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We determine the impact of anharmonic thermal vibrations on the fundamental band gap of CsPbBr$_3$, a prototypical model system for the broader class of halide perovskite semiconductors. Through first-principles molecular dynamics and stochastic calculations, we find that anharmonic fluctuations are a key effect in the electronic structure of these materials. We present experimental and theoretical evidence that important characteristics, such as a mildly changing band-gap value across a temperature range that includes phase-transitions, cannot be explained by harmonic phonons thermally perturbing an average crystal structure and symmetry. Instead, the thermal characteristics of the electronic structure are microscopically connected to anharmonic vibrational contributions to the band gap that reach a fairly large magnitude of 450 meV at 425 K.

We have found that the polarization dependence of Raman scattering in organic crystals at finite temperatures can only be described by a fourth-rank formalism. This generalization of the second-rank Raman tensor $\mathcal{R}$ stems from the effect of off-diagonal components in the crystal self-energy on the light scattering mechanism. We thus establish a novel manifestation of phonon-phonon interaction in inelastic light scattering, markedly separate from the better-known phonon lifetime.

$δ$-Bi$_2$O$_3$ is one of the fastest known solid oxide ion conductors owing to its intrinsically defective fluorite-like structure with 25\% vacant sites in the O sub-lattice. Numerous diffraction measurements and molecular dynamics simulations indicate that the Bi ions construct a cubic, fcc lattice, and the O ions are %distributing and migrating through it. Nonetheless, in this study we present Raman scattering measurements that clearly show that the Bi sub-lattice preserves the monoclinic symmetry of the low temperature phase ($α$-Bi$_2$O$_3$) up to the melting temperature of the crystal. The apparent contradiction between our observations and previous findings suggests that Bi ions oscillate between local minima of the effective potential energy surface. These minima represent the monoclinic phase while the time-averaged structure is the cubic phase. We discuss the implication of these low-frequency oscillations on ion conduction., 4 pages, 4 figures

The anharmonic lattice dynamics of oxide and halide perovskites play a crucial role in their mechanical and optical properties. Raman spectroscopy is one of the key methods used to study these structural dynamics. However, despite decades of research, existing interpretations cannot explain the temperature dependence of the observed Raman spectra. We demonstrate the non-monotonic evolution with temperature of the scattering intensity and present a model for 2nd-order Raman scattering that accounts for this unique trend. By invoking a low-frequency anharmonic feature, we are able to reproduce the Raman spectral line-shapes and integrated intensity temperature dependence. Numerical simulations support our interpretation of this low-frequency mode as a transition between two minima of a double-well potential surface. The model can be applied to other dynamically disordered crystal phases, providing a better understanding of the structural dynamics, leading to favorable electronic, optical, and mechanical properties in functional materials.

Crystals and fibers doped with Rare Earth (RE) ions provide the basis to most of today's solid-state optical systems, from lasers and telecom devices to emerging potential quantum applications such as quantum memories and optical to microwave conversion. The two platforms, doped crystals and doped fibers, seem mutually exclusive, each having its own strengths and limitations- the former providing high homogeneity and coherence, and the latter offering the advantages of robust optical waveguides. Here we present a hybrid platform that does not rely on doping but rather on coating the waveguide - a tapered silica optical fiber - with a monolayer of complexes, each containing a single RE ion. The complexes offer an identical, tailored environment to each ion, thus minimizing inhomogeneity and allowing tuning of their properties to the desired application. Specifically, we use highly luminescent Yb$^{+3}$[Zn(II)$_{MC}$(QXA)] complexes, which isolate the RE ion from the environment and suppress non-radiative decay channels. We demonstrate that the beneficial optical transitions of the Yb$^{+3}$ are retained after deposition on the tapered fiber, and observe an excited-state lifetime of over 0.9 ms, on par with state-of-the-art Yb doped inorganic crystals.

Halide perovskite (HP) semiconductors exhibit unique strong coupling between the electronic and structural dynamics. The high-temperature cubic phase of HPs is known to be entropically stabilized, with imaginary frequencies in the calculated phonon dispersion relation. Similar calculations, based on the static average crystal structure, predict a stable tetragonal phase with no imaginary modes. This work shows that in contrast to standard theory predictions, the room-temperature tetragonal phase of CH$_{3} $NH$_{3} $PbI$_{3}$ is strongly anharmonic. We use Raman polarization-orientation (PO) measurements and \textit{ab initio} molecular dynamics (AIMD) to investigate the origin and temperature evolution of the strong structural anharmonicity throughout the tetragonal phase. Raman PO measurements reveal a new spectral feature that resembles a soft mode. This mode shows an unusual continuous increase in damping with temperature which is indicative of an anharmonic potential surface. The analysis of AIMD trajectories identifies two major sources of anharmonicity: the orientational unlocking of the [CH$_{3} $NH$_{3}$]$^+$ ions and large amplitude octahedral tilting that continuously increases with temperature. Our work suggests that the standard phonon picture cannot describe the structural dynamics of tetragonal CH$_{3} $NH$_{3} $PbI$_{3}$., 3 figures

In the last decade, hybrid organic-inorganic halide perovskites have emerged as a new type of semiconductor for photovoltaics and other optoelectronic applications. Unlike standard, tetrahedrally bonded semiconductors (e.g. Si and GaAs), the ionic thermal fluctuations in the halide perovskites (i.e. structural dynamics) are strongly coupled to the electronic dynamics. Therefore, it is crucial to obtain accurate and detailed knowledge about the nature of atomic motions within the crystal. This has proved to be challenging due to low thermal stability and the complex, temperature dependent structural phase sequence of the halide perovskites. Here, these challenges are overcome and a detailed analysis of the mode symmetries is provided in the low-temperature orthorhombic phase of methylammonium-lead iodide. Raman measurements using linearly- and circularly- polarized light at 1.16 eV excitation are combined with density functional perturbation theory (DFPT). By performing an iterative analysis of Raman polarization-orientation dependence and DFPT mode analysis, the crystal orientation is determined. Subsequently, accounting for birefringence effects detected using circularly polarized light excitation, the symmetries of all the observed Raman-active modes at 10 K are assigned.

We report a strongly temperature dependent luminescence Stokes shift in the electronic spectra of both hybrid and inorganic lead-bromide perovskite single crystals. This behavior stands in stark contrast to that exhibited by more conventional crystalline semiconductors. We correlate the electronic spectra with the anti-Stokes and Stokes Raman vibrational spectra. Dielectric solvation theories, originally developed for excited molecules dissolved in polar liquids, reproduce our experimental observations. Our approach, which invokes a classical Debye-like relaxation process, captures the dielectric response originating from an anharmonic LO phonon at about 20 meV (160 cm-1) in the lead-bromide framework. We reconcile the liquid-like picture with more standard solid-state theories of the Stokes shift in crystalline semiconductors.

Organic-inorganic coupling in the hybrid lead-halide perovskite is a central issue in rationalizing the outstanding photovoltaic performance of these emerging materials. Here we compare and contrast the evolution of structure and dynamics of the hybrid CH3NH3PbBr3 and the inorganic CsPbBr3 lead-halide perovskites with temperature, using Raman spectroscopy and single-crystal X-ray diffraction. Results reveal a stark contrast between their order-disorder transitions, abrupt for the hybrid whereas smooth for the inorganic perovskite. X-ray diffraction observes an intermediate incommensurate phase between the ordered and the disordered phases in CH3NH3PbBr3. Low-frequency Raman scattering captures the appearance of a sharp soft mode in the incommensurate phase, ascribed to the theoretically predicted amplitudon mode. Our work highlights the interaction between the structural dynamics of organic cation CH3NH3+ and the lead-halide framework, and unravels the competition between tendencies of the organic and inorganic moieties to minimize energy in the incommensurate phase of the hybrid perovskite structure.