Session H24: Many-Body Perturbation Theory for Electronic Excitations: Excitonic Phenomena

A direct approach to the calculation of many-body Green' s functions: quasi-particles and more

Many-body perturbation theory is a powerful approach to describe many properties of materials. Most often one uses Dyson equations with self-energy kernels that are approximated to low order in the interaction. In Hedin's GW approximation, for example, the self-energy is a product of the one-body Green's function and the screened Coulomb interaction. This is the state-of-the art method for bandstructure calculations in a wide range of materials. However, sometimes the GW approximation and related approaches are not sufficient, for example when one is interested in satellite structure beyond the quasi-particle peaks in the spectral function, or in the case of strong coupling, where the quasi-particle picture is no longer adequate. We explore an alternative route to the calculation of interacting electron Green's functions. It is based on a set of functional differential equations relating the one-body Green’s function to its functional derivative with respect to an external perturbing potential [1]. This set of equations can be used to generate the perturbation series. Here we will show that working directly with the differential equations yields precious insight concerning some fundamental questions, guidelines for practical calculations, and methods that lead to an improved description of spectra, in particular advanced versions of the cumulant expansion. Results will be illustrated on various levels of approximation starting from simple models [2], but with a focus on full ab inito calculations [3] and comparison with, and interpretation of, experiment. In particular, we will discuss various kinds of photoemission satellites, and also address questions linked to strong correlation. [1] L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics (New York: Benjamin, 1962) [2] A. Stan et al., New J. Phys. 17, 093045 (2015) [3] M. Guzzo et al., Phys. Rev. Lett. 107, 166401 (2011); Phys. Rev. B 89, 085425 (2014)   

Multiple Exciton Generation in Semiconductor Nanostructures: DFT-based Computation

Multiple exciton generation (MEG) in nm-sized H-passivated Si nanowires (NWs), and quasi 2D nanofilms depends strongly on the degree of the core structural disorder as shown by the perturbation theory calculations based on the DFT simulations. In perturbation theory, we work to the 2$^{nd}$ order in the electron-photon coupling and in the (approximate) RPA-screened Coulomb interaction. We also include the effect of excitons for which we solve Bethe-Salpeter Equation. To describe MEG we calculate exciton-to-biexciton as well as biexciton-to-exciton rates and quantum efficiency (QE). We consider 3D arrays of Si29H36 quantum dots, NWs, and quasi 2D silicon nanofilms, all with both crystalline and amorphous core structures. Efficient MEG with QE of 1.3 up to 1.8 at the photon energy of about 3$E_{gap}$ is predicted in these nanoparticles except for the crystalline NW and film where QE$\simeq$1. MEG in the amorphous nanoparticles is enhanced by the electron localization due to structural disorder. The exciton effects significantly red-shift QE vs. photon energy curves. Nm-sized a-Si NWs and films are predicted to have effective MEG within the solar spectrum range. Also, we find efficient MEG in the chiral single-wall Carbon nanotubes and in a perovskite nanostructure.   

Excitons in solids with time-dependent density-functional theory: the bootstrap kernel and beyond

Time-dependent density-functional theory (TDDFT) is an efficient method to describe the optical properties of solids. Lately, a series of bootstrap-type exchange-correlation (xc) kernels have been reported to produce accurate excitons in solids, but different bootstrap-type kernels exist in the literature, with mixed results. In this presentation, we reveal the origin of the confusion and show a new empirical TDDFT xc kernel to compute excitonic properties of semiconductors and insulators efficiently and accurately. Our method can be used for high-throughput screening calculations and large unit cell calculations.   

Stability of excitonic complexes in a multi-valley/band semiconductor

Whether bound states are present for few-particle quantum systems is far from axiomatic and has been a hot topic for decades. For example, three-positronium and -/hydrogen bound states are not present in the vacuum. On the other hand, it has also been proposed that three excitons can be bound with each other in multi-valley/band semiconductors [J. S. Wang {\&} C. Kittel, Phys. Lett. 42A, No. 3 (1972)]. Indeed, an array of photoluminescence peaks have been recently observed in diamond [J. Omachi et al., Phys. Rev. Lett. 111, 026402(2013)], which could suggest the existence of possible multi-exciton bound states. We theoretically examine if such bound states are possible by a variational method. For the electron-hole Hamiltonian including the valley and band degrees of freedom, we expressed trial many-body wave function with the correlated Gaussian bases and optimized it with the stochastic variational method [J. Mitroy et al., Rev. of Mod. Phys., 85, 2013]. We have shown bound states for N-exciton systems with N more than two. In the talk, we discuss the dependence of the bound states on the model settings and its relation to the experimental observation.   

Exploring the nature of low-lying excited-states in molecular crystals from many-body perturbation theory beyond the Tamm-Dancoff Approximation

Organic semiconductors have attracted attention due to their potential for optoelectronics and novel phenomena, such as singlet fission. Here, we use many-body perturbation theory to simulate neutral excitations in acene and perylene crystals. By diagonalizing the full Bethe-Salpether (BSE) Hamiltonian beyond the Tamm Dancoff approximation (TDA) [1], we find that both low-lying excitation energies and oscillator strengths are in improved agreement with experiments relative to the TDA. We characterize the low-lying excitons, focusing in the degree of charge-transfer and spatial delocalization, connecting their relevance to singlet fission. [2] For perylene, we find overall good agreement with absorption measurements, and we see evidence for the formation of an “exciton-polariton” band in $\beta$-perylene. 1. da Jornada, F. H. et al., to be submitted. 2. Sharifzadeh. S. et al., J. Phys. Chem. Lett. 4, 2197 (2013).   

Effect of Crystal Packing on the Excitonic Properties of Rubrene Polymorphs

Singlet fission, the down-conversion of one singlet exciton into two triplet excitons, has been recently observed in molecular crystals of rubrene. The orthorhombic form of rubrene is the most stable in ambient conditions. However, rubrene has two additional known polymorphs, a triclinic form and a monoclinic form. To investigate the relative stability of the three polymorphs under different temperature and pressure conditions we use dispersion-inclusive density functional theory (DFT) with the pairwise Tkatchenko-Scheffler (TS) method and the many-body dispersion (MBD) method. Many-body perturbation theory is then employed to study the effect of crystal structure on the electronic and excitonic properties. Band structures are calculated within the GW approximation, where G is the one-particle Green's function and W is the screened Coulomb interaction, and optical properties are calculated by solving the Bethe-Salpeter equation (BSE). We find that crystal packing affects the band gaps, band dispersion, optical gaps, singlet-triplet gaps, and exciton localization in the three polymorphs of rubrene. Singlet fission efficiency may thus be improved by modulating the crystal packing.   

Multiscale modeling of excitation dynamics in molecular materials with GW-BSE/MM

Processes involving electronic excitations govern the functionality of molecular materials in which the dynamics of excitons and charges is determined by an interplay of molecular electronic structure and morphological order. To understand, e.g., charge separation and recombination at donor-acceptor heterojunctions in organic solar cells, knowledge about the microscopic details influencing these dynamics in the bulk and across the interface is required. For heterojunctions of small-molecule donor materials with C60, we employ a hybrid QM/MM approach [JCTC 7, 3335 (2011)]$^{\mathrm{\thinspace }}$ linking density-functional and many-body Green's functions theory$^{\mathrm{\thinspace }}$[JCTC 8, 2790 (2012)] (DFT/GW-BSE) to polarizable force-fields$^{\mathrm{\thinspace }}$[JCTC 10, 3140 (2014)] and analyze the charged and neutral electronic excitations therein. We develop models for both static and dynamic properties of the excitations, including (a) the diffusion of Frenkel excitons and (b) the relative energies of Frenkel and charge-transfer excitations at the donor-acceptor interface and the resulting charge separation dynamics. Our simulations allow linking the molecular architecture of the donor material, its orientation on the fullerene substrate as well as mesoscale order [Nat. Mater. 14, 434 (2015)] to the solar cell performance.   

Excited Biexcitons in Transition Metal Dichalcogenides

Recently, experimental measurements and theoretical modeling have been in a disagreement concerning the binding energy of biexctions in transition metal dichalcogenides.\footnote{Y. You, X.-X. Zhang, T. C. Berkelbach, M. S. Hybertsen, D. R. Reichman, T. F. Heinz, \textbf{Nat. Phys.} 11 477--481 (2015).} While theory predicts a smaller binding energy ($\sim$20 meV) that is, as logically expected, lower than that of the trion, experiment finds values much larger ($\sim$60 meV), actually exceeding those for the trion. In this work, we show that there exists an excited state of the biexciton which yields binding energies that match well with experimental findings and thus gives a plausible explanation for the apparent discrepancy. Furthermore, it is shown that the electron-hole correlation functions of the ground state biexciton and trion are remarkably similar, possibly explaining why a distinct signature of ground state biexcitons would not have been noticed experimentally.\footnote{D. K. Zhang, D. W. Kidd, K. Varga, \textbf{Nano. Lett.} Article ASAP (2015).}   

Exciton band structure in two-dimensional materials

In low-dimensional materials the screening of the Coulomb interaction is strongly reduced[1,2]. As a consequence, the binding energy of both Wannier and Frenkel excitons in the optical spectra is large and comparable in size. Therefore, contrarily to bulk materials, it cannot serve as a criterion to distinguish different kinds of excitons. Here we demonstrate that the exciton band structure, which can be accessed experimentally, instead provides a powerful way to identify the exciton character. By comparing the ab initio solution of the many-body Bethe-Salpeter equation for graphane and single-layer hexagonal BN, we draw a general picture of the exciton dispersion in two-dimensional materials, highlighting the different role played by the exchange electron-hole interaction and by the hopping terms related to the electronic band structure. 1 Pierluigi Cudazzo et. al. Phys. Rev. Letter 104 226804 (2010) 2 Pierluigi Cudazzo et. al. Phys Rev. B 84, 085406 (2011)   

Effect of Lattice Screening on Excitonic and Optical Properties in CH$_3$NH$_3$PbI$_3$ Solar Cell Materials

Hybrid Organo-Metallic Perovskites have made great strides towards becoming a next generation solar cell material. Though high performing experimental devices have been constructed from these perovskites, the fundamental optical and electronic physics of these systems remains an active area of research. A large lattice dielectric constant in the Methylammonium(CH$_3$NH$_3$)-Lead(Pb)-Iodide(I$_3$) system potentially contributes to the screening of the electron-hole interaction. The strongly increased dielectric screening due to lattice contributions has been suggested to reduce the exciton binding energy and strongly effects the optical band gap. In this study, we seek to understand, from first principles, the interplay between lattice screening and exciton binding energy. We use density functional theory for ground state calculations and the Bethe-Salpeter equation for the optical polarization function, from which we calculate optical spectra and excitonic properties. We will discuss differences between lattice and electronic screening and the effect on the optical properties of multiple CH$_3$NH$_3$PbI$_3$ phases.   

Substrate-induced renormalization of the quasiparticle and optical gaps in monolayer transition metal dichalcogenides from GW and GW-BSE calculations.

There has been a considerable effort to experimentally characterize the electronic and optical properties of novel atomically thin 2D semiconductors, such as mono- and few-layer transition metal dichalcogenides (TMDs). However, the role that different substrates play in these experiments still remains unclear. From a theoretical perspective, it is hard to include the substrate in an \textit{ab initio} framework, while in experiments, it is often difficult to suspend these samples. Here, we present a new method to compute the substrate effect on the quasiparticle and optical properties of quasi-2D materials based on state-of-the-art \textit{ab initio} GW and GW plus Bethe-Salpeter equation (GW-BSE) methods. We compute the effects of different metallic and semiconducting substrates, and show that the quasiparticle gap and exciton binding energy can be dramatically reduced even with semiconducting substrates. This work was supported by the National Science Foundation under Grant No. DMR15-1508412 and the DOE under Contract No. DE-AC02-05CH11231.   

Nonanalyticity, Valley Quantum Phases, and Massless Excitons in Monolayer Transition Metal Dichalcogenides

Exciton dispersion as a function of center-of-mass momentum \textbf{Q} is essential to the understanding of exciton dynamics, relaxation, and condensation. We use the ab initio GW-Bethe-Salpeter equation(GW-BSE) method to calculate the dispersion of excitons in monolayer MoS$_{2}$ and find a nonanalytic lightlike dispersion. This behavior arises from the interplay of an unusual $|Q|$-term in both the intra- and intervalley exchange of the electron-hole interaction, which concurrently gives rise to a valley quantum phase of winding number two. We have derived a simple, effective Hamiltonian and analytic solutions, which quantitatively describe this physics, and we predict that signatures of this unusual dispersion can be measured with a linearly polarized optical beam tilted away from normal incidence. The existence of a nonanalytic exciton dispersion can be generalized to other 2D semiconductors with excitons whose amplitudes are localized in a small region of the Brillioun zone.