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In the last 5 years, the search to understand how correlated phases emerge in condensedmatter systems has shifted away from the cuprate high temperature superconductors andtowards the realm of two dimensional materials, with twisted graphene being a particularpoint of focus. Due to the extremely high level of tunability of both interaction strength andelectron kinetic energy in twisted graphene, these systems are an excellent playground tounderstand the relationship between correlations, electronic structure, symmetry breaking,and quantum phase transitions. This thesis is an examination of the electronic propertiesof graphene devices in monolayer and twisted geometries, studied through the lens of angle-resolvedphotoemission spectroscopy (ARPES).This thesis is organized as follows. Chapter 1 provides a high-level introduction to correlationsand symmetry breaking, followed in Chapter 2 by an introduction to the electronicstructure of graphene, twisted bilayer and trilayer graphene.Chapter 3 describes the experimental techniques: first the mechanics of ARPES used tomeasure electronic structure, and then the methods for fabricating twisted graphene deviceswith a particular focus on van der Waals heterostrucure samples for ARPES.Chapter 4 presents the ARPES results in monolayer graphene devices, showing how correlationsand electron-electron interactions in particular drive electron-hole symmetry breaking.Chapter 5 investigates both the layer- and doping- tunability of electron-electron interactionsin bilayer graphene devices at intermediate twist angles, and explores a regime where thesignatures of symmetry breaking already present in the system can become further enhanced.Chapter 6 details Future directions for ARPES on twisted trilayer graphene, discussing howperiodic strain produced by alignment with an hBN substrate can support certain correlatedphases and suppress others.

Misorientation of two layers of bilayer graphene leaves distinct signatures in the electronic properties and the phonon modes. The effect on the thermal conductivity has received the least attention and is the least well understood.In this work, the in-plane thermal conductivity of twisted bilayer graphene (TBG) is investigated as a function of temperature and interlayer misorientation angle using nonequilibrium molecular dynamics (NEMD). The central result is that with rotation angles larger than 13 degrees, the calculated thermal conductivities decrease approximately linearly with the increasing lattice constant of the commensurate TBG unit cell. Comparisons of the phonon dispersions show that misorientation has a negligible effect on the low-energy phonon frequencies and velocities. However, the larger periodicity of TBG reduces the Brillouin zone size to the extent that the zone edge acoustic phonons are thermally populated. This allows Umklapp scattering to reduce the lifetimes of the phonons contributing to the thermal transport, and consequently, to reduce the thermal conductivity. This explanation is supported by direct calculation of reduced phonon lifetimes in TBG based on density functional theory (DFT) for larger rotation angles.Nothing was previously known about the questions about how small twist angles (< 13 degrees) affect the thermal conductivity of TBG, and how it approaches its aligned value as the twist angle approaches 0 degrees. To provide insight into these questions, we perform large scale NEMD calculations on commensurate TBG structures with angles down to 1.87 degrees. The results show a smooth, non-monotonic behavior of the thermal conductivity with respect to the commensurate lattice constant. As the commensurate lattice constant increases, the thermal conductivity initially decreases by 50%, and then it returns to 90% of its aligned value as the angle is reduced to 1.89 degrees. These same qualitative trends are followed by the trends in the shear elastic constant, the wrinkling intensity, and the out-of-plane ZA2 phonon frequency. The picture that emerges of the physical mechanism governing the thermal conductivity is that misorientation reduces the shear elastic constant; the reduced shear elastic constant enables greater wrinkling, and the greater wrinkling reduces the thermal conductivity. The small-angle behavior of the thermal conductivity raises the question of how do response functions approach their aligned values as the twist angle approaches 0 degrees. Is the approach gradual, discontinuous, or a combination of the two?Much attention has been given recently to the material data science. A particular emphasis is placed on low dimensional materials exhibiting novel electrical and thermal properties. An improved dimension classifier model has been created to identify the quasi-1D materials that are often classified within the 2D material family. The algorithm is based on the fact that quasi-1D materials contain different bond lengths within the unit cell. The model can identify known quasi-1D material based on the structural data from Material Project Database. Using the optimized distributed gradient boosting model (XGBoost), both the band gap and the magnetization properties can be predicted from structural and elemental features. By fitting the XGBoost model with 15,000 kinds of materials, the accuracy of the predictions on the 5000 testing samples is greater than 91%. The mean absolute error of the band gap prediction is only 0.148 eV. Additionally, 1,025 kinds of magnetic materials have been identified among 5000 kinds of materials. According to the feature importance analysis, the most correlated feature for band gap prediction is the number of the valence electrons. While, for the magnetic material classification, it is the elemental period.

We explore the excitonic, electronic, phononic and thermal properties of low-dimensional materials, specifically the two-dimensional and quasi-one-dimensional transition metal chalcogenides. The possibility of observing Bose-Einstein exciton condensation (BEC) in transition metal dichalcogenides (TMDs) has been analyzed at three different levels of theory. We find that, in the strong coupling regime, mean field theory with either an unscreened or screened interlayer interaction predicts a room-temperature condensate. However, intralayer interactions can essentially renormalize the quasiparticle dispersion, which can be captured by many-body GW formalism. In the strong coupling regime, the improved BEC theory predicts that intralayer interactions have a large impact on the condensate order parameter, as well as on its functional dependencies on effective mass and carrier density. We also explore the thermal properties of 2D materials, specifically in the misoriented bilayer graphene (m-BLG) system, using ab initio density functional theory (DFT) and phonon Boltzmann transport equation (BTE). we find that the lattice thermal conductivity of m-BLG reduces to almost half of its unrotated counterpart. To explain the phonon dynamics, we analyze the phonon dispersions, phonon velocity distributions, occupations, density of states and heat capacity, both before and after misorientation. Detailed calculation of the phonon-phonon scattering lifetime reveals that, the increased umklapp scattering in the acoustic and quasi-acoustic phonon branches is the main reason for the reduced thermal conductivity in m-BLG system. We also explore the thermal conductivity of quasi-1D materials, specifically TaSe3 and NbS3, using ab initio DFT and phonon BTE. We find that both materials exhibit highly anisotropic thermal transport. A thermal conductivity of 6.3 W/mK (70.6 W/mK) is observed for metallic TaSe3 (semiconducting NbS3) along the chain direction. In-depth study of velocity and lifetime distribution shows that lower scattering and higher phonon velocity in NbS3 are the reasons behind such higher thermal conductivity. The umklapp scattering process is found to be the dominant phonon scattering mechanism in this family of low-dimensional materials. We also investigate the electronic and vibrational properties of different phases of the quasi-1D material NbS3. We find that the dimerized phase NbS3-IV is a semiconductor, whereas the undimerized phase NbS3-V is a metal. Similarity between the band dispersions of phase-I and phase-IV arises from the similarity in their structures, in spite of some stacking and chiral faults. Both phase-I and phase-IV are dynamically stable, whereas the phonon dispersion in phase-V exhibits instability along the inter-chain and growth direction, indicating a possible charge density wave ground state. Finally, we explore the band alignment properties of different quasi-1D transition metal trichalcogenides (TMTs). From the DFT calculations, we can identify several TMTs as promising candidates for ohmic contacts and tunnel FET devices.

Highlights This article presents an overview of twisted bilayer graphene (tBLG) on their fabrication techniques and twisting angle-dependent properties.The properties of tBLG can be controlled by controlling the twisting angle between two graphene sheets., 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.

In this work, we investigate the role of an external electric field in modulating the spectrum and electronic structure behavior of twisted bilayer graphene (TBG) and its physical mechanisms. Through theoretical studies, it is found that the external electric field can drive the relative positions of the conduction band and valence band to some extent. The difference of electric field strength and direction can reduce the original conduction band, and through the Fermi energy level, the band is significantly influenced by the tunable electric field and also increases the density of states of the valence band passing through the Fermi level. Under these two effects, the valence and conduction bands can alternately fold, causing drastic changes in spectrum behavior. In turn, the plasmon spectrum of TBG varies from semiconductor to metal. The dielectric function of TBG can exhibit plasmon resonance in a certain range of infrared.

We describe how the out-of-plane dielectric polarizability of monolayer graphene influences the electrostatics of bilayer graphene -- both Bernal (BLG) and twisted (tBLG). We compare the polarizability value computed using density functional theory with the output from previously published experimental data on the electrostatically controlled interlayer asymmetry potential in BLG and data on the on-layer density distribution in tBLG. We show that monolayers in tBLG are described well by polarizability $\alpha_{exp} = 10.8 \unicode{x212B}^3$ and effective out-of-plane dielectric susceptibility $\epsilon_z = 2.5$, including their on-layer electron density distribution at zero magnetic field and the inter-layer Landau level pinning at quantizing magnetic fields., Comment: 4 pages

Graphene is a good candidate for protective material owing to its extremely high stiffness and high strength-to-weight ratio. However, the impact performance of twisted bilayer graphene is still obscure. Herein we have investigated the ballistic resistance capacity of twisted bilayer graphene compared to that of AA-stacked bilayer graphene using molecular dynamic simulations. The energy propagation processes are identical, while the ballistic resistance capacity of the twisted bilayer graphene is almost two times larger than the AA-bilayer graphene. The enhanced capacity of the twisted bilayer graphene is assumed to be caused by the mismatch between the two sheets of graphene, which results in earlier fracture of the first graphene layer and reduces the possibility of penetration.

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.

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.

Carbon-based nanomaterials, such as carbon dots (CDs) and graphene (Gr), feature outstanding optical and electronic properties. Hence, their integration in optoelectronic and photonic devices is easier thanks to their low dimensionality and offers the possibility to reach high-quality performances. In this context, the combination of CDs and Gr into new nanocomposite materials CDs/Gr can further improve their optoelectronic properties and eventually create new ones, paving the way for the development of advanced carbon nanotechnology. In this work, we have thoroughly investigated the structural and emission properties of CDs deposited on single-layer and bilayer graphene lying on a SiO2/Si substrate. A systematic Raman analysis points out that bilayer (BL) graphene grown by chemical vapor deposition does not always respect the Bernal (AB) stacking, but it is rather a mixture of twisted bilayer (t-BL) featuring domains with different twist angles. Moreover, in-depth micro-photoluminescence measurements, combined with atomic force microscopy (AFM) morphological analysis, show that CD emission efficiency is strongly depleted by the presence of graphene and in particular is dependent on the number of layers as well as on the twist angle of BL graphene. Finally, we propose a model which explains these results on the basis of photoinduced charge-transfer processes, taking into account the energy levels of the hybrid nanosystem formed by coupling CDs with t-BL/SiO2.

We report on the quantum Hall effect in two stacked graphene layers rotated by 2 degree. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a signature of Coulomb interaction induced interlayer coherence and Bose Einstein condensation of excitons that form at half filling of each layer. A density imbalance gives rise to reentrant behavior due to a phase transition from the interlayer coherent state to incompressible behavior caused by simultaneous condensation of both layers in different quantum Hall states. With increasing overall density, magnetic breakdown gains the upper hand. As a consequence of the enhanced interlayer tunneling, the interlayer coherent state and the phase transition vanish., Comment: accepted in Nano Letters

6 pags., 5 figs., We demonstrate that one-dimensional moiré patterns, analogous to those found in twisted bilayer graphene, can arise in collapsed chiral carbon nanotubes. Resorting to a combination of approaches, namely, molecular dynamics to obtain the relaxed geometries and tight-binding calculations validated against ab initio modeling, we find that magic angle physics occur in collapsed carbon nanotubes. Velocity reduction, flat bands, and localization in AA regions with diminishing moiré angle are revealed, showing a magic angle close to 1°. From the spatial extension of the AA regions and the width of the flat bands, we estimate that many-body interactions in these systems are stronger than in twisted bilayer graphene. Chiral collapsed carbon nanotubes stand out as promising candidates to explore many-body effects and superconductivity in low dimensions, emerging as the one-dimensional analogues of twisted bilayer graphene., We thank the Centro de Supercomputacion de Galicia, CESGA, ( ́ www.cesga.es, Santiago de Compostela, Spain) for providing access to their supercomputing facilities. L.C., R.F.P., and C.C. acknowledge the financial support of the Spanish MCIU and AEI and the European Union under Grants PGC2018-097018-B-I00 (MCIU/AEI/FEDER, UE) (L.C.) and Grant MAT2016- 75354-P (AEI/FEDER, UE) (C.C., R.F.P.). E.S.M. acknowledges financial support from FONDECYT 1170921.

Convergent beam electron diffraction is routinely applied for studying deformation and local strain in thick crystals by matching the crystal structure to the observed intensity distributions. Recently, it has been demonstrated that CBED can be applied for imaging two-dimensional (2D) crystals where a direct reconstruction is possible and three-dimensional crystal deformations at a nanometre resolution can be retrieved. Here, we demonstrate that second-order effects allow for further information to be obtained regarding stacking arrangements between the crystals. Such effects are especially pronounced in samples consisting of multiple layers of 2D crystals. We show, using simulations and experiments, that twisted multilayer samples exhibit extra modulations of interference fringes in CBED patterns, i. e., a CBED moir\'e. A simple and robust method for the evaluation of the composition and the number of layers from a single-shot CBED pattern is demonstrated.

The artificial stacking of atomically thin crystals suffers from intrinsic limitations in terms of control and reproducibility of the relative orientation of exfoliated flakes. This drawback is particularly severe when the properties of the system critically depend on the twist angle, as in the case of the dodecagonal quasicrystal formed by two graphene layers rotated by 30$^\circ$. Here we show that large-area 30$^\circ$-rotated bilayer graphene can be grown deterministically by chemical vapor deposition on Cu, eliminating the need of artificial assembly. The quasicrystals are easily transferred to arbitrary substrates and integrated in high-quality hBN-encapsulated heterostructures, which we process into dual-gated devices exhibiting carrier mobility up to $10^5$ cm$^2$/Vs. From low-temperature magnetotransport, we find that the graphene quasicrystals effectively behave as uncoupled graphene layers, showing 8-fold degenerate quantum Hall states: this result indicates that the Dirac cones replica detected by previous photo-emission experiments do not contribute to the electrical transport., Comment: This is the unedited authors' version of the submitted article, published in its final form on Nano Letters 2020 https://doi.org/10.1021/acs.nanolett.0c00172 , 21 pages, 3 figures and supporting information

A detailed understanding of interacting electrons in twisted bilayer graphene (tBLG) near the magic angle is required to gain insights into the physical origin of the observed broken symmetry phases including correlated insulator states and superconductivity. Here, we present extensive atomistic Hartree theory calculations of the electronic properties of tBLG in the (semi-)metallic phase as function of doping and twist angle. Specifically, we calculate quasiparticle properties, such as the band structure, density of states (DOS) and local density of states (LDOS), which are directly accessible in photoemission and tunnelling spectroscopy experiments. We find that quasiparticle properties change significantly upon doping - an effect which is not captured by tight-binding theory. In particular, we observe that the partially occupied bands flatten significantly which enhances the density of states at the Fermi level and explains the experimentally observed Fermi level pinning. We predict a clear signature of this band flattening in the LDOS in the AB/BA regions of tBLG which can be tested in scanning tunneling experiments. We also study the dependence of quasiparticle properties on the dielectric environment of tBLG and discover that these properties are surprisingly robust as a consequence of the strong internal screening. Finally, we present a simple analytical expression for the Hartree potential which enables the determination of quasiparticle properties without the need for self-consistent calculations.

The twistronics, which is arising from the moiré superlattice of the small angle between twisted bilayers of 2D materials like graphene, has attracted much attention in the field of 2D materials and condensed matter physics. The novel physical properties in such systems, like unconventional superconductivity, come from the dispersionless flat band that appears when the twist reaches some magic angles. By tuning the filling of the fourfold degeneracy flat bands, the desired effects are induced due to the strong correlation of the degenerated Bloch electrons. In this article, we review the twistronics in twisted bi- and multi-layer graphene (TBG and TMG), which is formed both by transfer assembly of exfoliated monolayer graphene and epitaxial growth of multilayer graphene on SiC substrates. Starting from a brief history, we then introduce the theory of flat band in TBG. In the following, we focus on the major achievements in this field: (a) van Hove singularities and charge order; (b) superconductivity and Mott insulator in TBG and (c) transport properties in TBG. In the end, we give the perspective of the rising materials system of twistronics, epitaxial multilayer graphene on the SiC.

The possibility of triggering correlated phenomena by placing a singularity of the density of states near the Fermi energy remains an intriguing avenue towards engineering the properties of quantum materials. Twisted bilayer graphene is a key material in this regard because the superlattice produced by the rotated graphene layers introduces a van Hove singularity and flat bands near the Fermi energy that cause the emergence of numerous correlated phases, including superconductivity. While the twist angle-dependence of these properties has been explored, direct demonstration of electrostatic control of the superlattice bands over a wide energy range has, so far, been critically missing. This work examines a functional twisted bilayer graphene device using in-operando angle-resolved photoemission with a nano-focused light spot. A twist angle of 12.2$^{\circ}$ is selected such that the superlattice Brillouin zone is sufficiently large to enable identification of van Hove singularities and flat band segments in momentum space. The doping dependence of these features is extracted over an energy range of 0.4 eV, expanding the combinations of twist angle and doping where they can be placed at the Fermi energy and thereby induce new correlated electronic phases in twisted bilayer graphene., Comment: 16 pages, 4 figures. A revised version of the manuscript has been accepted for publication in Advanced Materials

The electronic properties of graphene superlattices have attracted intense interest that was further stimulated by the recent observation of novel many-body states at "magic" angles in twisted bilayer graphene (BLG). For very small ("marginal") twist angles of 0.1 deg, BLG has been shown to exhibit a strain-accompanied reconstruction that results in submicron-size triangular domains with the Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, marginally-twisted BLG is predicted to remain conductive due to a triangular network of chiral one-dimensional (1D) states hosted by domain boundaries. Here we study electron transport through this network and report giant Aharonov-Bohm oscillations persisting to temperatures above 100 K. At liquid helium temperatures, the network resistivity exhibits another kind of oscillations that appear as a function of carrier density and are accompanied by a sign-changing Hall effect. The latter are attributed to consecutive population of the flat minibands formed by the 2D network of 1D states inside the gap. Our work shows that marginally twisted BLG is markedly distinct from other 2D electronic systems, including BLG at larger twist angles, and offers a fascinating venue for further research., Comment: 11 pages, 8 figures

The recently observed superconductivity in twisted bilayer graphene emerges from insulating states believed to arise from electronic correlations. While there have been many proposals to explain the insulating behaviour, the commensurability at which these states appear suggests that they are Mott insulators. Here we focus on the insulating states with $\pm 2$ electrons or holes with respect to the charge neutrality point. We show that the theoretical expectations for the Mott insulating states are not compatible with the experimentally observed dependence on temperature and magnetic field if, as frequently assumed, only the correlations between electrons on the same site are included. We argue that the inclusion of non-local (inter-site) correlations in the treatment of the Hubbard model can bring the predictions for the magnetic and temperature dependencies of the Mott transition to an agreement with experiments and have consequences for the critical interactions, the size of the gap, and possible pseudogap physics. The importance of the inter-site correlations to explain the experimental observations indicates that the observed insulating gap is not the one between the Hubbard bands and that antiferromagnetic-like correlations play a key role in the Mott transition., 8 pages (including appendix), 5 figures