight-binding model. The effect of the Coulomb interaction is measured by the ratio of Coulomb elements to the SP level spacing. As we increase the interaction strength, we find the electrons in a series of spin and valley symmetry-broken phases with increasing valley and spin polarizations. The phase transitions result from the competition of the SP, exchange, and correlation energy scales. A phase diagram for N = 1-6 electrons is mapped out as a function of the Coulomb interaction strength.

Effect of gamma irradiation on the physical properties of MoS2 monolayer

Two-dimensional transition metal dichalcogenides (2D-TMDs) have been proposed as novel optoelectronic materials for space applications due to their relatively light weight. MoS2 has been shown to have excellent semiconducting and photonic properties. Although the strong interaction of ionizing gamma radiation with bulk materials has been demonstrated, understanding its effect on atomically thin materials has scarcely been investigated. Here, we report the effect of gamma irradiation on the structural and electronic properties of a monolayer of MoS2. We perform Raman spectroscopy and X-ray photoelectron spectroscopy (XPS) studies of MoS2, before and after gamma ray irradiation with varying doses and density functional theory (DFT) calculations. The Raman spectra and XPS results demonstrate that point defects dominate after the gamma irradiation of MoS2. DFT calculations elucidate the electronic properties of MoS2 before and after irradiation. Our work makes several contributions to the field of 2D materials research. First, our study of the electronic density of states and the electronic properties of a MoS2 monolayer irradiated by gamma rays sheds light on the properties of a MoS2 monolayer under gamma irradiation. Second, our study confirms that point defects are formed as a result of gamma irradiation. And third, our DFT calculations qualitatively suggest that the conductivity of the MoS2 monolayer may increase after gamma irradiation due to the creation of additional defect states.

Electrostatic Tuning of Bilayer Graphene Edge Modes

We study the effect of a local potential shift induced by a side electrode on the edge modes at the boundary between gapped and ungapped bilayer graphene. A potential shift close to the gapped-ungapped boundary causes the emergence of unprotected edge modes, propagating in both directions along the boundary. These counterpropagating edge modes allow edge backscattering, as opposed to the case of valley-momentum-locked edge modes. We then calculate the conductance of a bilayer graphene wire in presence of finger-gate electrodes, finding strong asymmetries with energy inversion and deviations from conductance quantization that can be understood with the gate-induced unprotected edge modes.

Specular Electron Focusing between Gate-Defined Quantum Point Contacts in Bilayer Graphene

We report multiterminal measurements in a ballistic bilayer graphene (BLG) channel, where multiple spin- and valley-degenerate quantum point contacts (QPCs) are defined by electrostatic gating. By patterning QPCs of different shapes along different crystallographic directions, we study the effect of size quantization and trigonal warping on transverse electron focusing (TEF). Our TEF spectra show eight clear peaks with comparable amplitudes and weak signatures of quantum interference at the lowest temperature, indicating that reflections at the gate-defined edges are specular, and transport is phase coherent. The temperature dependence of the focusing signal shows that, despite the small gate-induced bandgaps in our sample (≲45 meV), several peaks are visible up to 100 K. The achievement of specular reflection, which is expected to preserve the pseudospin information of the electron jets, is promising for the realization of ballistic interconnects for new valleytronic devices.

Particle-hole symmetry protects spin-valley blockade in graphene quantum dots

Particle-hole symmetry plays an important role in the characterization of topological phases in solid-state systems¹. It is found, for example, in free-fermion systems at half filling and it is closely related to the notion of antiparticles in relativistic field theories². In the low-energy limit, graphene is a prime example of a gapless particle-hole symmetric system described by an effective Dirac equation^3,4 in which topological phases can be understood by studying ways to open a gap by preserving (or breaking) symmetries^5,6. An important example is the intrinsic Kane-Mele spin-orbit gap of graphene, which leads to a lifting of the spin-valley degeneracy and renders graphene a topological insulator in a quantum spin Hall phase⁷ while preserving particle-hole symmetry. Here we show that bilayer graphene allows the realization of electron-hole double quantum dots that exhibit near-perfect particle-hole symmetry, in which transport occurs via the creation and annihilation of single electron-hole pairs with opposite quantum numbers. Moreover, we show that particle-hole symmetric spin and valley textures lead to a protected single-particle spin-valley blockade. The latter will allow robust spin-to-charge and valley-to-charge conversion, which are essential for the operation of spin and valley qubits.

Theory of Excitons in Gated Bilayer Graphene Quantum Dots

We present a theory of excitons in gated bilayer graphene (BLG) quantum dots (QDs). Electrical gating of BLG opens an energy gap, turning this material into an electrically tunable semiconductor. Unlike in laterally gated semiconductor QDs, where electrons are attracted and holes repelled, we show here that lateral structuring of metallic gates results in a gated lateral QD confining both electrons and holes. Using an accurate atomistic approach and exact diagonalization tools, we describe strongly interacting electrons and holes forming an electrically tunable exciton. We find these excitons to be different from those found in semiconductor QDs and nanocrystals, with exciton energy tunable by voltage from the terahertz to far infrared (FIR) range. The conservation of spin, valley, and orbital angular momentum results in an exciton fine structure with a band of dark low-energy states, making this system a promising candidate for storage, detection and emission of photons in the terahertz range.

An Atomistic Insight into Moiré Reconstruction in Twisted Bilayer Graphene beyond the Magic Angle

Twisted bilayer graphene exhibits electronic properties strongly correlated with the size and arrangement of moiré patterns. While rigid rotation of the two graphene layers results in a moiré interference pattern, local rearrangements of atoms due to interlayer van der Waals interactions result in atomic reconstruction within the moiré cells. Manipulating these patterns by controlling the twist angle and externally applied strain provides a promising route to tuning their properties. Atomic reconstruction has been extensively studied for angles close to or smaller than the magic angle (θ _m = 1.1°). However, this effect has not been explored for applied strain and is believed to be negligible for high twist angles. Using interpretive and fundamental physical measurements, we use theoretical and numerical analyses to resolve atomic reconstruction in angles above θ _m . In addition, we propose a method to identify local regions within moiré cells and track their evolution with strain for a range of representative high twist angles. Our results show that atomic reconstruction is actively present beyond the magic angle, and its contribution to the moiré cell evolution is significant. Our theoretical method to correlate local and global phonon behavior further validates the role of reconstruction at higher angles. Our findings provide a better understanding of moiré reconstruction in large twist angles and the evolution of moiré cells under the application of strain, which might be potentially crucial for twistronics-based applications.

A two-dimensional tunable double Weyl fermion in BL-α borophene

Two-dimensional (2D) materials with nontrivial band crossings, namely linear or double Weyl points, have been attracting tremendous attention. However, it remains a challenge to find existing 2D materials that host such nontrivial states. Here, based on first-principles calculations and symmetry analysis, we discover that the recently synthesized BL-α borophene is a metal with a tunable double Weyl point. Remarkably, both bands forming the double Weyl point have upward band bending. In addition, it shows an anisotropic band dispersion when away from the double Weyl point. To characterize its anisotropy, we define a quantity G, which could be changed from 1 to infinity when going from the energy of the double Weyl point to the Fermi level. Furthermore, the outer band of the double Weyl point is sensitive to biaxial strain, and could be changed from upward bending to downward bending. During this process, it has a critical case, in which the outer-band becomes flat. The changes in outer-band induce a variation in the density of states around the double Weyl point, thus giving rise to changes in its macroscopic physical properties. Applying a uniaxial strain enables the double Weyl point to transform into a pair of Weyl points by breaking the threefold rotation of BL-α borophene. When breaking the inversion symmetry and in-plane twofold rotation symmetry by a vertical symmetry, the double Weyl point still persisted; meanwhile, an additional pair of linear Weyl points appears on the high-symmetry path, giving rise to a Weyl complex case. Overall, our work thus provides an existing 2D material, BL-α borophene, to study the nontrivial band crossings in 2D.

Strong gate-tunability of flat bands in bilayer graphene due to moiré encapsulation between hBN monolayers

When using hexagonal boron-nitride (hBN) as a substrate for graphene, the resulting moiré pattern creates secondary Dirac points. By encapsulating a multilayer graphene within aligned hBN sheets the controlled moiré stacking may offer even richer benefits. Using advanced tight-binding simulations on atomistically-relaxed heterostructures, here we show that the gap at the secondary Dirac point can be opened in selected moiré-stacking configurations, and is independent of any additional vertical gating of the heterostructure. On the other hand, gating can broadly tune the gap at the principal Dirac point, and may thereby strongly compress the first moiré mini-band in width against the moiré-induced gap at the secondary Dirac point. We reveal that in hBN-encapsulated bilayer graphene this novel mechanism can lead to isolated bands flatter than 10 meV under moderate gating, hence presenting a convenient pathway towards electronically-controlled strongly-correlated states on demand.

Optimal twist angle for a graphene-like bilayer

The first optimal-or 'magic'-angle leading to the nullity of the Dirac/Fermi velocity for twisted bilayer graphene is re-evaluated in the Bistritzer-MacDonald set-up (Bistritzer and MacDonald 2011Proc. Natl Acad. Sci.10812233-7). From the details of that calculation we study the resulting alterations when the properties of the two layers are not exactly the same. A moiré combination of lattices without relative rotation but with different spacing lengths may also lead to a vanishing Dirac velocity. Hopping amplitudes can vary as well, and curvature is one of the possible causes for their change. In the case of small curvature values and situations dominated by hopping energy scales, the optimal angle becomes wider than in the 'flat' case.

Diamane-like Films Based on Twisted G/BN Bilayers: DFT Modelling of Atomic Structures and Electronic Properties

Diamanes are unique 2D carbon materials that can be obtained by the adsorption of light atoms or molecular groups onto the surfaces of bilayer graphene. Modification of the parent bilayers, such as through twisting of the layers and the substitution of one of the layers with BN, leads to drastic changes in the structure and properties of diamane-like materials. Here, we present the results of the DFT modelling of new stable diamane-like films based on twisted Moiré G/BN bilayers. The set of angles at which this structure becomes commensurate was found. We used two commensurate structures with twisted angles of θ = 10.9° and θ = 25.3° with the smallest period as the base for the formation of the diamane-like material. Previous theoretical investigations did not take into account the incommensurability of graphene and boron nitride monolayers when considering diamane-like films. The double-sided hydrogenation or fluorination of Moiré G/BN bilayers and the following interlayer covalent bonding led to the opening of a gap up to 3.1 eV, which was lower than the corresponding values of h-BN and c-BN. The considered G/BN diamane-like films offer great potential in the future for a variety of engineering applications.

A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp²carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.

Topological superconducting vortex from trivial electronic bands

Superconducting vortices are promising traps to confine non-Abelian Majorana quasi-particles. It has been widely believed that bulk-state topology, of either normal-state or superconducting ground-state wavefunctions, is crucial for enabling Majorana zero modes in solid-state systems. This common belief has shaped two major search directions for Majorana modes, in either intrinsic topological superconductors or trivially superconducting topological materials. Here we show that Majorana-carrying superconducting vortex is not exclusive to bulk-state topology, but can arise from topologically trivial quantum materials as well. We predict that the trivial bands in superconducting HgTe-class materials are responsible for inducing anomalous vortex topological physics that goes beyond any existing theoretical paradigms. A feasible scheme of strain-controlled Majorana engineering and experimental signatures for vortex Majorana modes are also discussed. Our work provides new guidelines for vortex-based Majorana search in general superconductors.

Probing interlayer van der Waals strengths of two-dimensional surfaces and defects, through STM tip-induced elastic deformations

A methodology to test the interlayer bonding strength of two-dimensional (2D) surfaces and associated one (1D)- and two (2D)- dimensional surface defects using scanning tunneling microscope tip-induced deformation, is demonstrated. Surface elastic deformation characteristics of soft 2D monatomic sheets of graphene and graphite in contrast to NbSe₂indicates related association with the underlying local bonding configurations. Surface deformation of 2D graphitic moiré patterns reveal the inter-layer van der Waals strength varying across its domains. These results help in the understanding of the comparable interlayer bonding strength of 1D grain boundary as well as the grains. Anomalous phenomena related to probing 2D materials at small gap distances as a function of strain is discussed.

Gate-tunable bolometer based on strongly coupled graphene mechanical resonators

Bolometers based on graphene have demonstrated outstanding performance with high sensitivity and short response time. In situ adjustment of bolometers is very important in various applications, but it is still difficult to implement in many systems. Here we propose a gate-tunable bolometer based on two strongly coupled graphene nanomechanical resonators. Both resonators are exposed to the same light field, and we can measure the properties of one bolometer by directly tracking the resonance frequency shifts, and indirectly measure the other bolometer through mechanical coupling. We find that the sensitivity and the response bandwidth of both bolometers can be independently adjusted by tuning the corresponding gate voltages. Moreover, the properties of the indirectly measured bolometer show a dependence on the coupling between the two resonators, with other parameters being fixed. Our method has the potential to optimize the design of large-scale bolometer arrays, and open new horizons in infrared/terahertz astronomy and communication systems.

Enhanced superconductivity in spin-orbit proximitized bilayer graphene

In the presence of a large perpendicular electric field, Bernal-stacked bilayer graphene (BLG) features several broken-symmetry metallic phases^1-3 as well as magnetic-field-induced superconductivity¹. The superconducting state is quite fragile, however, appearing only in a narrow window of density and with a maximum critical temperature T_c≈ 30 mK. Here we show that placing monolayer tungsten diselenide (WSe₂) on BLG promotes Cooper pairing to an extraordinary degree: superconductivity appears at zero magnetic field, exhibits an order of magnitude enhancement in T_c and occurs over a density range that is wider by a factor of eight. By mapping quantum oscillations in BLG-WSe₂ as a function of electric field and doping, we establish that superconductivity emerges throughout a region for which the normal state is polarized, with two out of four spin-valley flavours predominantly populated. In-plane magnetic field measurements further reveal that superconductivity in BLG-WSe₂ can exhibit striking dependence of the critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly obeyed on one end of the superconducting dome, yet sharply violated on the other. Moreover, the superconductivity arises only for perpendicular electric fields that push BLG hole wavefunctions towards WSe₂, indicating that proximity-induced (Ising) spin-orbit coupling plays a key role in stabilizing the pairing. Our results pave the way for engineering robust, highly tunable and ultra-clean graphene-based superconductors.

Breaking of Inversion Symmetry and Interlayer Electronic Coupling in Bilayer Graphene Heterostructure by Structural Implementation of High Electric Displacement Fields

Controlling the interlayer coupling in two-dimensional (2D) materials generates novel electronic and topological phases. Its effective implementation is commonly done with a transverse electric field. However, phases generated by high displacement fields are elusive in this standard approach. Here, we introduce an exceptionally large displacement field by structural modification of a model system: AB-stacked bilayer graphene (BLG) on a SiC(0001) surface. We show that upon intercalation of gadolinium, electronic states in the top graphene layers exhibit a significant difference in the on-site potential energy, which effectively breaks the interlayer coupling between them. As a result, for energies close to the corresponding Dirac points, the BLG system behaves like two electronically isolated single graphene layers. This is proven by local scanning tunneling microscopy (STM)/spectroscopy, corroborated by density functional theory, tight binding, and multiprobe STM transport. The work presents metal intercalation as a promising approach for the synthesis of 2D graphene heterostructures with electronic phases generated by giant displacement fields.

Feature-Rich Electronic Properties of Sliding Bilayer Germanene

This study employs first-principles calculations to elucidate the properties of sliding bilayer germanene (BLGe). The buckled structure of germanene can afford a greater number of metastable stacking configurations than planar graphene and enrich the electronic properties. Herein, a detailed analysis of the structural variety, shift-dependent energy bands, and spatial charge densities of BLGe is presented. The projected density of states (PDOS) reveals diverse structures such as plateaus, dips, symmetric/asymmetric peaks, and shoulders. The low-lying ones of the prominent structures could correspond to single or multiorbital hybridization, depending on the stacking configuration.

Vacancy clustering effect on the electronic and transport properties of bilayer graphene nanoribbons

Experimental realizations of two-dimensional materials are hardly free of structural defects such as e.g. vacancies, which, in turn, modify drastically its pristine physical defect-free properties. In this work, we explore effects due to point defect clustering on the electronic and transport properties of bilayer graphene nanoribbons, for AA and AB stacking and zigzag and armchair boundaries, by means of the tight-binding approach and scattering matrix formalism. Evident vacancy concentration signatures exhibiting a maximum amplitude and an universality regardless of the system size, stacking and boundary types, in the density of states around the zero-energy level are observed. Our results are explained via the coalescence analysis of the strong sizeable vacancy clustering effect in the system and the breaking of the inversion symmetry at high vacancy densities, demonstrating a similar density of states for two equivalent degrees of concentration disorder, below and above the maximum value.

Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices

This work reports the three-band structure associated with a Lieb lattice with arbitrary nearest and next-nearest neighbors hopping interactions. For specific configurations, the system admits a flat band located between two dispersion bands, where three inequivalent Dirac valleys are identified. Furthermore, quasi-particles are effectively described by a spin-1 Dirac-type equation. Under external homogeneous magnetic fields, the Landau levels are exactly determined as the third-order polynomial equation for the energy can be solved using Cardano's formula. It is also shown that an external anti-symmetric field promotes the existence of current-carrying states, so-called snake states, confined at the interface where the external field changes its sign.

Strain-induced stacking transition in bilayer graphene

Strain, both naturally occurring and deliberately engineered, can have a considerable effect on the structural and electronic properties of 2D and layered materials. Uniaxial or biaxial heterostrain modifies the stacking arrangement of bilayer graphene (BLG) which subsequently influences the electronic structure of the bilayer. Here, we use density functional theory (DFT) calculations to investigate the interplay between an external applied heterostrain and the resulting stacking in BLG. We determine how a strain applied to one layer is transferred to a second, 'free' layer and at what critical strain the ground-state AB-stacking is disrupted. To overcome limitations introduced by periodic boundary conditions, we consider an approximate system consisting of an infinite graphene sheet and an armchair graphene nanoribbon. We find that above a critical strain of∼1%, it is energetically favourable for the free layer to be unstrained, indicating a transition between uniform AB-stacking and non-uniform mixed stacking. This is in agreement with a simple model estimate based on the individual energy contributions of strain and stacking effects. Our findings suggest that small levels of strain provide a platform to reversibly engineer stacking order and Moiré features in bilayers, providing a viable alternative to twistronics to engineer topological and exotic physical phenomena in such systems.

Direct geometric probe of singularities in band structure

A quantum system’s energy landscape may have points where multiple energy surfaces are degenerate and that exhibit singular geometry of the wave function manifold, with major consequences for the system’s properties. Ultracold atoms in optical lattices have been used to indirectly characterize such points in the band structure. We measured the non-Abelian transformation produced by transport directly through the singularities. We accelerated atoms along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic band-touching points of a honeycomb lattice. Measurements after transport identified the topological winding numbers of these singularities to be 1 and 2, respectively. Our work introduces a distinct method for probing singularities that enables the study of non-Dirac singularities in ultracold-atom quantum simulators.

Facet engineering of ultrathin two-dimensional materials

Ultrathin two-dimensional (2D) materials exhibit broad application prospects in many fields due to the enhanced specific surface area to volume ratio and quantum confinement effect. Because of the atomic thickness and various orientations, ultrathin 2D materials exposing specific facets have drawn great attention for various applications in catalysis, batteries, optoelectronics, magnetism, epitaxial template for material growth, etc. Though maintaining the atomic thickness of 2D materials while controlling crystal facets is an enormous challenge, breakthroughs are being made. This review provides a comprehensive overview of the recent advances in the facet engineering of 2D materials, ranging from a basic understanding of facets and the corresponding approaches and the significance of facet engineering. We also propose current challenges and forecast future development directions including the establishment of a facet database, the fabrication of new 2D materials, the design of specific substrates, and the introduction of theoretical calculations and in situ characterization techniques. This review can guide researchers to design ultrathin 2D materials with unique and distinct facets and provide an insight into the applications of energy, magnetism, optics, biomedicine, and other fields.

WSe2 as Transparent Top Gate for Infrared Near-Field Microscopy

Independent control of carrier density and out-of-plane displacement field is essential for accessing novel phenomena in two-dimensional (2D) material heterostructures. While this is achieved with independent top and bottom metallic gate electrodes in transport experiments, it remains a challenge for near-field optical studies as the top electrode interferes with the optical path. Here, we characterize the requirements for a material to be used as the top-gate electrode and demonstrate experimentally that few-layer WSe₂ can be used as a transparent, ambipolar top-gate electrode in infrared near-field microscopy. We carry out nanoimaging of plasmons in a bilayer graphene heterostructure tuning the plasmon wavelength using a trilayer WSe₂ gate, achieving a density modulation amplitude exceeding 2 × 10¹² cm^-2. The observed ambipolar gate-voltage response allows us to extract the energy gap of WSe₂, yielding a value of 1.05 eV. Our results provide an additional tuning knob to cryogenic near-field experiments on emerging phenomena in 2D materials and moiré heterostructures.

Spin relaxation in a single-electron graphene quantum dot

The relaxation time of a single-electron spin is an important parameter for solid-state spin qubits, as it directly limits the lifetime of the encoded information. Thanks to the low spin-orbit interaction and low hyperfine coupling, graphene and bilayer graphene (BLG) have long been considered promising platforms for spin qubits. Only recently, it has become possible to control single-electrons in BLG quantum dots (QDs) and to understand their spin-valley texture, while the relaxation dynamics have remained mostly unexplored. Here, we report spin relaxation times (T₁) of single-electron states in BLG QDs. Using pulsed-gate spectroscopy, we extract relaxation times exceeding 200 μs at a magnetic field of 1.9 T. The T₁ values show a strong dependence on the spin splitting, promising even longer T₁ at lower magnetic fields, where our measurements are limited by the signal-to-noise ratio. The relaxation times are more than two orders of magnitude larger than those previously reported for carbon-based QDs, suggesting that graphene is a potentially promising host material for scalable spin qubits.

Graphene has long been considered to be a promising host for spin qubits, however a demonstration of long spin relaxation times for a potential qubit has been lacking. Here, the authors report the electrical measurement of the single-electron spin relaxation time exceeding 200 μs in a bilayer graphene quantum dot.

Interaction between Electromechanical Fields and Carriers in a Multilayered Piezoelectric Semiconductor Beam

This study discusses the interaction between electromechanical fields and carriers in a multilayered ZnO beam where the c-axis of every two adjacent layers is alternately opposite along the thickness direction. A multi-field coupling model is proposed from the Timoshenko beam theory together with the phenomenological theory of piezoelectric semiconductors, including Gauss’s law and the continuity equation of currents. The analytical solutions are obtained for a bent beam with different numbers of layers. Numerical results show that polarized charges occur at the interfaces between every two adjacent layers due to the opposite electromechanical coupling effects. It was found that a series of alternating potential-barrier/well structures are induced by the polarized charges, which can be used to forbid the passing of low-energy mobile charges. Moreover, it was also observed that the induced polarized charges could weaken the shielding effect of carrier redistribution. These results are useful for the design of piezotronic devices.

Intrinsic superflat bands in general twisted bilayer systems

Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moiré superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such localized states exhibit negligible inter-cell coupling and support the formation of superflat bands in a wide and continuous parameter space, which can be mimicked using a twisted bilayer nanophotonic system. Our finding suggests that general twisted bilayer systems can realize continuously tunable superflat bands and the corresponding localized states for various photonic, phononic, and mechanical waves.

Spin-orbit coupling effects on transport properties of electronic Lieb lattice in the presence of magnetic field

In this paper, the transport properties of a two-dimensional Lieb lattice that is a line-centered square lattice are investigated in the presence of magnetic field and spin-orbit coupling. Specially, we address the temperature dependence of electrical and thermal conductivities as well as Seebeck coefficient due to spin-orbit interaction. We have exploited Green’s function approach in order to study thermoelectric and transport properties of Lieb lattice in the context of Kane–Mele model Hamiltonian. The results for Seebeck coefficient show the sign of thermopower is positive in the presence of spin-orbit coupling. Also the temperature dependence of transport properties indicates that the increase of spin-orbit coupling leads to decrease thermal conductivity however the decrease of gap parameter causes the reduction of thermal conductivity. There is a peak in temperature dependence of thermal conductivity for all values of magnetic fields and spin-orbit coupling strengths. Both electrical and thermal conductivities increase with increasing the temperature at low amounts of temperature due to the increasing of transition rate of charge carriers and excitation of them to the conduction bands. Also we have studied the temperature dependence of Seebeck coefficient of Lieb monolayer due to both spin orbit coupling and magnetic field factors in details.

Phonon-Limited Mobility in h-BN Encapsulated AB-Stacked Bilayer Graphene

The weak acoustic phonon scattering in graphene monolayer leads to high mobilities even at room temperatures. We identify the dominant role of the shear phonon mode scattering on the carrier mobility in AB-stacked graphene bilayer, which is absent in monolayer graphene. Using a microscopic tight-binding model, we reproduce experimental temperature dependence of mobilities in high-quality boron nitride encapsulated bilayer samples at temperatures up to ∼200  K. At elevated temperatures, the surface polar phonon scattering from boron nitride substrate contributes significantly to the measured mobilities of 15 000 to 20000  cm^{2}/Vs at room temperature and carrier concentration n∼10^{12}  cm^{-2}. A screened surface polar phonon potential for a dual-encapsulated bilayer and transferable tight-binding model allows us to predict mobility scaling with temperature and band gap for both electrons and holes in agreement with the experiment.

Dissipation-enabled hydrodynamic conductivity in a tunable bandgap semiconductor

Electronic transport in the regime where carrier-carrier collisions are the dominant scattering mechanism has taken on new relevance with the advent of ultraclean two-dimensional materials. Here, we present a combined theoretical and experimental study of ambipolar hydrodynamic transport in bilayer graphene demonstrating that the conductivity is given by the sum of two Drude-like terms that describe relative motion between electrons and holes, and the collective motion of the electron-hole plasma. As predicted, the measured conductivity of gapless, charge-neutral bilayer graphene is sample- and temperature-independent over a wide range. Away from neutrality, the electron-hole conductivity collapses to a single curve, and a set of just four fitting parameters provides quantitative agreement between theory and experiment at all densities, temperatures, and gaps measured. This work validates recent theories for dissipation-enabled hydrodynamic conductivity and creates a link between semiconductor physics and the emerging field of viscous electronics.