Session N59: First Principles Modeling of Excited-State Phenomena in Materials: TDDFT and Applications

Towards real-time TDDFT for excitons in solids

Time-dependent density-functional theory (TDDFT) has been established as an accurate and efficient method to simulate real-time electron and spin dynamics in solids from first principles. However, excitonic effects are challenging since standard semilocal exchange-correlation functionals fail to produce the required electron-hole interaction. In linear response, simple long-range corrected (LRC) functionals can qualitatively capture excitonic features in optical spectra; moreover, dielectrically screened hybrid functionals achieve excellent agreement with the Bethe-Salpeter equation at a fraction of the computational cost. Here we discuss, for a two-dimensional model solid, how these approaches carry over to the real-time domain and into the nonlinear, ultrafast regime. Two important issues will be highlighted: the numerical stability of the LRC functionals and the implementation of hybrid functionals with time-dependent screening. We also show how TDDFT can conveniently visualize time-dependent exciton wave functions. This opens up new opportunities for simulating exciton dynamics in a wide range of materials.   

Wigner-Seitz Truncated TDDFT Approach for the Calculation of Exciton Binding Energies in Solids

Time-Dependent Density Functional Theory (TDDFT) is a computationally efficient alternative to the Many-Body Perturbation Theory (MBPT) for calculating the optical properties of solids. However, the family of exchange-correlation kernels, known as long-range-corrected (LRC) kernels, which accurately capture excitonic features, still face some challenges that need to be addressed¹. In this work, we study the role of the Coulomb interaction in the calculations concerning excitonic effects within the TDDFT². We conduct a meticulous investigation of the impact of the long-range Coulomb term in both pure-TDDFT and hybrid approaches using a Wigner-Seitz truncated kernel. 

On the one hand, in the LRC-TDDFT framework, we find that the numerical method that is used throughout the literature to overcome the singularities of the Coulomb kernel often misses the effect of a surface term C_ck,vk that must be considered in periodic systems³. On the other hand, we propose a hybrid Wigner-Seitz Truncated kernel that regularizes the Coulomb kernel by employing a real space truncation in a Wigner-Seitz supercell of the crystal. We observe that while this kernel underestimates exciton binding energies of wide gap insulators, it yields exciton binding energies in good agreement with the BSE for small gap semiconductors^2,4. 

[1] Y. M. Byun et al., Phys. Rev. B 95, 205136 (2017)

[2] M. Arruabarrena et al., arXiv:2303.13389 (2023)

[3] B. Gu et al., Phys. Rev. B 87, 125301 (2013)

[4] J. Sun et al., Phys. Rev. Res. 2, 013091 (2020)   

High Harmonic Generation in VO2: First Principles Study

We studied the effect of High Harmonic Generation (HHG) in VO₂ in the insulating (M₁) phase by using Time-Dependent Density-Functional Theory (TDDFT) with the exchange-correlation (XC) potential obtained with Dynamical Mean-Field Theory (DMFT). In detail, we first studied the static properties of the system by using DFT+DMFT to take into account strong electron correlations and to derive an analytical (large-U limit) TDDFT XC potential.  We used the resulting XC to analyze the HH spectrum of the system with a focus on the effects of electron-electron correlations. We have found that the odd harmonics, seen experimentally, are generated by correlations. It was also found that as correlation strength increases, the system generates a richer HH spectrum, with the spectrum weight shifted towards higher harmonics. In the limit of strong correlations and laser pulse frequencies <!--[if gte msEquation 12]> style='mso-bidi-font-style:normal'>~0.3
eV the spectrum demonstrates super-harmonics - an energy-periodic enhancement and suppression of certain harmonic orders. Obtained results may help to better understand the ultrafast and emissive properties of vanadium dioxide.   

Hubbard-corrected Liouville-Lanczos TDDFT for accurate modeling of spin-wave excitations

Leveraging the efficiency of time-dependent density functional theory (TDDFT), we enhance the accuracy of magnon predictions in transition-metal (TM) compounds by incorporating Hubbard corrections. Our approach, implemented in the turboMagnon code of Quantum ESPRESSO [1], extends the Liouville-Lanczos method within a noncollinear DFT+Hubbard framework [2]. Importantly, Hubbard parameters are computed from first principles using density-functional perturbation theory [3]. Unlike conventional TDDFT with local-density approximation, our method mitigates strong self-interaction errors in TM compounds. We validate our approach by computing magnons in selected TM compounds, showcasing its potential for advancing predictive modeling of magnons in complex magnetic solids.

[1] T. Gorni et al., CPC 280, 108500 (2022)

[2] L. Binci et al., PRB 108, 115157 (2023)

[3] I. Timrov et al., PRB 98, 085127 (2018)   

Real-time proton-induced electron and ion dynamics in MgO slab

Ion beam irradiation has been extensively employed to precisely tailor the electronic and optical properties of thin film materials with nanometric precision. The success of these experiments underscores the need for a comprehensive understanding of the interaction between the ion projectile and the electronic and ionic systems of host materials, which is under development. In this project, we use real-time time-dependent density functional theory, which provides a unified framework for ion-induced electron excitation and the initial stages of nuclear damage, to investigate the response of MgO to proton irradiation. Our results reveal that, the excited electrons, localized near proton impact point, do not promptly reach equilibrium due to the relatively low electron mobility in an insulator. Consequently, this non-equilibrium state leads to an enhancement of the Coulomb repulsion, resulting in a constant force of approximately 1-2 eV/Å on atoms closest to the proton impact point, after the proton exits the MgO slab. Furthermore, these forces rapidly diminish as the distance from the proton impact point increases, indicating the potential utility of light ion irradiation for inducing localized defects with nanoscale precision. Moreover, this proof of concept drives our ongoing investigations into other materials systems with greater experimental interest.   

First Principles Investigations of NV-like centers in oxides

Recent predictions¹ suggest that oxides, such as MgO, may possess long coherence times and thus could serve as promising hosts for point defects for quantum applications. This points at the exciting prospect of going beyond the NV- center in diamond to design defects and hosts that are compatible with present telecommunication and manufacturing infrastructure. However, specific, promising defects are yet to be identified in most oxides. Leveraging a high-throughput first principles workflow², we predict that MgO can host NV-like centers with favorable electronic and optical properties. Using time-dependent density functional theory³, we find that these defects have a stable spin triplet state, and we report their absorption, emission, and zero-phonon lines. The defects identified here have a large relaxation in the excited state via the pseudo-Jahn Teller effect due to significant vibronic interaction between excited states. We expect such substantial electron-lattice interaction to be a general feature of oxide hosts. We also discuss the role of strain in tuning the excited state potential energy surface, thereby providing crucial insight into engineering the electronic and optical properties of point defects in a class of promising oxide hosts for quantum applications.

Work funded by the Midwest Integrated Center for Computational Materials (MICCoM) which is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DOE-BES).

References:

¹Shun Kanai et al. PNAS 119.15 (2022): e2121808119.

²Joel Davidsson et al. Comput. Phys. Commun. 269 (2021): 108091.

³Yu Jin et al. npj Comput. Mater. 8.1 (2022): 238.   

Exploration of the Optical Properties of Point Defects in Semiconductors and Insulators using Time-dependent Density Functional Theory

Optically active point defects in semiconductors and insulators hold great potential for quantum technology applications. First-principles investigations of excited state properties of point defects are instrumental in characterizing the defects through the interpretation of spectroscopic experimental results and the prediction of spin defects with tailored optical properties. Time-dependent density functional theory (TDDFT) enables the exploration of not only excited-state energies and wavefunctions of localized defect states but also potential energy surfaces by performing geometry optimizations. Here, I will present the study of the properties of several point defects using TDDFT, including the negatively charged nitrogen-vacancy center in diamond, the neutral silicon-vacancy center in diamond, the neutral divacancy center in silicon carbide, and the neutral oxygen-vacancy center in magnesium oxide. These calculations were made possible by our recent implementation of TDDFT with analytical forces in the West code. By using a GPU accelerated code and controlled numerical approximations, TDDFT calculations with hybrid functionals become feasible for systems comprising thousands of atoms, thus enabling detailed studies of excited-state geometries and finite-size effects of a wide range of point defects of interest to quantum technologies.   

Accurate defect electronic structure from non-empirical range-separated hybrid functionals: the case of oxygen vacancies in ZnO

Defects in semiconductors can act as a knob for tuning properties or as an undesirable feature affecting semiconductor performance. Density functional theory with semilocal functionals can fail to predict defect properties and absolute valence band maximum energies due to delocalization errors, leading to inaccurate defect level alignment. Here, we apply a recently developed nonempirical Wannier-localized optimally-tuned screened range-separated hybrid (WOT-SRSH) functional [1] to properties of the oxygen vacancy in zinc oxide, a well-studied defect. We show that in addition to quantitatively capturing the wurtzite ZnO band gap, our WOT-SRSH calculations predict an accurate absolute valence band maximum energy. Moreover, we show the bulk WOT-SRSH parameters are transferable to point defects, and lead to predictions of oxygen vacancy charge transition levels in good agreement with experiments and prior calculations with empirically-tuned hybrid functionals. We discuss the implications for broader application of the WOT-SRSH approach and the transferability of bulk nonempirical parameters to defects in other systems.   

Excited-State Dynamics and Optically Detected Magnetic Resonance of Solid-State Spin Defects from First-Principles

Optically detected magnetic resonance (ODMR) is an efficient and reliable method that enables initialization and readout of spin states through spin-photon interface. In general, high quantum efficiency and large spin-dependent photoluminescence (PL) contrast are desired for reliable spin information readout. However, first-principle tools for modeling ODMR contrast under external fields are not yet available, due to the complex dynamical processes, including optical excitation, and radiative and nonradiative excited-state relaxations. Therefore, we developed first-principles spin-dependent ODMR simulation method through solving kinetic master equation, with radiative, internal conversion and intersystem crossing (ISC) rates computed from first-principles, under microwave and magnetic fields. We show the importance of correct description of multireference electronic states for accurately predicting the excitation energy, spin-orbit coupling, and ISC by comparing CASSCF, TDDFT and DFT methods. We then underscore the importance of dynamical and pseudo Jahn-Teller effects for the spin-orbit coupling, a key factor determining ISC rates and ODMR contrast. Our first-principle method provides good agreement with the experimental ODMR contrast under magnetic field for NV center in diamond. Our work clarifies the important excited-state relaxation mechanisms determining ODMR contrast and provides a predictive computational tool for new solid-state spin defects with high readout fidelity and efficiency from first-principles.   

Attosecond electron dynamics in Floquet phases probed with time-resolved ARPES from TDDFT

Light-driven Floquet band engineering has recently emerged as a promising technique for controlling material properties. Floquet phases are typically probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the driven electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet bands themselves, their build-up, and their dephasing, but have not explored sub-laser-cycle dynamics within those bands. Given that Floquet theory is applicable only in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory – it requires probe pulse durations shorter than a single laser cycle, which inherently cannot discern the time-periodic nature of the light-matter system. We propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution, and a projection of Tr-ARPES spectra on the Floquet bands. We employ this approach in ab-initio calculations of light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as ‘non-Floquet’ bands. This work indicates that the Floquet-Bloch states are not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.