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Twisted bilayer graphene (TBG) provides a tunable platform to study emergent properties that are absent in single-layer graphene by the van der Waals (vdW) interlayer interaction. The vdW interlayer interaction can also lead to notable lattice reconstruction at the interface, promoting interlayer commensurability while minimizing intralayer lattice distortion. The lattice reconstruction in TBG is a pivotal phenomenon that significantly influences the optical and electronic properties. Currently, the study of lattice reconstruction in TBG attracts much attention in condensed matter physics. In this article, we review the experimental advances in the field of TBG lattice reconstruction. The formation and atomic-scale characterization within reconstructed TBG are overviewed comprehensively. In addition, lattice reconstruction-induced electronic modulations are introduced. Moreover, coexistence and transition between reconstructed and unreconstructed phases within a critical transition regime are described. Furthermore, we discuss the prospects of tunable reconstruction within TBG and other 2D material heterostructures., (© 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.)

We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08 ∘ . The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic field, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic field modifies the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling., (© 2024 IOP Publishing Ltd.)

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures., (© 2024 IOP Publishing Ltd.)

We theoretically study the impurity effects on the zeroth pseudo-Landau level (PLL) representation of the flat band in a twisted bilayer graphene (TBG) system. Our research investigates the impact of both short-range and long-range charged impurities on the PLL using the self-consistent Born approximation and random phase approximation. Our findings indicate that short-range impurities have a significant effect on the broadening of the flat band due to impurity scattering. In contrast, the impact of long-range charged impurities on the broadening of the flat band is relatively weak, and the primary impact of the Coulomb interaction is the splitting of the PLL degeneracy when a certain purity condition is satisfied. As a result, spontaneous ferromagnetic flat bands with nonzero Chern numbers emerge. Our work sheds light on the effect of impurities on the quantum Hall plateau transition in TBG systems., (© 2023 IOP Publishing Ltd.)

We study the properties of edge states for a selected (10,1)[(4,3)] twisted bilayer graphene (TBG) nanoribbon with minimal edges but a majority of zigzag edges. By using the tight-binding and Green's function methods, we find a remarkable rule of a local electronic transfer for the edge states. As the energy away from the Fermi level, the transfer is in the order of convex AB-, concave AB-, concave AA- and convex AA-stacked regions of the ribbon curve edges. We illustrate that this rule comes from the difference in interlayer couplings among the four types of local geometries at edges. Further, an in-plane transverse electric field can rearrange the edge bands and enlarge the energy regimes, leading to the lowest energy states modified from AB-stacked edge states to AA-stacked ones. The realignment of the edge bands results from the interplay between the interlayer coupling and the potential difference induced by the transverse electric field, which results in different bonding and antibonding edge states, i.e. the edge bands. In contrast, the total energy regime of the edge bands remain nearly unchanged under a relative strong off-plane perpendicular electric field, and the typical AA-stacked edge states are still maintained even the rotational symmetry of two layers is broken. Until a sufficiently strong value, the TBG nanoribbon tends to behave as two noninteracting monolayer ribbons except for a band distortion in low-energy regime. The conductance spectra reflects the edge bands well. We also discussed the influence of edge defects in the TBG nanoribbon on transport properties. It is found that the contributed conductance of each type of edge states shows different degrees of suppression for a monatomic vacancy in the corresponding region of edges., (© 2022 IOP Publishing Ltd.)

Magic-angle twisted bilayer graphene (MATBG) is notable as a highly tunable platform for investigating strongly correlated phenomena such as unconventional superconductivity and quantum spin liquids, due to easy control of doping level through gating and sensitive dependence of the magic angle on hydrostatic pressure. Experimental observations of correlated insulating states, unconventional superconductivity and ferromagnetism in MATBG indicate that this system exhibits rich exotic phases. In this work, using density functional theory calculations in conjunction with the effective screening medium method, we find the MATBG under pressure at a twisting angle of 2.88 ∘ and simulate how its electronic states evolve when doping level and electric field perpendicular to plane are tuned by gating. Our calculations show that, at doping levels between two electrons and four holes per moiré unit cell, a ferromagnetic (FM) solution with spin density localized at AA stacking sites is lower in energy than the nonmagnetic solution. The magnetic moment of this FM state decreases with both electron and hole doping and vanishes at four electrons/holes doped per moiré unit cell. Hybridization between the flat bands at the Fermi level and the surrounding dispersive bands can take place at finite doping. On increasing the out-of-plane electric field at zero doping, a transition from the FM state to the nonmagnetic one is seen. An investigation of impurity effects shows that both absorption ofO2molecules and occurrence of Stone-Wales impurities suppress the FM state, and the mechanisms are understood from our calculations. We also analyze the interlayer bonding character due to flat bands via Wannier functions. Finally, we report trivial band topology of the flat bands in the FM state at a certain doping level., (© 2022 IOP Publishing Ltd.)

In recent years, the discovery of 'magic angle' graphene has given new inspiration to the formation of heterojunctions. Similarly, the use of hexagonal boron nitride, known as white graphene, as a substrate for graphene devices has more aroused great interest in the graphene/hexagonal boron nitride heterostructure system. Based on the first principles method of density functional theory, the band structure, density of states, Mulliken population, and differential charge density of a tightly packed model of twisted graphene/hexagonal boron nitride/graphene sandwich structure have been studied. Through the establishment of heterostructure models twisted bilayer-graphene inserting hBN with different twisted angles, it was found that the band gap, Mulliken population, and charge density, exhibited specific evolution regulars with the rotation angle of the upper graphene, showing novel electronic properties and realizing metal-insulator phase transition. We find that the particular value of the twist angle at which the metal-insulator phase transition occurs and propose a rotational regulation mechanism with angular periodicity. Our results have guiding significance for the practical application of heterojunction electronic devices., (© 2022 IOP Publishing Ltd.)

The optical properties of graphene in monolayer and bilayer structure is essential for the development of optical devices viz surface plasmon resonance (SPR) based bio-sensors. The band structure of the twisted bilayer graphene (BLG) is remarkably different than the normal AA or AB stacking. This provides an opportunity to control the optical and electrical properties of BLG by applying an in-plane twist to one of the layer relative to other in a BLG system. Here, we calculated the refractive index (RI) of AA and AB stacking of BLG system using density functional theory. Though the spectrum for AA stacking shows some similarity with that of monolayer graphene, the spectrum for AB stacking was found to be remarkably different. The spectrum of AB stacked layer is red-shifted and the absorption peaks in low energy regime increases nearly by three-folds. A large dependency of the twist angle on RI of twisted BLG were found. Based on the calculation, a schematic of phase diagram showing material behavior of such twisted BLG systems as a function of twist angle and photon energy was constructed. The twisted AA stacked BLG shows largely dielectric behavior whereas the twisted AB stacked BLG shows predominately semimetallic and semiconducting behavior. This study presents a RI landscape of twisted BLG dependent on important parameters viz photon energy and inplane relative twist angle. Our studies will be very useful for the design and development of optical devices employing BLG systems particularly SPR based bio-sensors which essentially measures change in RI due to adsorption of analytes., (© 2021 IOP Publishing Ltd.)

By employing a linearised Boltzmann equation, we calculate the magneto-optical properties of twisted bilayer graphene using non-magnetic wave functions. Both transverse and longitudinal responses are calculated up to the second order in applied magnetic field with their twist angle and Fermi level dependence examined. We find that increasing the twist angle increases the transverse metallic response so long as the Fermi level remains below the upper conduction band. Interlayer transitions provide an appreciable enhancement when the Fermi level traverses the gap between the two conduction bands. Interlayer transitions are also responsible for a nonzero anomalous Hall conductivity in this model. As the Fermi level moves towards zero, the longitudinal response begins to dominate and a highly anisotropic negative magneto-resistance is observed., (© 2021 IOP Publishing Ltd.)

The in-plane phonon-drag thermopower S g and the power factor PF are theoretically investigated in a twisted bilayer graphene (tBLG) as a function of twist angle S d and the power factor PF are theoretically investigated in a twisted bilayer graphene (tBLG) as a function of twist angle θ , temperature T and electron density n s in the region of low T (1-20 K). As θ approaches magic angle θ m , the S g and S d are found to be strongly enhanced, which is manifestation of great suppression of effective Fermi velocity v F * of electrons in moiré flat band near θ m . This enhancement decreases with increasing θ and T . In the Bloch-Grüneisen (BG) regime, it is found that S g ∼ v F *-2 , T 3 and n s -1/2 . As T increases, the exponent δ in S g ∼ T δ , changes from 3 to nearly zero and a maximum S g value of ∼10 mV K -1 at ∼20 K is estimated. S g is found to be larger (smaller) for smaller n s in low (high) temperature region. On the other hand, S d , taken to be governed by Mott formula with S d ∼ v F *-1 , T and n s -1/2 and S d ≪ S g for T > ∼2 K. The power factor PF is also shown to be strongly θ dependent and is very much enhanced. Consequently, possibility of a giant figure of merit is discussed. In tBLG, θ acts as a strong tuning parameter of both S g and S d and PF in addition to T and n s . Our results are qualitatively compared with the measured out-of-plane thermopower in tBLG., (© 2021 IOP Publishing Ltd.)