Session C20: First-principles Modeling of Excited-state Phenomena in Materials III: Recent Advances in Excited State Formalisms

Electronic and optical excitations from screened range-separated hybrid density functional theory

Some ten years ago, we have introduced the concept of optimal tuning (OT) of range-separated hybrid (RSH) functionals as a means of overcoming the fundamental gap problem and the charge transfer excitation problem in molecular systems. Here, this concept is extended to the solid state by introducing dielectric screening into the functional form. This approach, couched rigorously within the generalized Kohn-Sham formalism of density functional theory, can produce quantitatively the same one and two quasi-particle excitation picture given by many-body perturbation theory. Specifically, for molecular solids the approach predicts the correct gap renormalization without any empiricism. This can be achieved even from single molecule calculations if a polarizable continuum model is combined with the screened OT-RSH calculation in an electrostatically consistent manner. For covalent/ionic semiconductors and insulators, one empirical parameter is set to reproduce the direct bandgap. Accurate band structures and optical absorption spectra, which agree well with those obtained from GW and GW-BSE calculations, respectively, are then obtained.
  

Screened Range-Separated Hybrid Functional and GW + GW-BSE Calculations of Prototypical Semiconductors: A Comparison

We present band structure and optical absorption spectra obtained from a screened range-separated hybrid (SRSH) functional, including spin-orbit coupling, for seven prototypical semiconductors. The results are compared to those obtained from highly converged many body perturbation theory calculations using the GW approximation and the GW plus Bethe-Salpeter equation (GW-BSE) approaches. We use a single empirical parameter, fit such that the SRSH band gap reproduces the GW band gap at the Γ point. We then find that ground-state generalized Kohn-Sham SRSH eigenvalues accurately reproduce the band structure obtained from GW calculations, and optical absorption spectra obtained using linear-response time-dependent DFT with the SRSH functional agree well with those of GW-BSE, at a fraction of the computational cost.   

Transferable screened range-separated hybrids for layered materials

The optoelectronic properties of layered semiconductors can vary significantly between bulk (3D) phases and their single- or few-layer, 2D counterparts. In particular, the vastly different asymptotic behavior of dielectric screening in 2D and 3D structures poses a challenge for designing screened range-separated hybrid (SRSH) functionals that are accurate for both bulk and low-dimensional systems. We present a simple yet effective approach for simultaneously tuning the fraction of short-range exact exchange and the range-separation parameter that delivers tuned SRSH functionals for 2D sheets and 3D bulk phases of layered semiconductors. The ground-state SRSH eigenvalues are found to be in excellent agreement with bandstructures from accurate, manybody GW calculations. Excited state properties are predicted using time-dependent DFT calculations, based on the SRSH functional, and are also found to be in good agreement with absorption spectra obtained from GW and Bethe-Salpeter (BSE) calculations. The ability to develop SRSH functionals that are only material- but not structure-specific opens up avenues for systematic and accurate studies of layered materials and their nanostructures at a fraction of the cost of many-body calculations.   

First-principles study of bioinspired perylene diimide molecular nanowires

Perylene-3,4,9,10-tetracarboxylic diimide (PTCDI) has excellent electrochemical and photophysical properties that makes it a promising material for optoelectronic devices. Molecular nanowires consisted from PTCDI derivatives can be placed in DNA like base by standard automated oligonucleotide synthesis. Here, we study the electronic and optical properties of a series of recently synthesized bioinspired perylene diimide molecular nanowires by first-principles density functional theory (DFT) spectroscopy and molecular dynamics (MD). We apply time-dependent DFT with Franck-Condon analysis to study our material. Initial structures are taken from MD and the final vibronic spectra is an average over many structures. By stacking the molecules along a DNA-like backbone and varying the number of stacked molecules from one to four, we determine the role of inter-molecular interactions on the excited-state energetics, as well as vibrational excitations within the molecules. We demonstrate that strong inter-molecular interactions lead to distinct vibrational, electronic, and optical properties for design of new electronic and optoelectronic nanowires.   

Phase stability of MnSe, MnTe, and VO2 from total energies in the random phase approximation

While the limitations (semi-)local density functionals for the electronic structure are widely acknowledged, total energies are usually considered to be rather accurate. However, in transition metal compounds, standard density or even hybrid functionals often predict the wrong ground state structure. Total energy calculations in the random phase approximation (RPA) greatly improve the phase stability prediction, e.g., rock-salt vs wurtzite in MnO, but quantitative predictions are still sensitive on input wavefunction for the RPA energy [1]. Here, we calculate the phase stability for MnSe and MnTe in the rocksalt, nickeline, and wurtzite structures, for the "negative-pressure" phase in MnSeTe alloys [2]. To account for the wavefunction dependence, we perform a variational minimization of the RPA energy with respect to the onsite potentials U and V [1]. In VO2, the failure of standard DFT to produce a band gap can be remedied by simple DFT+U calculation, at the expense of the incorrect prediction that the undistorted antiferromagnetic phase is lower in energy than the experimentally known nonmagnetic monoclinic phase. We further discuss results based on the SCAN functional.
[1] H. Peng and S. Lany, PRB 87, 174113 (2013)
[2] S. Siol et al, Sci. Adv. 4, eaaq1442 (2018)

  

Can exact (local) Kohn-Sham potential reproduce band gaps?: Analysis using an analytically solvable two- and three-body models

We have clarified whether the exact (local) Kohn-Sham(KS) potential reproduces the exact band gap or not [1]. We have investigated the analytically solvable interacting two- and three-body models and calculated the exact electron levels through the one-particle Green's function of the two-body system analytically. Subsequently, we constructed the exact KS potential analytically and compared the obtained KS levels with exact ones. Then, we have found that KS-DFT even with the exact (local) KS potential does not reproduce the exact band gaps.

[1] J. Phys.: Condens. Matter 30, 435604 (2018).   

Wannier Koopmans method for band gap calculations of extended systems

We have developed a method to correct the density functional theory band gap problem, especially for extended systems. In this method, the Wannier functions are generated and the Hamiltonian is required to satisfy the Koopman theory (the total energy is linearly dependent on the occuption number) when a Wannier function is partially occupied. The resulting Hamiltonian gives a correction term for the Kohn-Sham eigen equation. This method can be considered as an extention of the delta DFT method to bulk systems. We have used this method to study common semiconductors, alkali halides, 2D materials, organic crystals, as well as oxides. We found in general, the accuracy of this Wannier Koopman method (WKM) is on a par with the GW results.
[1] J. Ma, L.W. Wang, Sci. Report, 6, 24924 (2016);
[2] J. Ma, Z.F. Liu, J.B. Neaton, L.W. Wang, Appl. Phys. Lett. 108, 262104 (2016);
[3] M. Weng, S. Li, J. Ma, J. Zheng, F. Fan, L.W. Wang, Appl. Phys. Lett. 111, 054101 (2017)
[4] M. Weng, S. Li, J. Zheng, F. Wang, L.W. Wang, J. Phys. Chem. Lett. 9, 281 (2017);
[5] S. Li, M. Weng, J. Jie, J. Zheng, F. Pan, L.W. Wang, Europ. Phys. Lett. 123, 37002 (2018)   

High-Harmonic Gereration with quantized fields: Minimal coupling of Pauli Spinors to quantized electromagnetic fields

Interaction between classical light and matter lies at the heart of a broad range of applications, such as the generation of spatially and temporally coherent ultaviolet light using the technique of high harmonic generation(HHG)[1]. The semi-classical treatment of HHG is, however, not able to capture the quantum features of light. In the present work, we consider Pauli spinors minimally coupled to quantized electromagnetic fields and investigate HHG with quantized fields. In this talk we will present a numerical implementation of the Pauli-Fierz Hamiltonian and first results for one-dimensional model systems and highlight differences to the usual semi-classical treatment.
[1] N. Tancogne-Dejean and A. Rubio, Sci. Adv. 4, eaao5207 (2018)   

Polaritonic chemistry: The influence of mass renormalization

If molecules are placed inside a cavity or near a plasmonic surface strong light-matter interaction can occur that mixes matter and photon degrees of freedom [1]. This can modify properties of molecules [2] and can even alter chemical reactions due to the changed electromagentic vacuum. The theoretical descriptions of such novel chemical situations is usually done with simplified few-level models and only recently more advanced ab-initio methods [4] have been developed and applied [5]. However, so far all these considerations have negelected the influence of the changed electromagentic vacuum on the masses of the particles. That is, while the mass of electrons and nuclei are usually defined with respect to the bare electromagnetic vacuum, in the above cases the electromagentic vacuum is changed considerably. Here we present first ab-initio studies of how multi-mode fields influence the total mass of the particles and thus change physical obervables.

[1] R. J. Thompson, G. Rempe, H. J. Kimble, Phys. Rev. Lett. 68 (1992)
[2] T. W. Ebbesen, Acc. Chem. Res. 49 2403(2016)
[4] M. Ruggenthaler, N. Tancogne-Dejean, J. Flick, H. Appel, A. Rubio, Nat. Rev. Chem. 2, 0118 (2018)
[5] J. Flick, D. M. Welakuh, M. Ruggenthaler, H. Appel, A. Rubio, arXiv:1803.02519   

First principles approaches to strong light-matter coupling

In recent years, research at the interface of chemistry, material science, and quantum optics has surged, now opens new possibilities to study strong light-matter interactions at different limits [1,2]. In this new regime, correlated electron, nuclear and photon interactions have to be treated on the same quantized footing [3] and towards this overarching goal, we have introduced a general time-dependent density-functional theory.

In this talk, we review recent developments and show how collective Rabi splitting under strong light-matter coupling emerges for CO₂ molecules in optical cavities. Further, we use this novel framework to study how the potential-energy surfaces (PES) of a CO bond stretching in an ensemble of Formaldehyde molecules is modified under collective strong-light matter coupling, demonstrating the novel abilities to alter and open new chemical reaction pathways as well as to create new hybrid states of light and matter in this regime [4].

[1] J. Flick, N. Rivera, P. Narang, Nanophotonics 7(9), 1479 (2018).
[2] F. Benz et al., Science, 354 6313, 726-729 (2016).
[3] J. Flick, P. Narang, Phys. Rev. Lett. 121, 113002 (2018).
[4] J. Flick, A. Winniki, P. Narang (in preparation) (2018).   

Time evolution methods for matrix-product states

Matrix-product states (MPS) have become the de facto standard for the investigation of one-dimensional quantum many body systems, also out-of-equilibrium.
Various approaches have been introduced for computing the time evolution of MPS, e.g., a time-dependent variational principle (TDVP) for MPS as well as matrix product operator (MPOs) representations of the time evolution operator.
In this talk I review important developments and compare four commonly used methods applied to five representative examples, including systems with long-ranged interactions or in 2D.
These results give insights to the state-of-the-art treatment of MPS out-of-equilibrium and a guideline for which method to choose for a problem at hand.   

Calculating Quantum Corrections to Electronic Transport in Disordered Nanostructures

Electronic transport in nanostructures shows strong dependencies on disorder and related quantum effects. The leading-order quantum corrections to the diffusive transport were identified as the weak-localization (WL) and the Altshuler-Aronov (AA) effects. An important issue is to develop a numerical method for computing these quantum corrections starting from the atomistic arrangement. To this end, a diagrammatic scheme based on nonequilibrium Green functions is put forward. We employ a nonlocal expansion technique to generate Cooperon diagrams in oder to capture WL. We implement this approach using a tight-binding Anderson model to simulate finite wires containing disorder. In WL regime, our computed conductance agrees well with the exact numerical solution, and the WL corrected resistance shows a nonlinear scaling versus the channel length. The WL induced negative magnetoresistance is also investigated. For AA correction, we extend the numerical GW method by dressing interaction vertices with diffusons, and we apply it to a finite Anderson-Hubbard model. Density of states anomalies are found at energies corresponding to bias voltages, and their size dependence is analyzed. The AA effect in nonlinear transport will also be reported.