Steven G. Louie, University of California, Berkeley
Understanding Excited-State Phenomena in Quasi-2D Materials
Written by Arthur L. Robinson
For a solid material, Steven G. Louie said, the quantum mechanics equation for the N-particle problem not only cannot be solved, its solution with 1023 coordinates would not be useful. As a theorist interested in ab initio calculations, Louie turned his attention to properties that can be measured. The spectroscopic properties as determined by excited-state behavior of a material, rather than the ground-state properties for which density functional theory is appropriate, typically give rise to a material’s defining attributes and determine its usefulness. These include electronic, optical, and transport characteristics that are essential in applications.
For his presentation, Louie divided spectroscopic properties into “N+1 particle” phenomena such as photoemission and tunneling that involve a single excited electron for which the electron self-energy is important (quasiparticles) and “N+2 particle” phenomena such as optical absorption for which electron–hole interactions must be included (excitons). He illustrated how these apply to typical devices like a photovoltaic cell which involves electron–hole creation by photon absorption, thermalization of the electron and holes by scattering, electron–hole pair transport by diffusion, and electron and hole separation that involve both exciton and quasiparticle properties.
Stepping deeper into theory, Louie discussed quasiparticle excitation, the problem of a single excited electron in a cloud of electrons. The energy spectrum (dispersion) now includes the electron self-energy, which includes contributions from electron–electron, electron–phonon, and possibly other interactions. A spectral function (probability of finding an electron with a given momentum and energy) is determined by the self-energy, which shifts and broadens the narrow energy-distribution peak obtained for non-interacting electrons. Calculating the spectral function involves interacting single-particle Green’s functions and what is called the GW approximation (keeping the first term in a perturbation theory expansion). Excitonic effects involving electron–hole interactions can be obtained using the GW approximation of the interacting two-particle Green’s function (GW-BSE approach).
With this background, Louie shifted to illustrating the necessity of including these many-particle effects in calculations of quasiparticle dispersion and lifetimes; optical absorption; exciton binding energies, wavefunctions, and radiative lifetimes; and forces in photo-excited states. For example, the theoretical bandgap in a large number of semiconductors does not agree with the experimental value unless the electron-self energy is included. Similarly, calculating the absorption spectrum of silicon requires electron–hole interactions to match experiment.
Nowadays, materials with small sizes and restricted geometry are of great interest owing to novel and useful properties that are either absent or not prominent in bulk materials and that arise from quantum confinement, enhanced many-electron interactions, reduced dimensionality, and symmetry effects. While graphene is the prototypical example of an atomically thin two-dimensional (2D) system, there are actually a large number of materials in which to study the effects of reduced dimensionality. Louie emphasized theoretical studies of quasi-2D systems, such as monolayer and few-layer transition metal dichalcogenides (e.g., MoS2, MoSe2, WS2, and WSe2) and metal monochalcogenides (such as GaSe) and mentioned the possibility of building van der Waals heterostructures from such materials. He concentrated on the electrical and optical spectra of MoS2. While it has the honeycomb structure of graphene, its lack of inversion symmetry combined with a strong spin-orbit coupling gives rise to new charge, spin, and valley degrees of freedom. Valley refers to energy minima at the vertices of the hexagonal Brillouin zone, which are no longer equivalent in MoS2.
As we by now expected, the self-energy and excitonic effects alter the band structure and absorption spectrum considerably with eV-level energy shifts. Large exciton binding energies also give rise to new exciton physics, such as quasi-2D screening that reverses the ordering of exciton energy levels relative to the hydrogenic model. Substrate screening is likewise important, shifting the exciton binding energy. Wanting his talk not to go overtime, Louie finished with a quick look at the results of excitons with a finite center of mass, in which electron–hole exchange interactions mix excitons in inequivalent Brillouin-zone minima, giving rise to what he called “massless” excitons!
The final message was that one size does not fit all; one must apply the appropriate theoretical treatment for the specific situations and properties.
[The Materials Theory Award, endowed by Toh-Ming Lu and Gwo-Ching Wang, recognizes exceptional advances made by materials theory to the fundamental understanding of the structure and behavior of materials. Steven G. Louie is honored "for his seminal contributions to the development of ab initio methods for and the elucidation of many-electron effects in electronic excitations and optical properties of solids and nanostructures."]