Theory and simulation of moiré graphene multilayers

Graphene has been hailed as a material which is going to revolutionise myriad technologies due to its extraordinary stability, mechanical strength yet flexibility, and remarkable transport properties. Furthermore, it was recently discovered that if two graphene layers are stacked and twisted relative to one another, referred to as twisted bilayer graphene (tBLG), correlated insulating states and superconductivity are observed, even though graphene does not intrinsically exhibit these properties. These phases only emerge at twist angles close to the "magic angle" of 1.1 degrees, and by tuning the temperature and doping level, the system can undergo electronic phase transitions between these states. I studied electron interactions and electronic screening in tBLG and other moiré graphene multilayers. In the absence of external and internal electronic screening, I found the on-site Hubbard parameter of the flat bands of tBLG scales linearly with twist angle. Upon considering internal screening, this linear scaling breaks down, where the Hubbard interaction energy decreases more rapidly towards the magic angle owing to increased screening. Moreover, external screening, from proximity to metallic gates which dope tBLG, was found to substantially affect these Hubbard interactions, owing to the moiré length scale of the magic-angle being comparable to the distance to these metallic gates. For a sufficiently small separation to these gates, I predicted that the correlated insulating states should be screened-out and the superconducting phase should be stabilised. Long-ranged Hartree interactions were found to induced doping-dependent band-flattening in tBLG that I predicted to increase the magic-angle range of tBLG. For moiré graphene multilayers, the role of these Hartree interactions were found to sensitively depend on the stacking sequence of the structure: systems with alternating twist angles have similar interaction-driven band flattening, but systems where there are also adjacent layers that are aligned have no such interaction-driven band flattening.Open Acces

Twist-angle dependence of electron correlations in moir\'e graphene bilayers

Motivated by the recent observation of correlated insulator states and unconventional superconductivity in twisted bilayer graphene, we study the dependence of electron correlations on the twist angle and reveal the existence of strong correlations over a narrow range of twist-angles near the magic angle. Specifically, we determine the on-site and extended Hubbard parameters of the low-energy Wannier states using an atomistic quantum-mechanical approach. The ratio of the on-site Hubbard parameter and the width of the flat bands, which is an indicator of the strength of electron correlations, depends sensitively on the screening by the semiconducting substrate and the metallic gates. Including the effect of long-ranged Coulomb interactions significantly reduces electron correlations and explains the experimentally observed sensitivity of strong correlation phenomena on twist angle.Comment: 17 pages, 6 figure

Theory of The Double Layer in Water-in-Salt Electrolytes

One challenge in developing the next generation of lithium-ion batteries is the replacement of organic electrolytes, which are flammable and most often contain toxic and thermally unstable lithium salts, with safer, environmentally friendly alternatives. Recently developed Water-in-Salt Electrolytes (WiSEs) were found to be a promising alternative, having also enhanced electrochemical stability. In this work, we develop a simple modified Poisson-Fermi theory, which demonstrates the fine interplay between electrosorption, solvation, and ion correlations. The phenomenological parameters are extracted from molecular simulations, also performed here. The theory reproduces the electrical double layer structure of WiSEs with remarkable accuracy.Comment: 29 pages, 8 figure

Effect of Coulomb impurities on the electronic structure of magic angle twisted bilayer graphene

In graphene, charged defects break the electron-hole symmetry and can even give rise to exotic collapse states when the defect charge exceeds a critical value which is proportional to the Fermi velocity. In this work, we investigate the electronic properties of twisted bilayer graphene (tBLG) with charged defects using tight-binding calculations. Like monolayer graphene, tBLG exhibits linear bands near the Fermi level but with a dramatically reduced Fermi velocity near the magic angle (approximately 1.1{\deg}). This suggests that the critical value of the defect charge in magic-angle tBLG should also be very small. We find that charged defects give rise to significant changes in the low-energy electronic structure of tBLG. Depending on the defect position in the moir\'e unit cell, it is possible to open a band gap or to induce an additional flattening of the low-energy valence and conduction bands. Our calculations suggest that the collapse states of the two monolayers hybridize in the twisted bilayer. However, their in-plane localization remains largely unaffected by the presence of the additional twisted layer because of the different length scales of the moir\'e lattice and the monolayer collapse state wavefunctions. These predictions can be tested in scanning tunnelling spectroscopy experiments

Correlated Ion Transport and the Gel Phase in Room Temperature Ionic Liquids

Here we present a theory of ion aggregation and gelation of room temperature ionic liquids (RTILs). Based on it, we investigate the effect of ion aggregation on correlated ion transport - ionic conductivity and transference numbers - obtaining closed-form expressions for these quantities.The theory depends on the maximum number of associations a cation and anion can form, and the strength of their association. To validate the presented theory, we perform molecular dynamics simulations on several RTILs, and a range of temperatures for one RTIL. The simulations indicate the formation of large clusters, even percolating through the system under certain circumstances, thus forming a gel, with the theory accurately describing the obtained cluster distributions in all cases. We discuss the possibility of observing a gel phase in neat RTILs, which has hitherto not been discussed in any detail.Comment: 44 pages, 11 figure

Theory of Ion Aggregation and Gelation in Super-Concentrated Electrolytes

In concentrated electrolytes with asymmetric or irregular ions, such as ionic liquids and solvent-in-salt electrolytes, ion association is more complicated than simple ion-pairing. Large branched aggregates can form at significant concentrations at even moderate salt concentrations. When the extent of ion association reaches a certain threshold, a percolating ionic gel networks can form spontaneously. Gelation is a phenomenon that is well known in polymer physics, but it is practically unstudied in concentrated electrolytes. However, despite this fact, the ion-pairing description is often applied to these systems for the sake of simplicity. In this work, drawing strongly from established theories in polymer physics, we develop a simple thermodynamic model of reversible ionic aggregation and gelation in concentrated electrolytes accounting for the competition between ion solvation and ion association. Our model predicts the populations of ionic clusters of different sizes as a function of salt concentration, it captures the onset of ionic gelation and also the post-gel partitioning of ions into the gel. We discuss the applicability of our model, as well as the implications of its predictions on thermodynamic, transport, and rheological properties

Spectroscopic signatures of tetralayer graphene polytypes

Tetralayer graphene has recently become a new addition to the family of few-layer graphene with versatile electronic properties. This material can be realised in three distinctive stacking configurations, for which we determine spectroscopic signatures in angle-resolved photoemission spectroscopy (ARPES), dynamical optical conductivity, and Raman spectra of inter-band excitations. The reported library of spectral features of tetralayer graphenes can be used for the non-invasive identification of the stacking order realised in a particular film.Comment: Pages 11, figures