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Scanning microwave impedance microscopy (sMIM) is a near‐field technique that enables the characterization of conductive materials with a resolution down to 1 nm. In hexagonal boron nitride (hBN)‐encapsulated devices, microwaves emitted from the sMIM tip penetrate and reach with the underlying 2D materials, allowing for the mapping of local conductivity variations. Using twisted bilayer graphene, it is demonstrated that this technique can characterize moiré patterns through hBN flakes up to 2.5 nm thick. Additionally, it is showed that sMIM can distinguish between conductive and insulating materials in samples encapsulated by hBN layers exceeding 15 nm. A key finding is that signal decay due to encapsulation is intrinsically linked to the tip's condition. This work overcomes limitations in the application of twistronics, enabling the verification of the periodicity of moiré patterns in high‐quality encapsulated devices between electrical contacts. [ABSTRACT FROM AUTHOR]

ABSTRACT In this paper, we investigate a twisted bilayer graphene on an h‐BN substrate. The graphene is grown using high‐quality chemical vapor deposition (CVD) and subsequently transferred onto the h‐BN substrate. Our focus is on the stacking transition within the bilayer system, based on fluctuations in both intralayer and interlayer processes. Our findings reveal that post‐annealing induces alterations in the electron–phonon interaction, corresponding to the spatially dependent stacking changes in the bilayer structure. This makes it possible to modify the electronic band structure of graphene and subsequently all its optoelectronic properties. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the K points that is qualitatively consistent with moiré models of the Hartree-Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

The recently synthesized 30° twisted bilayer graphene (30°-TBG) systems are unique quasicrystal systems possessing dodecagonal symmetry with graphene’s relativistic properties. We employ a real-space numerical atomistic framework that respects both the dodecagonal rotational symmetry and the massless Dirac nature of the electrons to describe the local density of states of the system. The approach we employ is very efficiency for systems with very large unit cells and does not rely on periodic boundary conditions. These features allow us to address a broad class of multilayer two-dimensional crystal with incommensurate configurations, particularly TBGs. Our results reveal that the 30°-TBG electronic spectrum consist of extended states together with a set of localized wave functions. The localized states exhibit fractal patterns consistent with the quasicrystal tiling.

The study of twisted bilayer graphene (TBG) is a hot topic in condensed matter physics with special focus on magic angles of twisting at which TBG acquires unusual properties. Mathematically, topologically non-trivial flat bands appear at those special angles. The chiral model of TBG pioneered by Tarnopolsky, Kruchkov, and Vishwanath (2019) has particularly nice mathematical properties and we survey, and in some cases, clarify, recent rigorous results which exploit them. [ABSTRACT FROM AUTHOR]

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 30° TBG naturally grown on Cu0.75Ni0.25 (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 Cu0.85Ni0.15 (111). The signature of moiré 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. [ABSTRACT FROM AUTHOR]

We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer--MacDonald PDE model, which is periodic with respect to the bilayer's moir\'e pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes--Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer--MacDonald model. [ABSTRACT FROM AUTHOR]

We study Dirac points of the chiral model of twisted bilayer graphene (TBG) with constant in-plane magnetic field. The striking feature of the chiral model is the presence of perfectly flat bands at magic angles of twisting. The Dirac points for zero magnetic field and non-magic angles of twisting are fixed at high symmetry points K and K' in the Brillouin zone, with r denoting the remaining high symmetry point. For a fixed small constant in-plane magnetic field, we show that as the angle of twisting varies between magic angles, the Dirac points move between K, K' points and the r point. In particular, near magic angles, the Dirac points are located near the Γ point. For special directions of the magnetic field, we show that the Dirac points move, as the twisting angle varies, along straight lines and bifurcate orthogonally at distinguished points. At the bifurcation points, the linear dispersion relation of the merging Dirac points disappears and exhibit a quadratic band crossing point (QBCP). The results are illustrated by links to animations suggesting interesting additional structure. [ABSTRACT FROM AUTHOR]

The optical properties and Landau quantisations in twisted bilayer graphene are investigated using a generalised tight-binding model that takes into account all interlayer and intralayer atomic interactions in the Moire superlattice. The system is a zero-gap semiconductor with double-degenerate Dirac-cone structures, and saddle-point energy dispersions appear at low energies for small twisting angles. The magnetic quantisation phenomena in this system are rich and unique, with Landau-level subgroups specified owing to specific Moire zone folding through modulation of the stacking angles. The Landau-level spectrum shows hybridised characteristics associated with those in monolayer, as well as AA and AB stackings. The detailed analysis explores the complex relations among the different sublattices on the same and different graphene layers. [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene (TBG) has emerged as a fascinating research frontier in condensed matter physics and materials science. This review article comprehensively overviews recent advances and future perspectives in studying TBG. The challenges associated with fabricating and characterizing TBG structures, including precise control of the twist angle and accurate determination of electronic properties, are discussed. Furthermore, the intriguing phenomena observed in TBG, such as superconductivity, insulating phases, and correlated electron states, shedding light on their underlying mechanisms, are explored. Scalability and device integration of TBG are explored, along with potential engineering strategies to tailor its properties for specific applications. By synthesizing and analyzing the latest scientific reports, a roadmap for further research is provided and the promising prospects for TBG are highlighted. [ABSTRACT FROM AUTHOR]

Graphene has nearly become an area that is experiencing rapid growth. The observation of moiré patterns in mechanically stacked graphene layers has triggered rapid progress in graphene research. These moiré patterns arise due to the relative difference in the orientation of the mechanically stacked graphene layers. Since their first appearance, moiré superlattices have become a platform for advanced materials and different quantum phenomena. Graphene bilayer, obtained from the mechanical stacking of two decoupled graphene layers, has become archetypal. Weak inter-layer forces can sometimes induce angular disorder in the array that causes unconventional stacking of layers. This unconventional stacking induces several angle-dependent properties in twisted bilayer graphene (t-BLG) which are unprecedented for graphene itself. This review examines recent advances in t-BLG covering aspects of its electronic structure, fabrication, angle-dependent properties and the spectroscopic signatures.

Abstract This study discusses the effect of long‐range interactions within the self‐consistent Hartree‐Fock (HF) approximation in comparison to short‐range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, it determines the quasi‐particle band structure of TBG with Hubbard interactions for three magnetic orderings: modulated anti‐ferromagnetic (MAFM), (NAFM) and hexagonal anti‐ferromagnetic (HAFM). Then, it develops an approach to incorporate these magnetic orderings along with the HF potential in the continuum approximation. Away from the magic angle, it observes a drastic effect of the magnetic order on the band structure of TBG compared to the influence of the HF potential. Near the magic angle, the HF potential plays a major role in the band structure, with HAFM and MAFM being secondary effects, but NAFM appears to still significantly distort the electronic structure at the magic angle. These findings suggest that the spin‐valley degenerate broken symmetry state often found in HF calculations of charge neutral TBG near the magic angle should favor magnetic order, since the atomistic Hubbard interaction will break this symmetry in favor of spin polarization.

Flat band has attracted more and more interest in recent years, motivated by its discovery in twisted bilayer graphene (TBG). In this work, we report our study of the impurity effect on this flat band system, which is an important issue for real materials. Employing the Lanczos recursive method, we solve the local density of states (LDOS) around a potential impurity. We find for large impurity size, a series of bound states are formed inside the impurity, and the flat band peak in LDOS is suppressed near the impurity boundary and shifted by the impurity potential deep inside the impurity. As the impurity size becomes smaller, the effect on the flat band becomes weaker, as anticipated from the large scale of the underlying Wannier function. This property distinguishes with the usual flat band systems with small localized Wannier orbitals, and indicates the flat band in TBG is more stable against small-size impurities. [ABSTRACT FROM AUTHOR]

Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions' chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases. [ABSTRACT FROM AUTHOR]

Cryogenic compute in- memory (CiM) is a promising alternative to room temperature von-Neumann technologies since cryogenic electronics can provide high speed and energy efficiency while CiM can solve the von-Neumann and memory wall bottlenecks. Moreover, CiM can reduce the energy requirement which can solve the cooling issues associated with the cryogenic systems. Here, we demonstrate a cryogenic in- memory full adder using Majority logic implemented in quantum anomalous Hall effect (QAHE)-based memory system. The utilization of QAHE-based memory enables a number of unique advantages for Majority logic– (i) Majority outputs correspond to voltages with two opposite polarities irrespective of the number of inputs and hence, only a simple voltage comparator can be used, (ii) in- memory Majority logic (and hence, full adder) does not require any modification in the peripheral circuitry, and (iii) the topologically protected Hall resistance states provide robustness against external variations. This work makes the first attempt to harness the unique advantages of QAHE phenomenon in implementing complex operations beyond the primitive bitwise Boolean operations.

The full optical response of twisted bilayer graphene at the neutrality point close to the magic angle within the continuum model (CM) is discussed. First, three different channels consistent with the underlying D3 symmetry are identified, yielding the total, magnetic, and chiral response. Second, the full optical response in the immediate vicinity of the magic angle θm is numerically calculated, which provides a direct mapping of the CM onto an effective two‐band model. It is, further, shown that the ground state of the CM in the immediate vicinity of θm is unstable toward transverse current fluctuations, a so‐called Condon instability. Third, due to the large counterflow, the acoustic plasmonic excitations with typical wave numbers have larger energies than the optical ones and their energy density may be largely enhanced at certain frequencies which are denominated as chiral resonances. Finally, symmetry relations for the optical response and their consequences for the chiral response are discussed. [ABSTRACT FROM AUTHOR]

The recently-introduced topological heavy fermion (THF) model [1] of twisted bilayer graphene (TBG) aims to reconcile the quantum-dot-like electronic structure of the latter observed by scanning tunneling microscopy, with its electron delocalization seen in transport measurements. The THF model achieves this by coupling localized (heavy) fermions with anomalous conduction electrons. Originally, the parameters of the THF model were obtained numerically from the Bistritzer–Macdonald (BM) model of TBG [1]. In this work, we derive analytical expressions for the THF model parameters as a function of the twist angle, the ratio between the tunneling amplitudes at the AA and AB regions (w0/w1), and the screening length of the interaction potential. By numerically computing the THF model parameters across an extensive experimentally-relevant parameter space, we show that the resulting approximations are remarkably good, i.e., within the 30% relative error for almost the entire parameter space. At the single-particle level, the THF model accurately captures the energy spectrum of the BM model over a large phase space of angles and tunneling amplitude ratios. When interactions are included, we also show that the THF description of TBG is good around the magic angle for realistic values of the tunneling amplitude ratios (0.6 ≤ w0/w1 ≤ 1.0), for which the hybridization between the localized and conduction fermions γ is smaller than the onsite repulsion of the heavy fermions U1 (i.e., |γ| < U1). [ABSTRACT FROM AUTHOR]

Graphene is the first experimentally discovered two‐dimensional material. This article reviews the unique properties of the so‐called twisted bilayer graphene (TBG), which can be considered a superstructure formed by stacking two graphene layers with a specific twisting angle. The main topics covered by this review include the correlated insulating phase, superconducting phase, quantum anomalous Hall effect, and the corresponding theoretical analysis. In addition, the twisted multilayer graphene, considered to have better tunability than the TBG, is discussed, followed by our conclusions and proposed research fields. [ABSTRACT FROM AUTHOR]

The electron valley pseudospin in two-dimensional hexagonal materials is a crucial degree of freedom for achieving their potential application in valleytronic devices. Here, bringing valleytronics to layered van der Waals materials, we theoretically investigate lightwave-controlled valley-selective excitation in twisted bilayer graphene (tBLG) with a large twist angle. It is demonstrated that the counter-rotating bicircular light field, consisting of a fundamental circularly-polarized pulse and its counter-rotating second harmonic, can manipulate the sub-cycle valley transport dynamics by controlling the relative phase between two colors. In comparison with monolayer graphene, the unique interlayer coupling of tBLG renders its valley selectivity highly sensitive to duration, leading to a noticeable valley asymmetry that is excited by single-cycle pulses. We also describe the distinct signatures of the valley pseudospin change in terms of observing the valley-selective circularly-polarized high-harmonic generation. The results show that the valley pseudospin dynamics can still leave visible fingerprints in the modulation of harmonic signals with a two-color relative phase. This work could assist experimental researchers in selecting the appropriate protocols and parameters to obtain ideal control and characterization of valley polarization in tBLG. [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene can demonstrate extraordinary optical and electrical characteristics due to its interlayer interactions. The strong coupling of normal and tangential van der Waals interactions at the interface results in inhomogeneous interlayer deformations and further changes the bilayer graphene's physical properties. Herein, theoretical and numerical models are established to study the torsional deformation behaviour of twisting a graphene flake over a rigid graphene substrate. It is found that in-plane deformations have significant influences on the interlayer potential energy density of AA stacking, but seldom affect other stacked domains. The deformation process is thus approximated by first twisting the graphene flake rigidly, and then relaxing the rigid constraints. The bilayer graphene system minimizes its energy by reducing (enlarging) the size of high-energy (low-energy) domains through additional rotations. The additional angles of the graphene flake are derived analytically based on a mechanical model following the principle of minimum potential energy. Results show that the influences of graphene film deformations get significant at small-twist-angles (typically less than 2∘). This work reveals the torsional deformation evolution mechanism of bilayer graphene and provides beneficial guidance on achieving intriguing physical properties. [ABSTRACT FROM AUTHOR]

We report the existence of moiré patterns and magic angle physics in all families of chiral collapsed carbon nanotubes. A detailed study of the electronic structure of all types of chiral nanotubes, previously collapsed via molecular dynamics, has been performed. We find that each family possesses a unique geometry and moiré disposition, as well as a characteristic number of flat bands. Remarkably, all kinds of nanotubes behave the same with respect to magic angle tuning, showing a monotonic behavior that gives rise to magic angles in full agreement with those of twisted bilayer graphene. Therefore, magic angle behavior is universally found in chiral collapsed nanotubes with a small chiral angle, giving rise to moiré patterns. Our approach comprises first-principles and semi-empirical calculations of the band structure, density of states and spatial distribution of the localized states signaled by flat bands. [Display omitted] [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene (TBG) has attracted great interest in the last decade due to the novel properties it exhibited. It was revealed that e–phonon interaction plays an important role in a variety of phenomena in this system, such as superconductivity and exotic phases. However, due to its complexity, the e–phonon interaction in TBG is not well studied yet. In this work, we study the electron interaction with the acoustic phonon mode in TBG and one of its consequences, i.e. the Kohn anomaly. The Kohn anomaly in ordinary metals usually happens at phonon momentum $q = 2k_\textrm{F}$ as a dramatic modification of the phonon frequency when the phonon wave vector nests the electron Fermi surface. However, novel Kohn anomaly can happen in topological semimetals, such as graphene and Weyl semimetals. In this work, we show that the novel dynamic Kohn anomaly can also take place in TBG due to the nesting of two different Moire Dirac points by the phonon wave vector. Moreover, by tuning the twist angle, the dynamic Kohn anomaly in TBG shows different features. Particularly, at magic angle when the electron bandwidth is almost flat, the dynamic Kohn anomalies of acoustic phonons disappear. We also studied the effects of finite temperature and doping on the dynamic Kohn anomaly in TBG and discussed the experimental methods to observe the Kohn anomaly in such system.

Band flattening has been observed in various materials with twisted bilayer structures, such as graphene, MoS _2 , and hexagonal boron nitride (hBN). However, the unique phenomenon of magic-angle has only been reported in the twisted bilayer graphene (tBG) and not in the twisted bilayer semiconductors or insulators. We aim to investigate the impact of gap opening and interlayer coupling strength on the magic-angle in the tBG. Our results based on the continuum model Hamiltonian with mass term indicate that the presence of a band gap hinders the occurrence of the magic-angle, but strengthening the interlayer coupling tends to restore it. By introducing layer asymmetry, such as interlayer bias or mass difference between layers, the flat bands become more dispersive. Furthermore, we have explored the influence of the Moiré’s potential due to the hBN substrate by calculating the quasi-band-structure of the hetero-structure tBG/hBN. Our findings indicate that the conclusions drawn from using the mass term remain valid despite the presence of the Moiré’s potential due to the hBN substrate.

The symmetry of twisted bilayer graphene (tBG) has been extensively studied in the continuum model but somewhat overlooked in the tight-binding (TB) framework. In contrast to the continuum model, which requires operators for both sublattice and layer spaces, the TB framework relies solely on operators in real space. This paper begins by discussing the symmetries of the TB Hamiltonian and the single-valley TB Hamiltonian of tBG. Subsequently, the band structures with specific irreducible representations (irreps) are obtained by diagonalizing the irrep-dependent Hamiltonian constructed through projection operators. We also investigate the impact of symmetry on intervalley coupling and the influence of a non-zero mass term on the $C_{2z}T$ symmetry of the single-valley Hamiltonian. To understand the irrep change as the wavevector moves inside the Brillouin zone and the irrep change after considering the intervalley coupling or introducing a non-zero mass term at a fixed wavevector, we derive two kinds of compatibility relationships. The methodology presented here can be applied to other layered materials because the basis functions we employ are generic and unique to twisted bilayers.

Twisted bilayer graphene (TBLG) has emerged as an exciting new material with tunable electronic properties, but current methods of fabrication and identification of TBLG are painstaking and laborious. We combine Raman spectroscopy with Gaussian mixture model (GMM) data clustering to identify areas with particular twist angles, from a TBLG sample with a mixture of orientations. We present two approaches: training the GMM on Raman parameters returned by peak fits, and on full spectra with dimensionality reduced by principal component analysis. In both cases, GMM identifies regions of distinct twist angle from within Raman datacubes. We also show that once a model has been trained, and the identified clusters labelled, it can be reapplied to new scans to assess the similarity between the materials in the new region and the testing region. This could enable high-throughput fabrication of TBLG, by allowing computerized detection of particular twist angles from automated large-area scans. [Display omitted] [ABSTRACT FROM AUTHOR]

Twisted bilayer graphene (TBG) represents a highly tunable, strongly correlated electron system. However, understanding the single-particle band structure alone has been challenging due to a lack of spectroscopic measurements over a broad energy range. Here, we probe the band structure of TBG around the magic angle using infrared spectroscopy and reveal spectral features that originate from interband transitions. In combination with quantum transport, we connect spectral features over a broad energy range (10-700 meV) and track their evolution with the twist angle. We compare our data with calculations of the band structures obtained via the continuum model and find good agreement only when considering a variation of interlayer/intralayer tunneling parameters with the twist angle. Our analysis suggests that the magic angle also shifts due to lattice relaxation and is better defined for a wide angular range of 0.9-1.1°. Additionally, our measurements offer an optical fingerprint of the magic angle for screening heterostructures before nanofabrication.

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.)

Magic-angle twisted bilayer graphene (TBG) is a tunable material with remarkably flat energy bands near the Fermi level, leading to fascinating transport properties and correlated states at low temperatures. However, grown pristine samples of this material tend to break up into landscapes of twist-angle domains, strongly influencing the physical properties of each individual sample. This poses a significant problem to the interpretation and comparison between measurements obtained from different samples. In this work, we study numerically the effects of twist-angle disorder on quantum electron transport in mesoscopic samples of magic-angle TBG. We find a significant property of twist-angle disorder that distinguishes it from onsite-energy disorder: it leads to an asymmetric broadening of the energy-resolved conductance. The magnitude of the twist-angle variation has a strong effect on conductance, while the number of twist-angle domains is of much lesser significance. We further establish a relationship between the asymmetric broadening and the asymmetric density of states of TBG at angles smaller than the first magic angle. Our results show that the qualitative differences between the types of disorder in the energy-resolved conductance of TBG samples can be used to characterize them at temperatures above the critical temperatures of the correlated phases, enabling systematic experimental studies of the effects of the different types of disorders also on the other properties such as the competition of the different types of correlated states appearing at lower temperatures., (Creative Commons Attribution license.)

Using molecular simulation and continuum dielectric theory, we consider how electrochemical kinetics are modulated by the twist angle in bilayer graphene electrodes. By establishing a connection between the twist angle and the screening length of charge carriers within the electrode, we investigate how tunable metallicity modifies the statistics of the electron transfer energy gap. Constant potential molecular simulations show that the activation free energy for electron transfer increases with screening length, leading to a non-monotonic dependence on the twist angle. The twist angle alters the density of states, tuning the number of thermally accessible channels for electron transfer and the reorganization energy by affecting the stability of the vertically excited state through attenuated image charge interactions. Understanding these effects allows us to express the Marcus rate of interfacial electron transfer as a function of the twist angle in a manner consistent with experimental observations.

Abstract Twisted bilayer graphene (tBLG) possesses various novel physical properties. Most of tBLG are fabricated by using artificial methods of stacking or folding single‐layer graphene. Chemical vapor deposition (CVD) has been verified that it holds great potential for preparation of large‐size high‐quality graphene. Therefore, it is significant for preparing tBLG in situ by using CVD technology. In this work, a novel approach is developed to directly prepare tBLGs on liquid Cu substrate. When the growth temperature exceeds a certain critical value, the state of aligned high‐quality single‐layer graphene domains grown on liquid Cu will be broken. Then, tBLG with twisted double‐layer regions is prepared in situ by rotating and intercalating between graphene domains. Experimental observations suggest that the liquid phase of Cu substrate and gas flow play a crucial role for the formation of tBLGs. These results demonstrate that the liquid Cu is an ideal potential substrate for preparing tBLGs with a full range of twisted angles and studying the formation mechanism of layer‐stacked materials.

Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions’ chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases.

This study has investigated the adsorption of phosphine toxic gas molecule on monolayer graphene, bilayer graphene and twisted bilayer graphene with, and without Magnesium impurity. The results of absorption energy studies using density functional theory (DFT) showed that bilayer graphene provides better adsorption than monolayer graphene and a difference in adsorption energy will be observed for twisted bilayer graphene with a rotation angle of 21.78°. By adding Mg impurity to the configurations, the sensitivity, and working temperature of the twisted bilayer graphene with Mg impurity increase compared to twisted bilayer graphene. Also, working temperature, and value of adsorption energy were calculated for bilayer graphene with Mg impurity less than Mg-doped twisted bilayer graphene, and monolayer graphene with Mg impurity. [ABSTRACT FROM AUTHOR]

We theoretically study the broadband near-field optical spectrum of twisted bilayer graphene (TBG) at various twist angles near the magic angle using two different models. The spectrum at low Fermi energy is characterized by a series of peaks that are almost at the same energies as the peaks in the far-field optical conductivity of TBG. When the Fermi energy is near a van Hove singularity, an additional strong peak appears at finite energy in the near-field spectrum, which has no counterpart in the optical conductivity. Based on a detailed calculation of the plasmon dispersion, we show that these spectroscopic features are associated with interband and intraband plasmons, which can provide critical information about the local band structure and plasmonic excitations in TBG. The near-field peaks evolve systematically with the twist angle, so they can serve as fingerprints for identifying the spatial dependent twist angle in TBG samples. Our findings pave the way for future experimental studies of the novel optical properties of TBG in the nanoscale. [ABSTRACT FROM AUTHOR]

Graphene has demonstrated great potential in new-generation electronic applications due to its unique electronic properties such as large carrier Fermi velocity, ultrahigh carrier mobility, and high material stability. Interestingly, the electronic structures can be further engineered in multilayer graphene by the introduction of a twist angle between different layers to create van Hove singularities (vHSs) at adjustable binding energy. In this work, using angle-resolved photoemission spectroscopy with sub-micrometer spatial resolution, the band structures and their evolution are systematically studied with twist angle in bilayer and trilayer graphene sheets. A doping effect is directly observed in graphene multilayer system as well as vHSs in bilayer graphene over a wide range of twist angles (from 5° to 31°) with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is also observed in trilayer graphene. The large tuning range of vHS binding energy in twisted multilayer graphene provides a promising material base for optoelectrical applications with broadband wavelength selectivity from the infrared to the ultraviolet regime, as demonstrated by an example application of wavelength selective photodetector.

The electron valley pseudospin in two-dimensional hexagonal materials is a crucial degree of freedom for achieving their potential application in valleytronic devices. Here, bringing valleytronics to layered van der Waals materials, we theoretically investigate lightwave-controlled valley-selective excitation in twisted bilayer graphene (tBLG) with a large twist angle. It is demonstrated that the counter-rotating bicircular light field, consisting of a fundamental circularly-polarized pulse and its counter-rotating second harmonic, can manipulate the sub-cycle valley transport dynamics by controlling the relative phase between two colors. In comparison with monolayer graphene, the unique interlayer coupling of tBLG renders its valley selectivity highly sensitive to duration, leading to a noticeable valley asymmetry that is excited by single-cycle pulses. We also describe the distinct signatures of the valley pseudospin change in terms of observing the valley-selective circularly-polarized high-harmonic generation. The results show that the valley pseudospin dynamics can still leave visible fingerprints in the modulation of harmonic signals with a two-color relative phase. This work could assist experimental researchers in selecting the appropriate protocols and parameters to obtain ideal control and characterization of valley polarization in tBLG.

We present transport measurements of bilayer graphene with a 1.38? interlayer twist. As with other devices with twist angles substantially larger than the magic angle of 1.1?, we do not observe correlated insulating states or band reorganization. However, we do observe several highly unusual behaviors in magnetotransport. For a large range of densities around half filling of the moir'e bands, magnetoresistance is large and quadratic. Over these same densities, the magnetoresistance minima corresponding to gaps between Landau levels split and bend as a function of density and field. We reproduce the same splitting and bending behavior in a simple tight-binding model of Hofstadter's butterfly on a triangular lattice with anisotropic hopping terms. These features appear to be a generic class of experimental manifestations of Hofstadter's butterfly and may provide insight into the emergent states of twisted bilayer graphene. [ABSTRACT FROM AUTHOR]

Few atom thick, twisted bilayer graphene (tBLG) possesses a rotation angle (θ) dependent van Hove singularity (vHs). Fine-tuning vHs serves a potential method to enhance charge transfer (CT) in surface enhanced Raman spectroscopy. This study shows that tBLG having a specific θ promotes as high as a 1.7 times enhancement of the Raman signals of copper phthalocyanine (CuPc) as compared to that caused by single layer graphene (SLG). The results of a combination of reflection imaging spectroscopy and widefield Raman provide spatial and spectral information about both tBLG with θ ranging from 10.9 to 13.7° and the corresponding vHs. Comparison of Raman spectra of CuPc in presence and absence of tBLG demonstrates that a significant enhancement of certain CuPc vibrational modes occurs when the underlying tBLG possesses a θ = 12.2°, showing as high as 6.8 and 1.7 times enhancements of certain vibrational mode as compared to those of CuPc on bare and SLG substrates, respectively. Theoretical calculations indicate that a match between the energies of vHs of tBLG with those of frontier orbitals of CuPc facilitates CT from the distant SLG to CuPc. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract 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.

We analyze the elastic properties, structural effects, and low-energy physics of a sheared nanoribbon placed on top of graphene, which creates a gradually changing moiré pattern. By means of a classical elastic model we derive the strains in the ribbon and we obtain its electronic energy spectrum with a scaled tight-binding model. The size of the sheared region is determined by the balance between elastic and van der Waals energy, and different regimes are identified. Near the clamped edge, moderate strains and small twist angles lead to one-dimensional channels. Near the sheared edge, a long region behaves like magic angle twisted bilayer graphene (TBG), showing a sharp peak in the density of states, mostly isolated from the rest of the spectrum. We also calculate the band topology along the ribbon and we find that it is stable for large intervals of strains and twist angles. Together with the experimental observations, these results show that the sheared nanoribbon geometry is ideal for exploring superconductivity and correlated phases in TBG in the very sought-after regime of ultralow twist angle disorder.

Electron collimation via a graphene p-n junction allows electrostatic control of ballistic electron trajectories akin to that of an optical circuit. Similar manipulation of novel correlated electronic phases in twisted-bilayer graphene (tBLG) can provide additional probes to the underlying physics and device components toward advanced quantum electronics. In this work, we demonstrate collimation of the electron flow via gate-defined moiré barriers in a tBLG device, utilizing the band-insulator gap of the moiré superlattice. A single junction can be tuned to host a chosen combination of conventional pseudo barrier and moiré tunnel barriers, from which we demonstrate improved collimation efficiency. By measuring transport through two consecutive moiré collimators separated by 1 μm, we demonstrate evidence of electron collimation in tBLG in the presence of realistic twist-angle inhomogeneity.

Van Hove singularities enhance many-body interactions and induce collective states of matter ranging from superconductivity to magnetism. In magic-angle twisted bilayer graphene, van Hove singularities appear at low energies and are malleable with density, leading to a sequence of Lifshitz transitions and resets observable in Hall measurements. However, without a magnetic field, linear transport measurements have limited sensitivity to the band's topology. Here, we utilize nonlinear longitudinal and transverse transport measurements to probe these unique features in twisted bilayer graphene at zero magnetic field. We demonstrate that the nonlinear responses, induced by the Berry curvature dipole and extrinsic scattering processes, intricately map the Fermi surface reconstructions at various fillings. Importantly, our experiments highlight the intrinsic connection of these features with the moiré bands. Beyond corroborating the insights from linear Hall measurements, our findings establish nonlinear transport as a pivotal tool for probing band topology and correlated phenomena.

Theory of superconductivity in twisted bilayer graphene (tBLG) is presented, based on the fact that Dirac fermions are pairing creating the topological bosons as consequence of topologically protected Lifshitz topological transition (TPLTT). We have shown that multiple TPLTTs are realised at low twisting angles in tBLG. At TPLTT the Berry phase changes from 2π in bilayer graphene to π in tBLG. It is favourable to form the Bardeen Cooper Schrieffer – Bose Einstein unconventional crossover (BCS-BEUC) when the attractive interaction for pairing dominates the repulsive screened Coulomb interaction. The theory yields a second-order phase transition for BCS-BEUC, and values of specific heat and the Ginzburg−Landau coherence length are calculated. The problem has been solved of emergent mystery in the magic angles at which there exists possibility for observation of BCS-BEUC. The solution is connected with the Umklapp processes when the quasiwave vector of the superconducting carriers is shifted from the Brillouin zone to other cell of the reciprocal space. The table is given of the allowed magic angles which include the corresponding effective masses of the pairing Dirac fermions. [ABSTRACT FROM AUTHOR]

External electric field and interlayer twist introduce diverse changes in their confined electronic states of bilayer graphene quantum dots. Using a quantum-dot model, the band gaps of twisted bilayer graphene in finite sizes of about 1.4–2.4 nm with varying twist angles are studied in the presence of an electrostatic field perpendicular to the flakes by means of first-principles calculations. The size-dependent gaps are widened by the interlayer twist, but narrowed by the applied field. Their coupling, however, results in an enhanced Stark response in the twisted structures of which the field-induced band-gap variations are about 3–4 times as large as that of the corresponding untwisted structures under the same field strength. The exceptional Stark shifts come from the field-induced asynchronous shifts in their occupied and virtual energy levels, which are further enhanced by strong interlayer coupling at specific twist angles. Moreover, the shift of band gaps with the field strength follows the quadratic Stark response with large second-order shifting coefficients. The enhanced and tunable Stark shift suggests a gateway to the band engineering of bilayer graphene quantum dots by tuning their sizes, twist angles and their coupling with applied field. [ABSTRACT FROM AUTHOR]

Graphene/silicon hybrid photodetector operating at communication wavelength has attracted enormous attention recently due to its potential to realize bandwidth larger than 100 GHz. However, the responsivity is intrinsically limited by the low absorption from the atomic-thick graphene monolayer, which imposes significant obstacles towards its practical application. Although plasmonic structures has been widely applied to enhance the responsivity, it may induce the metallic absorption thus limit the responsivity lower than 0.6 A/W. Twisted bilayer graphene (TBG) has been reported to hold the ability to dramatically enhance the optical absorption due to the unique twist-angle-dependent van Hove singularities. In this article, we present a design of a silicon/TBG hybrid photodetector with a responsivity higher than 1 A/W and bandwidth exceeding 100 GHz. The enhanced responsivity is achieved by tuning the twisted angle of TBG to increase the absorption within the 1550 nm as well as utilizing the silicon slot waveguide to boost the mode overlap with TBG. The fabrication process of proposed design is also discussed demonstrating the advantages of low fabrication complexity. The proposed silicon/TBG photodetector could not only exhibit superior performance compared to previously reported silicon/monolayer graphene photodetector, but also pave the way for the practical application of graphene-based silicon optoelectronic devices.

Van der Waals heterostructures obtained by artificially stacking two-dimensional crystals represent the frontier of material engineering, demonstrating properties superior to those of the starting materials. Fine control of the interlayer twist angle has opened new possibilities for tailoring the optoelectronic properties of these heterostructures. Twisted bilayer graphene with a strong interlayer coupling is a prototype of twisted heterostructure inheriting the intriguing electronic properties of graphene. Understanding the effects of the twist angle on its out-of-equilibrium optical properties is crucial for devising optoelectronic applications. With this aim, we here combine excitation-resolved hot photoluminescence with femtosecond transient absorption microscopy. The hot charge carrier distribution induced by photo-excitation results in peaked absorption bleaching and photo-induced absorption bands, both with pronounced twist angle dependence. Theoretical simulations of the electronic band structure and of the joint density of states enable to assign these bands to the blocking of interband transitions at the van Hove singularities and to photo-activated intersubband transitions. The tens of picoseconds relaxation dynamics of the observed bands is attributed to the angle-dependence of electron and phonon heat capacities of twisted bilayer graphene. [ABSTRACT FROM AUTHOR]

Raman spectroscopy is an extremely useful tool to characterize graphene systems. The strongest Raman features are the first-order G band and the second-order 2D and 2D′ bands, which are the overtones of the double resonance D and D' bands. However, the 2G band, which is the overtone of the G band, is not usually observed in the spectra of monolayer graphene and of crystalline graphite. In this work, we present an experimental and theoretical investigation of the resonance Raman spectra in twisted bilayer graphene (TBG) with different twisting angles and using several laser excitation energies in the NIR and visible ranges. We observed that the 2G band is enhanced when the incident photons are in resonance with the transition between the van Hove singularities in the density of states of the TBG. We show that the 2G band has three contributions (2G 1 , 2G 2 and 2G 3), that are not dispersive by changing the laser excitation energy. We also present theoretical calculations showing that the 2G 1 and 2G 2 bands are related to combinations of the in-phase (IP) and out-of-phase (OP) vibrations of the atoms in the different layers. The Raman excitation profiles (REPs) of the 2G peaks are upshifted in comparison with the REP of the G band. This behavior was confirmed theoretically using a graphene tight binding model. We conclude that the different resonance behavior comes from the fact that the G band is a first-order process whereas the 2G band is second-order processes giving rise to overall different resonance conditions. [Display omitted] • Resonant Raman study of the overtone 2G band in twisted bilayer graphene samples. • 2G band is composed of three individual peaks corresponding to different processes. • Theoretical calculations show that twisted bilayer graphene presents two vibrational modes at the zone-center. • Placzek's approximation shows that one mode is the main contribution to the G band in resonance with the van Hove singularities. • The overtone 2G band is mainly composed by the combination of the two zone-center phonons. [ABSTRACT FROM AUTHOR]

To pinpoint the electronic and structural mechanisms that affect intrinsic and extrinsic performance limits of 2D material devices, it is of critical importance to resolve the electronic properties on the mesoscopic length scale of such devices under operating conditions. Herein, angle‐resolved photoemission spectroscopy with nanoscale spatial resolution (nanoARPES) is used to map the quasiparticle electronic structure of a twisted bilayer graphene device. The dispersion and linewidth of the Dirac cones associated with top and bottom graphene layers are determined as a function of spatial position on the device under both static and operating conditions. The analysis reveals that microscopic rotational domains in the two graphene layers establish a range of twist angles from 9.8° to 12.7°. Application of current and electrostatic gating lead to strong electric fields with peak strengths of 0.75 V/μm at the rotational domain boundaries in the device. These proof‐of‐principle results demonstrate the potential of nanoARPES to link mesoscale structural variations with electronic states in operating device conditions and to disentangle such extrinsic factors from the intrinsic quasiparticle dispersion.