Quasiparticle scattering, lifetimes, and spectra using the GW approximation

Computer simulations are an increasingly important pillar of science, along with exper-/niment and traditional pencil and paper theoretical work. Indeed, the development of the/nneeded approximations and methods needed to accurately calculate the properties of the/nrange of materials from molecules to nanostructures to bulk materials has been a great tri-/numph of the last 50 years and has led to an increased role for computation in science. The/nneed for quantitatively accurate predictions of material properties has never been greater,/nas technology such as computer chips and photovoltaics require rapid advancement in the/ncontrol and understanding of the materials that underly these devices. As more accuracy is/nneeded to adequately characterize, e.g. the energy conversion processes, in these materials,/nimprovements on old approximations continually need to be made. Additionally, in order/nto be able to perform calculations on bigger and more complex systems, algorithmic devel-/nopment needs to be carried out so that newer, bigger computers can be maximally utilized/nto move science forward./nIn this work we discuss our endeavors to improve approximations and algorithms to an-/nswer the challenge of better describing material properties. After an introduction to define/nand discuss all the important concepts that appear later, we first discuss the calculation of/nso-called satellite properties in the photoemission spectra (PES) of doped graphene. While/nthe GW approximation accurately produces the quasiparticle energies across a range of/nmaterials from nanostructures and molecules to bulk metals and semiconductors, it does/nnot accurately produce the satellite properties seen in PES experiments. We find that a/nmore advanced treatment of the Green’s function, the cumulant expansion, is needed to/nadequately describe the satellite properties of doped graphene on SiC. In addition to this/nmore advanced Green’s function treatment, a novel technique is devised for including the/nscreening due to the SiC substrate on which the doped graphene is placed. This more ad-/nvanced treatment of the substrate is also crucial for obtaining agreement with experiment./nNext, we show how the cumulant expansion can be used to accurately predict the ARPES/nspectra of bulk Si and the time-domain capacitance spectra of two-dimensional electron/ngases (2DEGs) in semiconductor quantum wells, with both the quasiparticle and satellite/nfeatures given correctly (unlike in GW theory, in which only the quasiparticle properties/nare predicted accurately). We then discuss carrier lifetimes from the GW approximation/nin bulk Si and GaAs, showing how theory can provide access to detailed microscopic in-/nformation that could be of use in designing more efficient photovoltaics. In chapter 6, we/ndiscuss the effect of the pseudopotential approximation on excited-state GW calculations./nFinding a small amount of error due to the use of nodeless pseudowavefunctions when us-/ning pseudopotentials, we are able to understand the tendency of GW calculations that use/npseudowavefunctions to overestimate the band gap in many common semiconductors. We/nquantify this error and suggest improved techniques for applications where this error is/ntoo large. In the last section on research, we discuss the effect of self-consistency in GW/ncalculations. Chapter 7 is on computational algorithm development, and there we discuss/nsome algorithmic advances made in improving the BerkeleyGW code. A technique for bet-/nter distributing the data during the calculation of the inverse dielectric matrix is discussed/nand shown to give very good performance improvements, especially for the large systems/nthat are becoming increasingly common. Other small improvements that allow for a more/naccurate calculation of quasiparticle lifetimes are also discussed. Finally, a few appendices/nare included for completeness.

Advisor: Louie, Steven G