We study excited electronic states and their dynamics and magnetic properties in various materials using accurate computational methods. To this end, we use modern super computers in order to understand, for instance, how light is absorbed in photo-voltaic materials. You can check out the following video that illustrates some of our work.

In order to connect atomic-scale simulation to the scale of real materials, we also develop multi-scale approaches, in particular for optical properties. In addition, we apply machine learning to facilitate materials discovery. Ultimately, this may lead to the knowledge necessary to design new and better materials for various applications entirely based on simulations.

## Ground-state properties

Modern computational methods based on density functional theory are used in order to understand the ground-state properties of materials: When exploring a new or unknown material in computer simulations, oftentimes, the starting point is to calculate ground-state properties such as the positions of all individual atoms, e.g. in thermodynamic equilibrium. Bond lengths and bond angles in molecules or lattice parameters in bulk crystals as derived from the computer simulations can then directly be compared to experimental results.

It is important to achieve a good understanding of the atomic geometries because different compounds feature different types of elements and the actual arrangements of atoms ultimately define how materials behave. A well-known example for this is carbon: it's polymorphs (e.g. diamond, graphite, graphene, ...) have extremely different properties.

If JAVA works in your Web Browser, you can click here to take an interactive look at this supercell (96 atom-cell of TiO_{2(1-x)}S_{2x}). The purpose of mixing sulfur into TiO_{2} is to increase the optical absorption in the visible spectral range and, hence, the photocatalytic activity. Read more details in Ref. [1].

In the past we studied, for instance, strain in zinc oxide semiconductors [2] that occurs when the material is grown on top of a lattice-mismatched substrate. We were also able to explore the stability range of different phases of oxide semiconductors under pressure [3] and for non-equilibrium conditions [4] that can be achieved in experiment nowadays. In addition, we investigated oxide [5] and nitride alloys [6] as well as different surfaces of tin dioxide [7].

Strained crystals, alloys, and non-equilibrium lattice structures are examples for intentionally tailoring material properties. Typically for ground-state properties our computational results are very similar to experimental findings and allow not just for direct comparison but also accurate predictions – another requirement for computational materials design.

## Excited electronic states and their dynamics

While density functional theory is very successful in describing ground-state properties for many materials, it oftentimes fails to capture excited-state properties. However, for many practical applications those are most relevant: For instance, for photovoltaics, optoelectronic devices, or transparent electronics it is critically important to understand the interaction of a material with excitations (such as light). It is exactly this interaction that determines the intriguing properties of many materials that are currently paving the way for new developments in these fields.

This figure (see Ref. [8]) shows the band gap of different oxide and nitride materials (as well as oxide alloys) as a function of the respective lattice parameter. It can be seen where the band gap is in relation to the visible spectral range.

We use and (further) develop cutting-edge approaches in the context of many-body perturbation theory to go beyond density functional theory in order to describe excited-state properties of materials. This provides us, for instance, with quasiparticle energies that can be directly compared to experimental results from photoelectron spectroscopies, which has allowed us to investigate band gaps of various oxide [9] and nitride [10] materials as well as their alloys [6] [11] [12]. In such cases numerical simulations can be particularly helpful to understand the influence of real-structure effects on quasiparticle band structures (including spin-orbit coupling), densities of states, band alignments, and electron-energy loss functions.

In addition, our calculations are also capable of describing optical-absorption experiments with very high accuracy and without experimental fit parameters by taking excitonic effects into account. This allowed us to understand the optical properties of defects in magnesium oxide [13] and also the influence of doping on the optical properties of zinc oxide [14].

## Non-adiabatic electron-ion dynamics

In many situations it is not enough to study the electronic and the ionic system of a material independently, since they can evolve on comparable time scales and also influence each other. Those situations are more and more the focus of experimental research, e.g. due to the advent of femto-second lasers and pump-probe techniques that allow ultrafast experiments and insight with unprecedented accuracy. We use real-time approaches (e.g. based on time-dependent density functional theory) [15] to study both the time dynamics of electronic states and excitations as well as non-adiabatic electron-ion dynamics (based on Ehrenfest dynamics)

Here you can see the electron density as it is influenced by a fast particle moving through the cell. Those calculations are used to understand the stopping power of a material as well as the creation of defects under radiation conditions.

While those approaches have proven very useful for understanding the electronic stopping power of metals [16] (as an important mechanism for energy transfer leading, e.g., to radiation damage in solar cells on satellites), they also provide important insight into different materials. We have applied those modern techniques to understand various materials systems such as 2D materials and semiconductors with existing defects.

## Materials Discovery

Online there are large, publicly accessible experimental and computational databases of materials properties. Applying DFT to calculate materials properties to every entry in such databases is not computationally feasible. Instead, we use a machine learning-based approach: DFT calculations for the desired properties are performed on a smaller subset of the database entries. This forms the training set to machine learn models. These models can then be rapidly applied to entire databases to discover materials of interest. These materials can then be studied more thoroughly with DFT.

## Magnetic Properties of Antiferromagnetic Materials

Weak response to external magnetic fields and THz frequency range spin dynamics makes antiferromagnetic (AFM) materials attractive. However, there are still uncovered characters of AFM materials related to optical induced magnetization, magnetic order of AFM, magnetic symmetry and so on. In order to use these useful properties of AFM, high Neel temperature that AFM becomes paramagnetic is required. Through ab initio density functional theory (DFT) calculation, spin spiral model with frozen magnon method can give chance to investigate magnon dispersion and Neel temperature. Interaction between electromagnetic wave and magnetized materials is able to be presented by magneto-optical Kerr effect (MOKE). A fully relativistic band structure from DFT calculation can makes us calculate dielectric tensor. Based on dielectric tensor, MOKE parameter is able to be computed.

## Multi-scale Simulation of Optical Properties

With atomic scale simulations providing very useful information about materials properties, we are also interested in connecting these simulations to actual (meso-scale) structure. Currently, we are exploring possible routes for us to apply our highly accurate optical spectra results from first-principles calculations to meso-scale structures and study their optical response. We use Matlab and COMSOL to solve Maxwell's equations and to obtain transmission/reflection/absorption for different geometries and generate library for these structures.

Ultimately, we aims at using machine learning techniques to so that for complicated structures. This will allow us to generate optical responses of these structures reasonably well with reduced computational cost. Thus we can provide guidance for experiments to obtain certain optical features.

### References

- . Enhanced Optical Absorption Due to Symmetry Breaking in TiO_{2(1-x)} S_{2x} Alloys. J. Phys. Chem. C. 2013 ;117:4189–4193.
- . Strain influence on valence-band ordering and excitons in ZnO: An ab initio study. Appl. Phys. Lett. 2007 ;91:241915.
- . First-principles study of ground- and excited-state properties of MgO, ZnO, and CdO polymorphs. Phys. Rev. B. 2006 ;73:245212.
- . Band-structure and optical-transition parameters of wurtzite {MgO}, {ZnO}, and {CdO} from quasiparticle calculations. Phys. Status Solidi B. 2009 ;246:2150–2153.
- . Ab initio description of heterostructural alloys: Thermodynamic and structural properties of Mg_x Zn_{1-x} O and Cd_x Zn_{1-x} O. Phys. Rev. B. 2010 ;81:245210.
- . Distribution of cations in wurtzitic In_x Ga_{1-x} N and In_x Al_{1-x} N alloys: Consequences for energetics and quasiparticle electronic structures. Phys. Rev. B. 2012 ;85:115121.
- . Energetics and approximate quasiparticle electronic structure of low-index surfaces of SnO_2. Phys. Rev. B. 2012 ;86:075320.
- . Real-structure effects: Absorption edge of Mg_x Zn_{1-x} O, Cd_x Zn_{1-x} O, and n-type ZnO from ab-initio calculations. Proc. SPIE. 2012 ;8263:826309.
- Ab-initio Studies of Electronic and Spectroscopic Properties of {MgO}, {ZnO}, and {CdO}. J. Kor. Phys. Soc. 2008 ;53:2811–2815.
- . Influence of exchange and correlation on structural and electronic properties of {AlN}, {GaN}, and {InN} polytypes. Phys. Rev. B. 2011 ;84:195105.
- . Electronic and optical properties of Mg_x Zn_{1-x} O and Cd_x Zn_{1-x} O from ab initio calculations. New J. Phys. 2011 ;13:085012.
- . Ab initio calculation of optical properties with excitonic effects in wurtzite In_x Ga_{1-x} N and In_x Al_{1-x} N alloys. Phys. Rev. B. 2013 ;87:195211.
- . First-Principles Optical Spectra for F Centers in MgO. Phys. Rev. Lett. 2012 ;108:126404.
- . Optical Absorption in Degenerately Doped Semiconductors: Mott Transition or Mahan Excitons?. Phys. Rev. Lett. 2011 ;107:236405.
- . Plane-wave pseudopotential implementation of explicit integrators for time-dependent Kohn-Sham equations in large-scale simulations. J. Chem. Phys. 2012 ;137:22A546.
- . Accurate atomistic first-principles calculations of electronic stopping. Phys. Rev. B. 2015 ;91:014306.