Valley-dependent transport in a mescoscopic twisted bilayer graphene device

We study the valley-dependent electron transport in a four-terminal mesoscopic device of the two monolayer graphene nanoribbons vertically stacked together, where the intersection forms a bilayer graphene lattice with a controllable twist angle. Using a tight-binding lattice model, we show that the longitudinal and transverse conductances exhibit significant valley polarization in the low energy regime for small twist angles. As the twist angle increases, the valley polarization shifts to the high energy regime. This arises from the regrouping effect of the electron band in the twisted bilayer graphene region. But for relatively large twist angles, no significant valley polarization is observed. These results are consistent with the spectral densities of the twisted bilayer graphene.

Spin-polarized pairing induced by the magnetic field in the Bernal bilayer graphene

Recent experimental findings have demonstrated the occurrence of superconductivity in Bernal bilayer graphene when induced by a magnetic field.In this study,we conduct a theoretical investigation of the potential pairing symmetry within this superconducting system.By developing a theoretical model,we primarily calculate the free energy of the system with p+ip-wave parallel spin pairing,p+ip-wave anti-parallel spin pairing and d+i d-wave pairing symmetry.Our results confirm that the magnetic field is indeed essential for generating the superconductivity.We discover that the p+ip-wave parallel spin pairing leads to a lower free energy for the system.The numerical calculations of the energy band structure,zero-energy spectral function and density of states for each of the three pairing symmetries under consideration show a strong consistency with the free energy results.

Effect of interlayer bonded bilayer graphene on friction

We study the friction properties of interlayer bonded bilayer graphene by simulating the movement of a slider on the surface of bilayer graphene using molecular dynamics.The results show that the presence of the interlayer covalent bonds due to the local sp^(3) hybridization of carbon atoms in the bilayer graphene seriously reduces the frictional coefficient of the bilayer graphene surface to 30%,depending on the coverage of interlayer sp^(3) bonds and normal loads.For a certain coverage of interlayer sp3bonds,when the normal load of the slider reaches a certain value,the surface of this interlayer bonded bilayer graphene will lose the friction reduction effect on the slider.Our findings provide guidance for the regulation and manipulation of the frictional properties of bilayer graphene surfaces through interlayer covalent bonds,which may be useful for applications of friction related graphene based nanodevices.

Wafer-scale 30°twisted bilayer graphene epitaxially grown on Cu_(0.75)Ni_(0.25)(111)

Twisted bilayer graphene(TBG) has been extensively studied because of its novel physical properties and potential application in electronic devices.Here we report the synthesis and characterization of 300 TBG naturally grown on Cu_(0.75)Ni_(0.25)(111) film and investigate the electronic structure by angle-resolved photoemission spectroscopy.Compared with other substrates,our TBG with a wafer scale is acquired with a shorter growth time.The Fermi velocity and energy gap of Dirac cones of TBG are comparable with those of a monolayer on Cu_(0.85)Ni_(0.15)(111).The signature of moré lattices has not been observed in either the low-energy electron diffraction patterns or the Fermi surface map within experimental resolution,possibly due to different Cu and Ni contents in the substrates enhancing the different couplings between the substrate and the first/second layers and hindering the formation of a quasiperiodic structure.

Machine learning of theΓ-point gap and flat bands of twisted bilayer graphene at arbitrary angles

The novel electronic properties of bilayer graphene can be fine-tuned via twisting,which may induce flat bands around the Fermi level with nontrivial topology.In general,the band structure of such twisted bilayer graphene(TBG)can be theoretically obtained by using first-principles calculations,tight-binding method,or continuum model,which are either computationally demanding or parameters dependent.In this work,by using the sure independence screening sparsifying operator method,we propose a physically interpretable three-dimensional(3D)descriptor which can be utilized to readily obtain theΓ-point gap of TBG at arbitrary twist angles and different interlayer spacings.The strong predictive power of the descriptor is demonstrated by a high Pearson coefficient of 99%for both the training and testing data.To go further,we adopt the neural network algorithm to accurately probe the flat bands of TBG at various twist angles,which can accelerate the study of strong correlation physics associated with such a fundamental characteristic,especially for those systems with a larger number of atoms in the unit cell.

Opportunities and Challenges in Twisted Bilayer Graphene:A Review

Two-dimensional(2D)materials exhibit enhanced physical,chemical,electronic,and optical properties when compared to those of bulk materials.Graphene demands significant attention due to its superior physical and electronic characteristics among different types of 2D materials.The bilayer graphene is fabricated by the stacking of the two monolayers of graphene.The twisted bilayer graphene(tBLG)superlattice is formed when these layers are twisted at a small angle.The presence of disorders and interlayer interactions in tBLG enhances several characteristics,including the optical and electrical properties.The studies on twisted bilayer graphene have been exciting and challenging thus far,especially after superconductivity was reported in tBLG at the magic angle.This article reviews the current progress in the fabrication techniques of twisted bilayer graphene and its twisting angle-dependent properties.

Fano Resonance Enabled Infrared Nano-Imaging of Local Strain in Bilayer Graphene

Detection of local strain at the nanometer scale with high sensitivity remains challenging.Here we report near-field infrared nano-imaging of local strains in bilayer graphene by probing strain-induced shifts of phonon frequency.As a non-polar crystal,intrinsic bilayer graphene possesses little infrared response at its transverse optical phonon frequency.The reported optical detection of local strain is enabled by applying a vertical electrical field that breaks the symmetry of the two graphene layers and introduces finite electrical dipole moment to graphene phonon.The activated phonon further interacts with continuum electronic transitions,and generates a strong Fano resonance.The resulted Fano resonance features a very sharp near-field infrared scattering peak,which leads to an extraordinary sensitivity of-0.002%for the strain detection.Our results demonstrate the first nano-scale near-field Fano resonance,provide a new way to probe local strains with high sensitivity in non-polar crystals,and open exciting possibilities for studying strain-induced rich phenomena.

Quantum anomalous Hall effect in twisted bilayer graphene quasicrystal

The nontrivial topology is investigated in a dodecagonal quasicrystal made of 30° twisted bilayer graphene (TBG). Based on tight-binding model with both exchange field and Rashba spin–orbit coupling, the topological index, chiral edge states, and quantum conductance are calculated to distinguish its unique topological phase. A high Bott index (B = 4) quantum anomalous Hall effect (QAHE) is identified in TBG quasicrystal, which is robust to a finite perturbation without closing the nontrivial gap. Most remarkably, we have found that the multiple Dirac cone replicas in TBG quasicrystal are only a spectra feature without generating extra chiral edge states. Our results not only propose a possible way to realize the QAHE in quasicrystal, but also identify the continuity of nontrivial topology in TBG between crystal and quasicrystal.

Perfect spin filtering controlled by an electric field in a bilayer graphene junction:Effect of layer-dependent exchange energy

Magneto transport of carriers with a spin-dependent gap in a ferromagnetic-gated bilayer of graphene is investigated.We focus on the effect of an energy gap induced by the mismatch of the exchange fields in the top and bottom layers of an AB-stacked graphene bilayer. The interplay of the electric and exchange fields causes the electron to acquire a spindependent energy gap. We find that, only in the case of the anti-parallel configuration, the effect of a magnetic-induced gap will give rise to perfect spin filtering controlled by the electric field. The resolution of the spin filter may be enhanced by varying the bias voltage. Perfect switching of the spin polarization from ＋100% to -100% by reversing the direction of electric field is predicted. Giant magnetoresistance is predicted to be easily realized when the applied electric field is smaller than the magnetic energy gap. It should be pointed out that the perfect spin filter is due to the layer-dependent exchange energy. This work points to the potential application of bilayer graphene in spintronics.

Spectroscopic Evidence for Electron Correlations in Epitaxial Bilayer Graphene with Interface-Reconstructed Superlattice Potentials

Superlattice potentials are theoretically predicted to modify the single-particle electronic structures. The resulting Coulomb-interaction-dominated low-energy physics would generate highly novel many-body phenomena. Here,by in situ tunneling spectroscopy, we show the signatures of superstructure-modulated correlated electron states in epitaxial bilayer graphene(BLG) on 6H-Si C(0001). As the carrier density is locally quasi-‘tuned’ by the superlattice potentials of a 6 × 6 interface reconstruction phase, the spectral-weight transfer occurs between the two broad peaks flanking the charge-neutral point. Such a detected non-rigid band shift beyond the single-particle band description implies the existence of correlation effects, probably attributed to the modified interlayer coupling in epitaxial BLG by the 6×6 reconstruction as in magic-angle BLG by the moiré potentials. Quantitative analysis suggests that the intrinsic interface reconstruction shows a high carrier tunability of ~1/2 filling range, equivalent to the back gating by a voltage of ~70 V in a typical gated BLG/SiO_(2)/Si device. The finding in interfacemodulated epitaxial BLG with reconstruction phase extends the BLG platform with electron correlations beyond the magic-angle situation, and may stimulate further investigations on correlated states in graphene systems and other van der Waals materials.

Theoretical investigation of structural and optical properties of semi-fluorinated bilayer graphene

We have studied the structural and optical properties of semi-fluorinated bilayer graphene using density functional theory. When the interlayer distance is 1.62A, the two graphene layers in AA stacking can form strong chemical bonds. Under an in-plane stress of 6.8 GPa, this semi-fluorinated bilayer graphene becomes the energy minimum. Our calculations indicate that the semi-fluorinated bilayer graphene with the AA stacking sequence and rectangular fluorinated configuration is a nonmagnetic semiconductor （direct gap of 3.46 eV）. The electronic behavior at the vicinity of the Fermi level is mainly contributed by the p electrons of carbon atoms forming C=C double bonds. We compare the optical properties of the semi- fluorinated bilayer graphene with those of bilayer graphene stacked in the AA sequence and find that the semi-fluorinated bilayer graphene is anisotropic for the polarization vector on the basal plane of graphene and a red shift occurs in the [010] polarization, which makes the peak at the low-frequency region located within visible light. This investigation is useful to design polarization-dependence optoelectronic devices.

Low-temperature charged impurity scattering-limited conductivity in relatively high doped bilayer graphene

Based on semiclassical Boltzamnn transport theory in random phase approximation, we develop a theoretical model to investigate low-temperature carrier transport properties in relatively high doped bilayer graphene. In the presence of both electron–hole puddles and band gap induced by charged impurities, we calculate low-temperature charged impurity scattering-limited conductivity in relatively high doped bilayer graphene. Our calculated conductivity results are in excellent agreement with published experimental data in all compensated gate voltage regime of study by using potential fluctuation parameter as only one free fitting parameter, indicating that both electron–hole puddles and band gap induced by charged impurities play an important role in carrier transport. More importantly, we also find that the conductivity not only depends strongly on the total charged impurity density, but also on the top layer charged impurity density, which is different from that obtained by neglecting the opening of band gap, especially for bilayer graphene with high top layer charged impurity density.

A comparison of the transport properties of bilayer graphene,monolayer graphene,and two-dimensional electron gas

We studied and compared the transport properties of charge carriers in bilayer graphene, monolayer graphene, and the conventional semiconductors （the two-dimensional electron gas （2DEG））. It is elucidated that the normal incidence transmission in the bilayer graphene is identical to that in the 2DEG but totally different from that in the monolayer graphene. However, resonant peaks appear in the non-normal incidence transmission profile for a high barrier in the bilayer graphene, which do not occur in the 2DEG. Furthermore, there are tunneling and forbidden regions in the transmission spectrum for each material, and the division of the two regions has been given in the work. The tunneling region covers a wide range of the incident energy for the two graphene systems, but only exists under specific conditions for the 2DEG. The counterparts of the transmission in the conductance profile are also given for the three materials, which may be used as high-performance devices based on the bilayer graphene.

Observation of quadratic magnetoresistance in twisted double bilayer graphene

Magnetoresistance(MR) provides rich information about Fermi surface, carrier scatterings, and exotic phases for a given electronic system. Here, we report a study of the magnetoresistance for the metallic states in twisted double bilayer graphene(TDBG). We observe quadratic magnetoresistance in both Moiré valence band(VB) and Moiré conduction band(CB). The scaling analysis shows validity of Kohler's rule in the Moiré valence band. On the other hand, the quadratic magnetoresistance appears near the halo structure in the Moiré conduction band, and it violates Kohler's rule, demonstrating the MR scaling related to band structure in TDBG. We also propose an alternative scaling near the halo structure. Further analysis implies that the observed quadratic magnetoresistance and alternative scaling in conduction band are related to the halo boundary. Our results may inspire investigation on MR in twisted 2D materials and provide new knowledge for MR study in condensed matter physics.

Projective representation of D_(6)group in twisted bilayer graphene

Within the framework of continuum model,we study the projective representation of emergent D_(6)point group in twisted bilayer graphene.We then construct tight-binding models of the lowest bands without and with external electromagnetic fields,based on the projective representation.

Correlated insulating phases in the twisted bilayer graphene

We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is SU(4)symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are neglected, the ground states are found to be in the SU(4) manifold with degeneracy. The kinetic terms, treated as perturbation, break this large SU(4) symmetry and propel the appearance of intervalley coherent state, quantum topological insulators, and other symmetry-breaking insulating states. We first present the theoretical analysis of moiré lattice model construction and then show how to solve the model with large-scale quantum Monte Carlo simulations in an unbiased manner. We further provide potential directions such that from the real-space model construction and its quantum many-body solutions how the perplexing yet exciting experimental discoveries in the correlation physics of twisted bilayer graphene can be gradually understood. This review will be helpful for the readers to grasp the fast growing field of the model study of twisted bilayer graphene.

Impurity effects on electrical conductivity of doped bilayer graphene in the presence of a bias voltage

We address the electrical conductivity of bilayer graphene as a function of temperature, impurity concentration, and scattering strength in the presence of a finite bias voltage at finite doping, beginning with a description of the tight-binding model using the linear response theory and Green＇s function approach. Our results show a linear behavior at high doping for the case of high bias voltage. The effects of electron doping on the electrical conductivity have been studied via changing the electronic chemical potential. We also discuss and analyze how the bias voltage affects the temperature behavior of the electrical conductivity. Finally, we study the behavior of the electrical conductivity as a function of the impurity concentration and scattering strength for different bias voltages and chemical potentials respectively. The electrical conductivity is found to be monotonically decreasing with impurity scattering strength due to the increased scattering among electrons at higher impurity scattering strength.

Orbital electronic heat capacity of hydrogenated monolayer and bilayer graphene

The tight-binding Harrison model and Green＇s function approach have been utilized in order to investigate the contribution of hybridized orbitals in the electronic density of states（DOS） and electronic heat capacity（EHC） for four hydrogenated structures, including monolayer chair-like, table-like, bilayer AA- and finally AB-stacked graphene. After hydrogenation, monolayer graphene and bilayer graphene are behave as semiconducting systems owning a wide direct band gap and this means that all orbitals have several states around the Fermi level. The energy gap in DOS and Schottky anomaly in EHC curves of these structures are compared together illustrating the maximum and minimum band gaps are appear for monolayer chair-like and bilayer AA-stacked graphane, respectively. In spite of these, our findings show that the maximum and minimum values of Schottky anomaly appear for hydrogenated bilayer AA-stacked and monolayer table-like configurations, respectively.

Evidence of abnormal hot carrier thermalization at van Hove singularity of twisted bilayer graphene

Interlayer twist evokes revolutionary changes to the optical and electronic properties of twisted bilayer graphene(TBG)for electronics,photonics and optoelectronics.Although the ground state responses in TBG have been vastly and clearly studied,the dynamic process of its photoexcited carrier states mainly remains elusive.Here,we unveil the photoexcited hot carrier dynamics in TBG by time-resolved ultrafast photoluminescence(PL)autocorrelation spectroscopy.We demonstrate the unconventional ultrafast PL emission between the van Hove singularities(VHSs)with a~4 times prolonged relaxation lifetime.This intriguing photoexcited carrier behavior is ascribed to the abnormal hot carrier thermalization brought by bottleneck effects at VHSs and interlayer charge distribution process.Our study on hot carrier dynamics in TBG offers new insights into the excited states and correlated physics of graphene twistronics systems.

Towards growth of pure AB-stacked bilayer graphene single crystals

Given its intriguing band structure and unique tunable bandgap,AB-stacked bilayer graphene has great potentials in the applications of high-end electronics,optoelectronics and semiconductors.The epitaxial growth of AB-stacked single-crystal bilayer graphene films requires a strict AB-stacked lattice,identical orientations and seamless stitching of bilayer graphene islands.However,the particles inevitably present on the metal surface that produced during high temperature growth would induce random orientations,twisted stacking islands,and uncontrollable multilayers,which is a great challenge to overcome.Here,we propose a heat-resisting-box assisted strategy to produce nearly pure AB-stacked bilayer graphene single-crystal films on Cu/Ni(111)foils.With our technique,the particles on the Cu/Ni(111)surface are effectively eliminated,which greatly minimizes the occurrence of randomly twisted islands and uncontrollable multilayers.The as-grown AB-stacked bilayer graphene films show>99%alignment and>99%AB stacking order.Our work provides a promising method towards the growth of pure AB-stacked bilayer graphene single crystals and would accelerate its device applications.