Quasiparticle scattering, lifetimes, and spectra using the GW approximation

Computer simulations are an increasingly important pillar of science, along with exper-iment and traditional pencil and paper theoretical work. Indeed, the development of theneeded approximations and methods needed to accurately calculate the properties of therange of materials from molecules to nanostructures to bulk materials has been a great tri-umph of the last 50 years and has led to an increased role for computation in science. Theneed for quantitatively accurate predictions of material properties has never been greater,as technology such as computer chips and photovoltaics require rapid advancement in thecontrol and understanding of the materials that underly these devices. As more accuracy isneeded to adequately characterize, e.g. the energy conversion processes, in these materials,improvements on old approximations continually need to be made. Additionally, in orderto be able to perform calculations on bigger and more complex systems, algorithmic devel-opment needs to be carried out so that newer, bigger computers can be maximally utilizedto move science forward.In this work we discuss our endeavors to improve approximations and algorithms to an-swer the challenge of better describing material properties. After an introduction to defineand discuss all the important concepts that appear later, we first discuss the calculation ofso-called satellite properties in the photoemission spectra (PES) of doped graphene. Whilethe GW approximation accurately produces the quasiparticle energies across a range ofmaterials from nanostructures and molecules to bulk metals and semiconductors, it doesnot accurately produce the satellite properties seen in PES experiments. We find that amore advanced treatment of the Green’s function, the cumulant expansion, is needed toadequately describe the satellite properties of doped graphene on SiC. In addition to thismore advanced Green’s function treatment, a novel technique is devised for including thescreening due to the SiC substrate on which the doped graphene is placed. This more ad-vanced treatment of the substrate is also crucial for obtaining agreement with experiment.Next, we show how the cumulant expansion can be used to accurately predict the ARPESspectra of bulk Si and the time-domain capacitance spectra of two-dimensional electrongases (2DEGs) in semiconductor quantum wells, with both the quasiparticle and satellitefeatures given correctly (unlike in GW theory, in which only the quasiparticle propertiesare predicted accurately). We then discuss carrier lifetimes from the GW approximationin bulk Si and GaAs, showing how theory can provide access to detailed microscopic in-formation that could be of use in designing more efficient photovoltaics. In chapter 6, wediscuss the effect of the pseudopotential approximation on excited-state GW calculations.Finding a small amount of error due to the use of nodeless pseudowavefunctions when us-ing pseudopotentials, we are able to understand the tendency of GW calculations that usepseudowavefunctions to overestimate the band gap in many common semiconductors. Wequantify this error and suggest improved techniques for applications where this error istoo large. In the last section on research, we discuss the effect of self-consistency in GWcalculations. Chapter 7 is on computational algorithm development, and there we discusssome algorithmic advances made in improving the BerkeleyGW code. A technique for bet-ter distributing the data during the calculation of the inverse dielectric matrix is discussedand shown to give very good performance improvements, especially for the large systemsthat are becoming increasingly common. Other small improvements that allow for a moreaccurate calculation of quasiparticle lifetimes are also discussed. Finally, a few appendicesare included for completeness.