arXiv subjects

Zachary A. H. Goodwin

Publications and source records attributed to Zachary A. H. Goodwin.

At least 37 records · Page 2Linked to original sources

arXiv2022

Moiré Modulation of Charge Density Waves

Here we investigate how charge density waves (CDW), inherent to a monolayer, are effected by creating twisted van der Waals structures. Homobilayers of metallic transition metal dichalcogenides (TMDs), at small twist angles where there is significant atomic reconstruction, are utilised as an example to investigate the interplay between the moiré domain structure and CDWs of different periods. For $\sqrt{3}\times\sqrt{3}$ CDWs, there is no geometric constraint to prevent the CDWs from propagating throughout the moiré structure. Whereas for $2\times2$ CDWs, to ensure the CDWs in each layer have the most favourable interactions in the domains, the CDW phase must be destroyed in the connecting domain walls. For $3\times3$ CDWs with twist angles close to 180 degree, moiré-scale triangular structures can form; while close to 0 degree, moiré-scale dimer domains occur. The star-of-David CDW ($\sqrt{13}\times\sqrt{13}$) is found to host CDWs in the domains only, since there is one low energy stacking configuration, similar to $2\times2$ CDWs. These predictions are offered for experimental verification in twisted bilayer metallic TMDs which host CDWs, and we hope this will stimulate further research on the interplay between the moiré supperlattice and CDW phases intrinsic to the comprising 2D materials.

cond-mat.mtrl-sci↗

arXiv2022

Cracking Ion Pairs in the Electrical Double Layer of Ionic Liquids

Here we investigate a limiting case of the theory for aggregation and gelation in the electrical double layer (EDL) of ionic liquids (ILs). The limiting case investigated only accounts for ion pairs, ignoring the possibility of larger clusters and a percolating ionic network. This simplification, however, permits analytical solutions for the properties of the EDL. The resulting equations demonstrate the competition between the free energy of an association and the electrostatic potential in the EDL. For small electrostatic potentials and large negative free energies of associations, the ion pairs dominate in the EDL. Whereas, for electrostatic potential energies larger than the free energy of an association, electric-field-induced cracking of ion pairs occurs. The differential capacitance for this consistent ion pairing theory has a propensity to have a ``double hump camel'' shape. We compare this theory against previous free ion approaches, which do not consistently treat the reversible associations in the EDL.

cond-mat.soft↗

arXiv2022

Gelation, Clustering and Crowding in the Electrical Double Layer of Ionic Liquids

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew \textit{et al.} developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible Cayley tree clusters and a percolating ionic network (gel). Here we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a regime dominated by free, crowded ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition.

cond-mat.soft↗

arXiv2022

Atomistic hartree theory and crystal field of twisted double bilayer graphene near the magic angle

Twisted double bilayer graphene (tDBLG) is a moiré material that has recently generated significant interest because of the observation of correlated phases near the magic angle. We carry out atomistic Hartree theory calculations to study the role of electron-electron interactions in the normal state. In contrast to twisted bilayer graphene (tBLG), we find that such interactions do not result in significant doping-dependent deformations of the electronic band structure. However, interactions play an important role for the electronic structure in the presence of a perpendicular electric field as they screen the external field. Finally, we analyze the contribution of the Hartree potential to the crystal field, i.e. the on-site energy difference between the inner and outer layers. We find that the on-site energy obtained from Hartree theory has the same sign, but a smaller magnitude compared to previous studies in which the on-site energy was determined by fitting tight-binding results to ab initio density-functional theory (DFT) band structures. To understand this quantitative difference, we analyze the ab initio Kohn-Sham potential obtained from DFT and find that a subtle interplay of electron-electron and electron-ion interactions determines the magnitude of the on-site potential.

cond-mat.mtrl-sci↗

arXiv2022

Unconventional Superconductivity in Magic-Angle Twisted Trilayer Graphene

Magic-angle twisted trilayer graphene (MATTG) recently emerged as a highly tunable platform for studying correlated phases of matter, such as correlated insulators and superconductivity. Superconductivity occurs in a range of doping levels that is bounded by van Hove singularities which stimulates the debate of the origin and nature of superconductivity in this material. In this work, we discuss the role of spin-fluctuations arising from atomic-scale correlations in MATTG for the superconducting state. We show that in a phase diagram as function of doping ($ν$) and temperature, nematic superconducting regions are surrounded by ferromagnetic states and that a superconducting dome with $T_c \approx 2\,\mathrm{K}$ appears between the integer fillings $ν=-2$ and $ν= -3$. Applying a perpendicular electric field enhances superconductivity on the electron-doped side which we relate to changes in the spin-fluctuation spectrum. We show that the nematic unconventional superconductivity leads to pronounced signatures in the local density of states detectable by scanning tunneling spectroscopy measurements.

cond-mat.supr-con↗

arXiv2021

Salt-in-Ionic-Liquid Electrolytes: Ion Network Formation and Negative Effective Charges of Alkali Metal Cations

Salt-in-ionic liquid electrolytes have attracted significant attention as potential electrolytes for next generation batteries largely due to their safety enhancements over typical organic electrolytes. However, recent experimental and computational studies have shown that under certain conditions alkali cations can migrate in electric fields as if they carried a net negative effective charge. In particular, alkali cations were observed to have negative transference numbers at small mole fractions of alkali metal salt that revert to the expected net positive transference numbers at large mole fractions. Simulations have provided some insights into these observations, where the formation of asymmetric ionic clusters, as well as a percolating ion network could largely explain the anomalous transport of alkali cations. However, a thermodynamic theory that captures such phenomena has not been developed, as ionic associations were typically treated via the formation of ion pairs. The theory presented herein, based on the classical polymer theories, describes thermoreversible associations between alkali cations and anions, where the formation of large, asymmetric ionic clusters and a percolating ionic network are a natural result of the theory. Furthermore, we present several general methods to calculate the effective charge of alkali cations in ionic liquids. We note that the negative effective charge is a robust prediction with respect to the parameters of the theory, and that the formation of a percolating ionic network leads to the restoration of net positive charges of the cations at large mole fractions of alkali metal salt. Overall, we find excellent qualitative agreement between our theory and molecular simulations in terms of ionic cluster statistics and the effective charges of the alkali cations.

cond-mat.stat-mech↗

arXiv2021

Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene

Starting with twisted bilayer graphene, graphene-based moiré materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene and demonstrate that this system can host flat bands when the twist angle is close to the magic-angle of 1.16$^\circ$. When monolayer graphene is twisted on ABA trilayer graphene, the flat bands are not isolated, but are intersected by a Dirac cone with a large Fermi velocity. In contrast, graphene twisted on ABC trilayer graphene (denoted AtABC) exhibits a gap between flat and remote bands. Since ABC trilayer graphene and twisted bilayer graphene are known to host broken-symmetry phases, we further investigate the ostensibly similar magic angle AtABC system. We study the effect of electron-electron interactions in AtABC using both Hartree theory and an atomic Hubbard theory to calculate the magnetic phase diagram as a function of doping, twist angle, and perpendicular electric field. Our analysis reveals a rich variety of magnetic orderings, including ferromagnetism and ferrimagnetism, and demonstrates that a perpendicular electric field makes AtABC more susceptible to magnetic ordering.

cond-mat.mes-hall↗

arXiv2021

Importance of long-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene

Electron-electron interactions are intrinsically long ranged, but many models of strongly interacting electrons only take short-ranged interactions into account. Here, we present results of atomistic calculations including both long-ranged and short-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene and demonstrate that qualitatively different results are obtained when long-ranged interactions are neglected. In particular, we use Hartree theory augmented with Hubbard interactions and calculate the interacting spin susceptibility at a range of doping levels and twist angles near the magic angle to identify the dominant magnetic instabilities. At the magic angle, mostly anti-ferromagnetic order is found, while ferromagnetism dominates at other twist angles. Moreover, long-ranged interactions significantly increase the twist angle window in which strong correlation phenomena can be expected. These findings are in good agreement with available experimental data.

cond-mat.str-el↗

arXiv2021

Ion Clusters and Networks in "Water-in-Salt Electrolytes"

Water-in-salt electrolytes (WiSEs) are a class of super-concentrated electrolytes that have shown much promise in replacing organic electrolytes in lithium-ion batteries. At the extremely high salt concentrations of WiSEs, ionic association is more complicated than the simple ion pair description. In fact, large branched clusters can be present in WiSEs, and past a critical salt concentration, an infinite percolating ionic network can form spontaneously. In this work, we simplify our recently developed thermodynamic model of reversible ionic aggregation and gelation, tailoring it specifically for WiSEs. Our simplified theory only has a handful of parameters, all of which can be readily determined from simulations. Our model is able to quantitatively reproduce the populations of ionic clusters of different sizes as a function of salt concentration, the critical salt concentration for ionic gelation, and the fraction of ions incorporated into the ionic gel, as observed from molecular simulations of three different lithium-based WiSEs. The extent of ionic association and gelation greatly affects the effective ionic strength of solution, the coordination environment of active cations that is known to govern the chemistry of the solid-electrolyte interface, and the thermodynamic activity of all species in the electrolyte.

physics.chem-ph↗

arXiv2020

Effect of bilayer stacking on the atomic and electronic structure of twisted double bilayer graphene

Twisted double bilayer graphene has recently emerged as an interesting moiré material that exhibits strong correlation phenomena that are tunable by an applied electric field. Here we study the atomic and electronic properties of three different graphene double bilayers: double bilayers composed of two AB stacked bilayers (AB/AB), double bilayers composed of two AA stacked bilayers (AA/AA) as well as heterosystems composed of one AB and one AA bilayer (AB/AA). The atomic structure is determined using classical force fields. We find that the inner layers of the double bilayer exhibit significant in-plane and out-of-plane relaxations, similar to twisted bilayer graphene. The relaxations of the outer layers depend on the stacking: atoms in AB bilayers follow the relaxations of the inner layers, while atoms in AA bilayers attempt to avoid higher-energy AA stacking. For the relaxed structures, we calculate the electronic band structures using the tight-binding method. All double bilayers exhibit flat bands at small twist angles, but the shape of the bands depends sensitively on the stacking of the outer layers. To gain further insight, we study the evolution of the band structure as the outer layers are rigidly moved away from the inner layers, while preserving their atomic relaxations. This reveals that the hybridization with the outer layers results in an additional flattening of the inner-layer flat band manifold. Our results establish AA/AA and AB/AA twisted double bilayers as interesting moiré materials with different flat band physics compared to the widely studied AB/AB system.

cond-mat.mtrl-sci↗

arXiv2020

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.

physics.chem-ph↗

arXiv2020

Interfacial layering in the electric double layer of ionic liquids

Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly-interacting environment, leading to the formation of discrete layers of charges at interfaces. Here, we propose a continuum theory that captures the transition from overscreening-- alternating layers of excess charge at low surface potential, to overcrowding-- the formation of dense layers of charge of the same sign at high surface potential. The model outputs slowly-decaying oscillations in the charge density with a wavelength of single ion diameters, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles.

cond-mat.soft↗

arXiv2020

Hartree theory calculations of quasiparticle properties in twisted bilayer graphene

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. 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. 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.

cond-mat.mes-hall↗

arXiv2020

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.

physics.chem-ph↗

arXiv2019

Attractive electron-electron interactions from internal screening in magic angle twisted bilayer graphene

Twisted bilayer graphene (tBLG) has recently emerged as a new platform for studying electron correlations, the strength of which can be controlled via the twist angle. Here, we study the effect of internal screening on electron-electron interactions in undoped tBLG. Using the random phase approximation, we find that the dielectric response of tBLG drastically increases near the magic angle and is highly twist-angle dependent. As a consequence of the abrupt change of the Fermi velocity as a function of wave vector, the screened interaction in real space exhibits attractive regions for certain twist angles near the magic angle. Attractive interactions can induce charge density waves and superconductivity and therefore our findings could be relevant to understand the microscopic origins of the recently observed strong correlation phenomena in undoped tBLG. The resulting screened Hubbard parameters are strongly reduced and exhibit a non-linear dependence on the twist angle. We also carry out calculations with the constrained random phase approximation and parametrize a twist-angle dependent Keldysh model for the resulting effective interaction.

cond-mat.str-el↗

arXiv2019

Critical role of device geometry for the phase diagram of twisted bilayer graphene

The effective interaction between electrons in two-dimensional materials can be modified by their environment, enabling control of electronic correlations and phases. Here, we study the dependence of electronic correlations in twisted bilayer graphene (tBLG) on the separation to the metallic gate(s) in two device configurations. Using an atomistic tight-binding model, we determine the Hubbard parameters of the flat bands as a function of gate separation, taking into account the screening from the metallic gate(s), the dielectric spacer layers and the tBLG itself. We determine the critical gate separation at which the Hubbard parameters become smaller than the critical value required for a transition from a correlated insulator state to a (semi-)metallic phase. We show how this critical gate separation depends on twist angle, doping and the device configuration. These calculations may help rationalise the reported differences between recent measurements of tBLG's phase diagram and suggests that correlated insulator states can be screened out in devices with thin dielectric layers.

cond-mat.str-el↗

arXiv2019

Twist-angle dependence of electron correlations in moiré 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.

cond-mat.str-el↗

arXiv2018

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.

cond-mat.stat-mech↗