Category Archives: Research spotlight

twisted bilayer graphene moire pattern

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

Z. A. H. Goodwin, V. Vitale, F. Corsetti, D. K. Efetov, A. A. Mostofi and J. Lischner, Critical role of device geometry for the phase diagram of twisted bilayer graphene, Phys. Rev. B 101, 165110 (2020).

Twisted bilayer graphene (tBLG) is made of two stacked sheets of graphene that are rotated with respect to one another. The relative twist of the two layers produces a moiré pattern that forms a superlattice whose repeat length is much greater than the carbon-carbon bond length of the individual layers. For small twist angles around a “magic angle” of 1.1°, the behaviour of electrons in the moiré superlattice is fundamentally different to that of electrons in graphene or in untwisted bilayers, and tBLG is seen to exhibit unexpected insulating and superconducting states, in addition to the expected metallic state.

Crucially, in experiments, the tBLG is not free-standing, but is encapsulated by a thin dielectric medium which, in turn, has metallic contacts. This is extremely important, since it determines the way in which electrons in tBLG interact with one another. In a paper appearing in Physical Review B, we develop and use an electronic model of tBLG within such a device configuration. Our model captures the influence of the device geometry on the competition between phases. In particular, we show that the correlated insulator phase can be switched on or off by controlling the thickness of the dielectric layers separating tBLG from the metallic gates.

The competition between the different phases observed in tBLG makes it a rich problem, and understanding what influences it has the potential to advance our understanding of the physics of strongly-correlated electrons and unconventional superconductors.

This work was part of Zachary Goodwin’s PhD in the Centre for Doctoral Training in Theory and Simulation of Materials. Zachary is supervised by Johannes Lischner and Arash Mostofi.

Wannier function in diamond

Wannier90 as a community code: new features and applications

G. Pizzi et al., Wannier90 as a community code: new features and applications, J. Phys.: Condens. Matter 32, 165902 (2020)

Wannier functions provide a local real-space description of electronic structure in materials and molecular systems. They are used, for example, to understand chemical bonding and as a compact and highly computationally efficient basis in which to compute electronic properties (see our review article in Reviews of Modern Physics for more details). Indeed, they have become an indispensable element in the tool-kit of contemporary materials and molecular computational science.

The Wannier90 code, an open-source software program that is developed in our research group, is the most prevalent code for computing maximally-localised Wannier functions. It is a paradigmatic example of interoperable software and, at the present time, has been interfaced to over 25 electronic structure codes and post-processing software tools.

In a paper that appears in the Journal of Physics: Condensed Matter we describe the recent evolution of Wannier90 from a code developed by a small group of developers to one in which enhancements in functionality are contributed by a wide, global community of developers. The paper describes how this transition has been achieved and some of the software enhancements it has enabled for the latest v3.x release.

This work was part of Dr Valerio Vitale’s postdoctoral work as part of the European Union’s Centre of Excellence E-CAM, supervised by Jonathan Yates and Arash Mostofi.

pentacene molecule in p-terphenyl molecular crystal

Combining embedded mean-field theory with linear-scaling density-functional theory

J. C. A. Prentice, R. J. Charlton, A. A. Mostofi and P. D. Haynes, Combining embedded mean-field theory with linear-scaling density-functional theory, Journal of Chemical Theory and Computation 16, 354 (2020)

Quantum embedding methods are a vital tool in the study of complex molecular or extended systems, where the most interesting physics or chemistry is associated with a particular region, but the rest of the system still interacts significantly with this “active region”, in a way that can only be described using quantum mechanics. Using an accurate quantum mechanical method (e.g., hybrid density functional theory (DFT)) may be necessary to correctly predict the properties of the active region, but using this level of theory for the entire system may be prohibitively expensive. Instead, quantum embedding schemes enable the active region to be treated at a high level of theory, whilst simultaneously treating the environment at a lower, less computationally demanding level of theory (e.g. semi-local DFT). The result is a calculation that has the accuracy of the high-level theory, but at a fraction of the cost.

In a paper published in the Journal of Chemical Theory and Computation, we present a novel implementation of embedded mean field theory (EMFT) into the linear-scaling DFT code ONETEP, enabling efficient hybrid DFT-in-semi-local DFT quantum embedding calculations on large-scale systems. We have applied our implementation to a range of systems, including pentacene, pentacene-doped crystalline p-terphenyl, and metallocene-doped carbon nanotubes, and show it provides excellent results compared to full system hybrid DFT calculations and experiment. In particular, in pentacene-doped p-terphenyl, the ability to include a much larger p-terphenyl environment than previous calculations, whilst still using hybrid DFT for the pentacene dopant itself, gives much better agreement with experimental measurements of the shift in the S0 to S1 excitation due to the presence of the p-terphenyl host. This calculation contained nearly 3000 atoms, an order of magnitude larger than any calculation attempted before with EMFT.

This work was done as part of Dr Joseph Prentice’s postdoctoral research funded by the EPSRC (grant no. EP/P02209X/1) and Robert Charlton’s PhD in the Centre for Doctoral Training in Theory and Simulation of Materials. The project was supervised by Peter Haynes and Arash Mostofi.

Wannier function in tBLG

Twist-angle dependence of electron correlations in twisted bilayer graphene

Z. A. H. Goodwin, F. Corsetti, A. A. Mostofi and J. Lischner, Twist-angle dependence of electron correlations in moiré graphene bilayers, Phys. Rev. B 100, 121106(R) (2019)

Since its experimental discovery and characterisation in 2018, the physics of magic-angle twisted bilayer graphene (tBLG) has captured the imagination of the condensed matter community and has proved to be a highly tunable platform for studying the behaviour of correlated electrons. Motivated by the theoretical prediction of magic twist angles at which the electron kinetic energy becomes small, experiments observed correlated insulator and unconventional superconducting phases in magic-angle tBLG. These findings have triggered an intense theoretical effort to study the electronic structure of tBLG and understand the microscopic mechanisms that give rise to the observed strong correlation phenomena.

In a paper that appears as a Rapid Communication in Physical Review B, we have taken essential steps towards understanding the electronic structure of tBLG by determining how electron correlations depend on twist-angle. We demonstrate that strong electron correlations are present over a range of twist-angles around the magic angle and that there is a strong influence from screening by the semiconducting substrate and metallic gates encapsulating tBLG. We calculate both on-site and extended Hubbard parameters and show that they exhibit universal behaviour upon rescaling and that long-ranged interactions significantly reduce electron correlations (even in the presence of metallic screening from the gates).

This work was part of Zachary Goodwin’s PhD in the Centre for Doctoral Training in Theory and Simulation of Materials. Zachary is supervised by Johannes Lischner and Arash Mostofi.

Acceptor charged impurity state in MoS2

Tuning electronic properties of transition-metal dichalcogenides via defect charge

M. Aghajanian, A. A. Mostofi and J. Lischner, Tuning electronic properties of transition-metal dichalcogenides via defect charge, Scientific Reports 8, 13611 (2018)

Since the experimental realisation and characterisation of monolayer graphene in 2004, there has been a focussed interest on so-called two-dimensional materials. One class of such materials is the transition metal dichalcogenides (TMDs). Monolayer TMDs, such as MoS2, are interesting because, unlike graphene, they are semiconductors and have potential technological applications in field-effect transistors, photovoltaics, and sensing.

The properties of monolayer TMDs are highly tunable via the addition of defects and absorbates, such as charged impurities. Understanding and controlling the effect of such impurities is essential for the rational design of defect-engineered TMDCs.

In a paper published in Scientific Reports, we use a multi-scale theory and simulation approach that combines first-principles and tight-binding simulations to calculate impurity wave functions and binding energies for both donor and acceptor adsorbed impurity atoms on MoS2 as function of the impurity charge. One of our main findings is that it is possible to control the ordering of the most strongly bound impurity state by varying the impurity charge, which has potentially important consequences for optical properties.

This work was part of Martik Aghajanian’s PhD in the Centre for Doctoral Training in Theory and Simulation of Materials. Martik is supervised by Johannes Lischner and Arash Mostofi.

polymer nanocomposite

Mechanisms of reinforcement in polymer nanocomposites

N. Molinari, A. P. Sutton and A. A. Mostofi, Mechanisms of reinforcement in polymer nanocomposites, Phys. Chem. Chem. Phys. 20, 23085 (2018)

Nanoparticles of carbon or silica, for example, are routinely added to polymers during their processing to tune the mechanical and chemical properties of the polymer. Such systems are known as polymer nanocomposites. In this work, which appears in Phys. Chem. Chem. Phys. this week, we have uncovered some of the molecular mechanisms that govern the mechanical strengthening of polymer nanocomposites. Using coarse-grained molecular dynamics simulations, we find that the mechanical response to tensile strain depends systematically on the fraction of the total volume of the nanocomposite that is occupied by the nanoparticles. We identify three predominant local structural motifs that are present at the molecular level and we show how and why the evolution of the these motifs with the concentration of nanoparticles and with strain governs the mechanical response.

This work was part of Nicola Molinari’s PhD in the Centre for Doctoral Training in Theory and Simulation of Materials. Nicola was supervised by Adrian Sutton and Arash Mostofi.

The origin of negative thermal expansion in layered perovskites

C. Ablitt, S. Craddock, M. S. Senn, A. A. Mostofi and N. C. Bristowe, The origin of uniaxial negative thermal expansion in layered perovskites,
Nature Computational Materials 3, 44 (2017)

Most materials expand when they are heated, but some do the opposite and shrink, a phenomenon known as negative thermal expansion (NTE). One particular puzzle has been: why is it that ABO3 perovskite materials generally do not exhibit uniaxial negative thermal expansion (NTE) over a wide temperature range, whereas layered perovskite materials of the same chemical family, e.g., A2BO4, often do? In this work, which appears in Nature Computational Materials, PhD student Chris Ablitt has answered this question. Using first principles calculations and symmetry analysis, he has shown that whilst ABO3 perovskites and layered perovskites both have the sort of soft vibrational modes that are needed for NTE, it is only the layered perovskites that additionally have large elastic anisotropy that predispose the material to the deformations associated with NTE. Chris has shown that this elastic anisotropy arises from the combined effect of layering and condensed rotations of oxygen octahedra and it is this feature, unique to layered perovskites of certain symmetry, that allows uniaxial NTE to persist over a large temperature range. This fundamental insight means that symmetry and the elastic tensor can be used as descriptors in high-throughput screening and to direct materials design.

This work forms part of Chris Ablitt‘s PhD in the Centre for Doctoral Training in Theory and Simulation of Materials. Chris is supervised by Nicholas Bristowe, Mark Senn and Arash Mostofi.

Charged adsorbates on graphene

[1] F. Corsetti, A. A. Mostofi and J. Lischner, First-principles multiscale modelling of charged adsorbates on doped graphene, 2D Materials 4, 025070 (2017)

[2] D. Wong, F. Corsetti, Y. Wang, V. W. Brar, H.-Z. Tsai, Q. Wu, R. K. Kawakami, A. Zettl, A. A. Mostofi, J. Lischner and M. F. Crommie, Spatially resolving density-dependent screening around a single charged atom in graphene, Phys Rev B 95, 205419 (2017)

A quotation often attributed to F. C. Frank goes along the lines of, “Crystals are like people — it’s the defects in them that make them interesting”. 2D materials, such as graphene, are no exception and adsorbates on graphene are known to affect many of its remarkable intrinsic properties. Furthermore, these adsorbed impurities can be electrically charged (so called “Coulomb” impurities) and their electronic and optical properties are not only interesting from a purely scientific perspective, but may have important implications for the development of future optoelectronic device technologies based on 2D materials.

In a pair of papers published recently, we have developed a multi-scale theory of Coulomb impurities on graphene that combines large-scale density-functional theory calculations, continuum Thomas-Fermi theory and tight-binding models in a parameter-free framework[1] that is able to predict and help interpret the most recent experimental measurements of individual adsorbates on graphene surfaces[2].

Fabiano Corsetti is a post-doctoral research associate in the Department of Materials at Imperial College London, supervised by Arash Mostofi. This work was a collaboration including Johannes Lischner of Imperial College London, Dillon Wong in the group of Mike Crommie at UC Berkeley.

Multi-scale model of membranes for water desalination

J. Muscatello, E. A. Muller, A. A. Mostofi and A. P. Sutton, Multiscale molecular simulations of the formation and structure of polyamide membranes created by interfacial polymerization, J. Membrane Sci. 527, 180 (2017).

One of the greatest societal challenges of the 21st century is to ensure the availability of fresh water to the world’s growing population in the backdrop of significant environmental change. Desalination of sea water to produce fresh water is a promising route to addressing this challenge.

Membranes can be used to desalinate sea water via a process known as reverse osmosis. Pressure is applied to sea water on one side of a selectively permeable membrane that allows water to flow through it, leaving behind the ions that cause sea water to be brackish.

A common type of membrane is a highly cross-linked polyamide thin layer formed by interfacial polymerisation of two monomers in solution. In these materials the separation of water from ions occurs in a thin layer than may only be a few nanometers thick — by contrast, the a human hair is about 10,000 times thicker.

In a paper published recently in the Journal of Membrane Science, Jordan Muscatello has developed a multi-scale model of the interfacial polymerisation process and representative atomic structures of the membrane. Two key observations from this computational study are: (1) the polymerisation process is self-limiting, resulting in a membrane thickness of 5-10 nm, in excellent agreement with experimental measurements; and (2) the membranes form by aggregation of oligomer clusters, with weaker bonding across interfaces between former separate clusters. The resulting morphology may have a direct bearing on transport of small molecules through the membrane where the less dense interfaces may provide easier channels for diffusion.

This work was supported by the BP International Centre for Advanced Materials. Jordan Muscatello is a post-doctoral research associate at Imperial College London and was supervised by Adrian Sutton, Erich Muller and Arash Mostofi.

Molecular simulations of nitrile rubber

M. Khawaja, A. P. Sutton and A. A. Mostofi, Molecular simulation of gas solubility in nitrile butadiene rubber, J. Phys. Chem. B 121, 287 (2017).

N. Molinari, M. Khawaja, A. P. Sutton and A. A. Mostofi, A molecular model for HNBR with tunable cross-link density,
J. Phys. Chem. B 120, 12700 (2016).

Nitrile butadiene rubber (NBR) and it’s hydrogenated relative HNBR are among the most widely used elastomers in the oil and gas industry where they are used to seal components in high temperature and pressure environments. Such seals can suffer permeation-driven failure as a result of absorption of gases that cause swelling and performance degradation.

In a pair of papers that have appeared recently in the Journal of Physical Chemistry B, PhD students Mohammed (Musab) Khawaja and Nicola Molinari have developed and used chemically-specific all-atom models of NBR and HNBR to study the properties of these elastomers. In the first paper, Musab studied the solubility of several gases known to be responsible for permeation-driven failure in NBR and found two key results: (1) that the presence of a particular chemical group (C-N cyano groups) in the polymer have a marked impact on the solubility of carbon dioxide and water; and (2) that at elevated pressures and temperatures such as those experienced in oil wells, the relative solubilities of different gases are likely to be different as compared to ambient conditions. These findings have implications for the chemical design of such elastomers for use at elevated temperature and pressure.

In the second paper, Nicola Molinari developed and tested all-atom model of HNBR that mimics the experimental process by which HNBR is produced from NBR by hydrogenation and cross-linking. In Nicola’s model, the degree of cross-linking is a tunable parameter that can be used to control some of its properties. This model paves the way for future studies of properties of HNBR, such as the solubility and diffusion of gas molecules, that are determined by chemically-specific interactions.

This work was supported by Baker Hughes. Mohammed Khawaja and Nicola Molinari are PhD students in the Centre for Doctoral Training in Theory and Simulation of Materials and they are supervised by Adrian Sutton and Arash Mostofi.