Dr. Charles Patterson

Summary

My research consists of developing and applying electronic structure methods to problems in molecular, condensed matter and materials physics. Electronic structure theory is now a relatively mature field and density functional theory codes are available for many applications. More accurate many body methods, based on electron Green's functions, and electron-hole polarization propagators yield the most accurate predictions of excited state properties (Excitons) of molecules and condensed matter. The Exciton code performs self-consistent field Hartree-Fock calculations as well as GW (Green's function) and Bethe-Salpeter Equation calculations. Electronic structure codes divide roughly into those which represent electron wave functions using plane waves and those which use local orbitals. The former are best suited to crystalline materials with limited numbers of atoms per unit cell, the latter have many advantages for molecules, especially large molecules and systems with little or no symmetry. Accurate electronic structure methods such as the GW Green's function method and Bethe-Salpeter Equation polarization propagator method have applications in optical excitations of biomolecules, photovoltaics and photocatalysts for light harvesting and chemical reaction promotion such as artificial photosynthesis. Development of the Exciton code was begun with two graduate students, Drs. Conor Hogan and Svjetlana Galamic-Mulaomerovic, over a decade ago. That first phase of code development was based on a plane wave representation of the Coulomb potential, which is straightforward to code. The original Exciton code resulted in two publications in Physical Review B in 2005. Based on experience gained in developing the first Exciton code, I began developing an entirely new version of the code during a sabbatical year spent at the Quantum Theory Project, University of Florida, hosted by Prof. Rodney Bartlett. The new code employs the Ewald representation of the Coulomb potential for periodic systems. It makes full use of point, layer or space group symmetries in real and reciprocal space as well as time-reversal symmetry in reciprocal space. Symmetry is also used to transform the Gaussian atomic orbital basis into a symmetry adapted basis, which results in block diagonalization of operators, a reduction of running time and increased accuracy of wave functions. The many-body part of the code relies on an approach called Density fitting, which greatly reduces the time required to calculate Coulomb integrals over molecular orbitals. Current applications of the self-consistent Hartree-Fock, GW and BSE modules in the code to moleclues and molecular complexes have been tested using up to 1800 basis functions in the wave function basis and 4500 basis functions in the density fitting basis. Future development of the code will include the capacity to perform GW and Bethe-Salpeter Equation calculations for crystalline systems. Applications where the code would have significant advantages over plane wave codes are metal organic framework (MOF) materials which have open structures. Exciton is developed in C++ and MPI and consists of around 50,000 lines of code. The current Exciton code is also interfaced to the Crystal code which allows it to perform single-particle optical excitations calculations using wave functions and energy band structures from Crystal. This part of Exciton led to 15 publications in the seven year period since 2010. This version of the code produced two publications in 2005.

Funding Agency

Higher Education Authority/Enterprise Ireland

Programme

PRTLI IITAC II / Basic Research Award

Project Type

Computational/Theoretical

Summary

Light can be used as a probe of the electronic properties of matter in situations where conventional light-in/charged particle-out spectroscopies such as photoelectron spectroscopies cannot. The ejected electron in photoelectron spectroscopy cannot be detected if the ambient surrounding the sample is not high vacuum. In contrast, light-in/light-out spectroscopies such as reflectance measurements can be used without a vacuum ambient. The surface and interface optics project is focussed on applying density functional theory (DFT) methods to calculation of optical spectra of surfaces and interfaces of semiconductors and oxides. The work is done in collaboration with experimentalists, notably Prof. John McGilp in the School of Physics. Recent work on the interface between GaP thin films and the underlying Si substrate has been done with Prof. T. Hannappel and Dr. O. Supplie at the Helmholtz-Zentrum, Berlin who are experimentalists working on this prototype system for III-V semiconductor growth on silicon. Reflection of light by a surface depends on the dielectric responses of atoms from the surface layer to many layers below the surface. In order to use visible light as a probe of electrons at surfaces, it is essential to distinguish the reflected signal coming from the layers immediately at the surface from that coming from many more layers near the surface. One way of doing this is to choose systems where the surface is anisotropic in the surface plane while the underlying layers are isotropic. An example of an isotropic surface is where surface atoms form pairs (or dimerize) in chains at (001) surfaces of silicon or III-V semiconductors. If the difference in reflectivity of light is measured in normal incidence with the optical polarization vector aligned parallel or perpendicular to the dimer chains, then the surface contribution to reflectivity arises only from the anisotropic surface. Reflectance anisotropy spectroscopy (RAS) consists of measuring this difference, usually in the photon energy range from 1 to 5 eV. The experimental measurement by itself yields only a fingerprint of the surface. In order to use RAS to obtain information about electronic properties of the surface, experimental data must be compared to results of our calculations using the Crystal and Exciton codes. These calculations show which features in a RAS spectrum arise from transitions between particular surface states. Armed with this analysis, experimentalists may use the RAS technique to diagnose the electronic properties of a surface on which a semiconductor is being grown under non-high vacuum conditions. One recent highlight of this work has been application of the methods that we have developed since 2010 for calculating RAS for surfaces, to the interface between GaP thin films grown on the Si(001) surface by Hannappel and Supplie in Berlin. They measured the dielectric anisotropy of the interface between the thin film and silicon substrate. My PhD student, Pankaj Kumar, calculated the dielectric anisotropy for this interface using Crystal and Exciton and found agreement between theory and experiment only when the silicon substrate was doped so that the interface was semiconducting. Our work showed that the measured interface dielectric anisotropy arises from electrons trapped in interface states localized in several layers of silicon atoms closest to the first P layer in the GaP thin film. It also showed that if the GaP layer was terminated by a Ga/Si interface, the interface dielectric anisotropy spectrum was quite different. Thus a combination of theory and experiment can show whether a buried interface is conducting or semiconducting and whether the GaP layer in contact with the Si substrate is Ga or P. Our work is, as far as we can tell, the first application of DFT to the optical anisotropy of an interface and it has been accepted for publication in Physical Review Letters.

Funding Agency

Science Foundation Ireland

Programme

Research Frontiers Programme

Summary

Many of the most exotic states and properties of matter such as superconductivity, charge and spin order, etc arise in materials with unpaired electron spins on metal ions such as Fe3+ or Cu2+. My work in this area includes first principles hybrid density functional theory (DFT) calculations on manganites, cuprates and magnetite. Magnetite is a ferrimagnet, also known as lodestone, which has an unusual phase transition between a conducting and semiconducting state at 120 K, known as the Verwey transition. The contribution that I and my student, Andrew Rowan, and Prof. Lev Gasparov at the University of North Florida made in this area is in understanding charge order in the above mentioned materials. My most recent work in this area has been on elucidating the charge order in magnetite in the semiconducting phase of magnetite which exists below the Verwey temperature. The transition has puzzled physicists, including many distinguished scientists, since its discovery by Verwey in 1939. The problem is quite simple to explain. Magnetite consists of Fe3+ ions in tetrahedral 'A' sites and an equal proportion of Fe2+ and Fe3+ ions in octahedral 'B' sites. Fe2+ and Fe3+ ions are in d6 and d5 electronic configurations, respectively. This means that half of the ions at 'B' sites contain one minority spin electron, which is responsible for conduction above the Verwey transition temperature and must somehow become immobile below the Verwey temperature. It is this question that has puzzled physicists for 75 years. A complicating factor in determining the cause of the Verwey transition was that the structure of magnetite in the low temperature phase was poorly resolved because if multiple twinning of domains. It was finally resolved by Attfield and coworkers who used x-ray diffraction on a micron sized grain with one dominant domain in 2012 [Nature 481, 173 (2012)]. The unit cell contains 112 ions and has 16 types of Fe 'B' site and 8 types of 'A' site. The low temperature phase shows charge ordering of electrons on Fe 'B' sites, which is associated with the change in electric conductivity and which was dubbed 'trimeron' formation by Attfield and coworkers. Some chains of 3 Fe ions showed on of the conduction electrons being localized on 3 Fe ions. My contribution to this problem was to calculate the NMR (nuclear magnetic resonance) spectra of 'A' and 'B' site Fe ions in the newly discovered structure of magnetite as a function of crystal orientation in an external magnetic field. NMR is a potentially powerful probe of charge order in Fe compounds because 57Fe is a spin " nucleus which will couple to the minority spin electron in d6 Fe2+. Measurement of the NMR resonance frequency as a function of orientation of the magnetite crystal in a magnetic field yields curves which are characteristic of the shape of the d orbital containing this electron. My paper published in Physical Review B in 2014 showed that hybrid DFT calculations using the Crystal code and the crystal structure published by Attfield and coworkers in 2012 could reproduce the variation of NMR frequency with crystal orientation, and therefore that the charge order in our calculations was correct. I concluded that molecular polarons and charge localization in zig-zag chains (Attfield's trimerons) was responsible for the Verwey transition. Hybrid DFT calculation of 57Fe NMR resonances and orbital order in magnetite , C. H. Patterson, Phys. Rev. B 90, 075134 (2014) Hybrid Density Functional Theory Applied to Magnetite: Crystal Structure, Charge Order and Phonons, A. D. Rowan, C. H. Patterson and L. V. Gasparov, Phys. Rev. B 79 205103 (2009)

Funding Agency

Science Foundation Ireland

Programme

Research Frontiers Programme