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Supplementary Materials

Assessing density functionals using many body theory for hybrid perovskites

One of the most important issues in the modelling of materials is the choice of an appropriate density functional. Many researchers employ functionals commonly used in their field or they have some sort of chemical intuition, why one density functional should be preferred over another one. This is an ill-advised strategy. In this paper, we present a concise approach to select the best functional for structure prediction of a particular materials system. We use the random phase approximation (RPA), which is placed one step above hybrid functionals on the metaphorical Jacob's Ladder towards the exact total energy. A new implementation of RPA-forces in VASP (by Ramberger and Kresse, 2016) allows us to perform molecular dynamics at the RPA level, something that seemed impossible just a few years ago. A finite temperature ensemble of realistic crystal structures and the associated energies are calculated. Comparing these energies to the ones obtained with commonly used density functionals allows to rank them based on their accuracy. To verify this new approach, we study an exciting novel solar cell material: MAPbI3. Its structure is a particularly hard nut to crack for DFT. This is due to the large dynamical degree of freedom of the Methylammonium molecules and the interplay of van der Waals forces and cage instabilities in the perovskite structure.

Role of Polar Phonons in the Photo Excited State of Metal Halide Perovskites

We have calculated the band structure and exciton binding energies of the most studied ABX3 hybrid perovskites. We have incorporated many body effects on the DFT calculated electronic structure in the GW0 approximation and consecutively solved the Bethe-Salpeter equation (BSE). Convergence of the red-shift of the optical band gap requires the use of very dense k-point grids. We have therefore implemented a modelBSE routine in VASP, where a model screening function, fitted to W0, is used.

Electrostatic Doping of Graphene through Ultrathin Hexagonal Boron Nitride Films

A model that accurately describes the doping level in graphene on a h-BN covered metal surface is presented. The model is based on the electrostatical description of a simple planar capacitor. Interface bonding effects are included as localized potential steps and are obtained independently by first principles calculations. The doping level can be tuned by an external electric field and the metal contact results in a non-trivial intrinsic doping.

Role of Polar Phonons in the Photo Excited State of Metal Halide Perovskites

We have solved an open issue in this field, whether ionic movement can screen an e-h pair and thereby effectively lower the exciton binding energy. For this purpose we have calculated the room temperature dielectric function from molecular dynamics. By following the fluctuations of the total dipole moment in time, the polarizability can be calculated in linear response.

Band gaps in incommensurable graphene on hexagonal boron nitride

Early DFT calculations of commensurate graphene on h-BN showed a small induced band gap of approximately 40 meV. Low temperature STM images later showed that the graphene|h-BN is in reality incommensurate as indicated by the formation of large moir ́e patterns. We have shown that this does not have to mean that the induced band gap disappears and that a band gap of similar order can form. Since the required super cells are so large, Kohn-Sham DFT is not a viable option. We have therefore constructed a tight-binding model based on GW calculations for commensurate structures.

Large potential steps at weakly interacting metal-insulator interfaces

At metal-insulator interfaces large potential steps (1 eV) can be formed even though the interaction is of a weak van der Waals type. We have used the interface between a metal and h-BN (M|BN) as a archetypical example to study the underlying physical mechanisms. As shown in the top figure, DFT is unable to predict the equilibrium binding distance. However, the induced potential step as a function of distance does not depend on the XC-functional. We have approximated the M|BN wavefunction by constructing an anti-symmetric product of the individual M and BN wavefunctions in a self-adapted version of VASP. The resulting system is a good description of the self-consistently calculated M|BN system. This proofs directly that the interface dipole is formed by Pauli exchange repulsion.

Phase Transitions of Hybrid Perovskites Simulated by Machine-Learning Force Fields Trained on the Fly with Bayesian Inference

Realistic finite temperature simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of computing time. Here we present an on-th e-fly machine learning scheme that generates force fields automatically during molecular dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chemical precision of first principle s methods and minimizing the need for human intervention. The method is widely applicable to multielement complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which hav e never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temperature s of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.

Peer-reviewed publications

Phd thesis