Disorder to order: how halide mixing in MAPbI3-xBrx perovskites restricts MA dynamics.

Mixed-halide lead perovskites are of particular interest for the design of tandem solar cells currently reaching record efficiencies. While halide phase segregation upon illumination of mixed perovskites is extensively studied, the effect of halide disorder on A cation dynamics is not well understood, despite its importance for charge carrier diffusion and lifetime. Here, we study the methylammonium (MA) reorientational dynamics in mixed halide MAPbI3-xBrx perovskites by a combined approach of experimental solid-state NMR spectroscopy and molecular dynamics (MD) simulations based on machine-learning force-fields (MLFF). 207Pb NMR spectra indicate the halides are randomly distributed over their lattice positions, whereas PXRD measurements show that all mixed MAPbI3-xBrx samples are cubic. The experimental 14N spectra and 1H double-quantum (DQ) NMR data reveal anisotropic MA reorientations depending on the halide composition and thus associated disorder in the inorganic sublattice. MD calculations allow us to correlate these experimental results to restrictions of MA dynamics due to preferred MA orientations in their local Pb8I12-nBrn "cages". Based on the experimental and simulated results, we develop a phenomenological model that correlates the 1H dipolar coupling and thus the MA dynamics with the local composition and reproduces the experimental data over the whole composition range. We show that the dominant interaction between the MA cations and the Pb-X lattice that influences the cation dynamics is the local electrostatic potential being inhomogeneous in mixed halide systems. As such, we generate a fundamental understanding of the predominant interaction between the MA cations and the inorganic sublattice, as well as MA dynamics in asymmetric halide coordinations.

Exploring Librational Pathways with on-the-Fly Machine-Learning Force Fields: Methylammonium Molecules in MAPbX3 (X = I, Br, Cl) Perovskites.

Two seemingly similar crystal structures of the low-temperature (∼100 K) MAPbX3 (X = I, Br, Cl) perovskites, but with different relative methylammonium (MA) ordering, have appeared as representatives of this orthorhombic phase. Distinguishing them by X-ray diffraction experiments is difficult, and conventional first-principles-based molecular dynamics approaches are often too computationally intensive to be feasible. Therefore, to determine the thermodynamically stable structure, we use a recently introduced on-the-fly machine-learning force field method, which reduces the computation time from years to days. The molecules exhibit a large degree of anharmonic motion depending on temperature: that is, rattling, twisting, and tumbling. We observe the crystal's "librational pathways" while slowly heating it in isothermal-isobaric simulations. Marked differences in the thermal evolution of structural parameters allow us to determine the real structure of the system via a comparison with experimentally determined crystal structures.

Microscopic (Dis)order and Dynamics of Cations in Mixed FA/MA Lead Halide Perovskites.

Recent developments in the field of high efficiency perovskite solar cells are based on stabilization of the perovskite crystal structure of FAPbI3 while preserving its excellent optoelectronic properties. Compositional engineering of, for example, MA or Br mixed into FAPbI3 results in the desired effects, but detailed knowledge of local structural features, such as local (dis)order or cation interactions of formamidinium (FA) and methylammonium (MA), is still limited. This knowledge is, however, crucial for their further development. Here, we shed light on the microscopic distribution of MA and FA in mixed perovskites MA1-x FA x PbI3 and MA0.15FA0.85PbI2.55Br0.45 by combining high-resolution double-quantum 1H solid-state nuclear magnetic resonance (NMR) spectroscopy with state-of-the-art near-first-principles accuracy molecular dynamics (MD) simulations using machine-learning force-fields (MLFFs). We show that on a small local scale, partial MA and FA clustering takes place over the whole MA/FA compositional range. A reasonable driving force for the clustering might be an increase of the dynamical freedom of FA cations in FA-rich regions. While MA0.15FA0.85PbI2.55Br0.45 displays similar MA and FA ordering as the MA1-x FA x PbI3 systems, the average cation-cation interaction strength increased significantly in this double mixed material, indicating a restriction of the space accessible to the cations or their partial immobilization upon Br- incorporation. Our results shed light on the heterogeneities in cation composition of mixed halide perovskites, helping to exploit their full optoelectronic potential.

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-the-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 principles 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 have 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 temperatures of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.

Assessing Density Functionals Using Many Body Theory for Hybrid Perovskites.

Which density functional is the "best" for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)-an accurate many body theory-is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI_{3}, a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approximate density functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) density functional yield very good agreement with the RPA. Finally, our study shows that in the room temperature tetragonal phase of MAPbI_{3}, the molecules are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.

Behavior of Methylammonium Dipoles in MAPbX3 (X = Br and I).

Dielectric constants of MAPbX3 (X = Br, I) in the 1 kHz-1 MHz range show strong temperature dependence near room temperature, in contrast to the nearly temperature-independent dielectric constant of CsPbBr3. This strong temperature dependence for MAPbX3 in the tetragonal phase is attributed to the MA+ dipoles rotating freely within the probing time scale. This interpretation is supported by ab initio molecular dynamics simulations on MAPbI3 that establish these dipoles as randomly oriented with a rotational relaxation time scale of ∼7 ps at 300 K. Further, we probe the intriguing possibility of transient polarization of these dipoles following a photoexcitation process with important consequences on the photovoltaic efficiency, using a photoexcitation pump and second harmonic generation efficiency as a probe with delay times spanning 100 fs-1.8 ns. The absence of a second harmonic signal at any delay time rules out the possibility of any transient ferroelectric state under photoexcitation.

Z_{2} Invariance of Germanene on MoS_{2} from First Principles.

We present a low energy Hamiltonian generalized to describe how the energy bands of germanene (Ge[over ¯]) are modified by interaction with a substrate or a capping layer. The parameters that enter the Hamiltonian are determined from first-principles relativistic calculations for Ge[over ¯]|MoS_{2} bilayers and MoS_{2}|Ge[over ¯]|MoS_{2} trilayers and are used to determine the topological nature of the system. For the lowest energy, buckled germanene structure, the gap depends strongly on how germanene is oriented with respect to the MoS_{2} layer(s). Topologically nontrivial gaps for bilayers and trilayers can be almost as large as for a freestanding germanene layer.

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

The development of high efficiency perovskite solar cells has sparked a multitude of measurements on the optical properties of these materials. For the most studied methylammonium(MA)PbI3 perovskite, a large range (6-55 meV) of exciton binding energies has been reported by various experiments. The existence of excitons at room temperature is unclear. For the MAPbX3 perovskites we report on relativistic Bethe-Salpeter Equation calculations (GW-BSE). This method is capable to directly calculate excitonic properties from first-principles. At low temperatures it predicts exciton binding energies in agreement with the reported 'large' values. For MAPbI3, phonon modes present in this frequency range have a negligible contribution to the ionic screening. By calculating the polarization in time from finite temperature molecular dynamics, we show that at room temperature this does not change. We therefore exclude ionic screening as an explanation for the experimentally observed reduction of the exciton binding energy at room temperature and argue in favor of the formation of polarons.

Tunable ferroelectric polarization and its interplay with spin-orbit coupling in tin iodide perovskites.

Ferroelectricity is a potentially crucial issue in halide perovskites, breakthrough materials in photovoltaic research. Using density functional theory simulations and symmetry analysis, we show that the lead-free perovskite iodide (FA)SnI3, containing the planar formamidinium cation FA, (NH2CHNH2)(+), is ferroelectric. In fact, the perpendicular arrangement of FA planes, leading to a 'weak' polarization, is energetically more stable than parallel arrangements of FA planes, being either antiferroelectric or 'strong' ferroelectric. Moreover, we show that the 'weak' and 'strong' ferroelectric states with the polar axis along different crystallographic directions are energetically competing. Therefore, at least at low temperatures, an electric field could stabilize different states with the polarization rotated by π/4, resulting in a highly tunable ferroelectricity appealing for multistate logic. Intriguingly, the relatively strong spin-orbit coupling in noncentrosymmetric (FA)SnI3 gives rise to a co-existence of Rashba and Dresselhaus effects and to a spin texture that can be induced, tuned and switched by an electric field controlling the ferroelectric state.

Electrostatic doping of graphene through ultrathin hexagonal boron nitride films.

When combined with graphene, hexagonal boron nitride (h-BN) is an ideal substrate and gate dielectric with which to build metal|h-BN|graphene field-effect devices. We use first-principles density functional theory (DFT) calculations for Cu|h-BN|graphene stacks to study how the graphene doping depends on the thickness of the h-BN layer and on a potential difference applied between Cu and graphene. We develop an analytical model that describes the doping very well, allowing us to identify the key parameters that govern the device behavior. A predicted intrinsic doping of graphene is particularly prominent for ultrathin h-BN layers and should be observable in experiment. It is dominated by novel interface terms that we evaluate from DFT calculations for the individual materials and for interfaces between h-BN and Cu or graphene.