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Many-body localization (MBL) has attracted significant attention because of its immunity to thermalization, role in logarithmic entanglement entropy growth, and opportunities to reach exotic quantum orders. However, experimental realization of MBL in solid-state systems has remained challenging. Here, we report evidence of a possible phonon MBL phase in disordered GaAs/AlAs superlattices. Through grazing-incidence inelastic X-ray scattering, we observe a strong deviation of the phonon population from equilibrium in samples doped with ErAs nanodots at low temperature, signaling a departure from thermalization. This behavior occurs within finite phonon energy and wavevector windows, suggesting a localization-thermalization crossover. We support our observation by proposing a theoretical model for the effective phonon Hamiltonian in disordered superlattices, and showing that it can be mapped exactly to a disordered 1D Bose-Hubbard model with a known MBL phase. Our work provides momentum-resolved experimental evidence of phonon localization, extending the scope of MBL to disordered solid-state systems.

The control of phonon propagation in nanoparticle arrays is one of the frontiers of nanotechnology, potentially enabling the discovery of materials with unknown functionalities for potential innovative applications. The exploration of the terahertz window appears quite promising as phonons in this range are the leading carriers of heat transport in insulators and their control is the key to implement devices for heat flow management. Unfortunately, this scientific field is still in its infancy, and even a basic topic such as the influence of floating nanoparticles on the terahertz phonon propagation of a colloidal suspension still eludes a firm answer. Shedding some light on this topic is the main motivation of the present work, which focuses an inelastic X-ray scattering (IXS) measurements on a dilute suspension of Au nanospheres in water. Measured spectra showed a nontrivial shape displaying multiple inelastic features that, based on a Bayesian inference analysis, we assign to phonon modes propagating throughout the nanoparticle interior. Surprisingly, the spectra bear no evidence of propagating modes, which are known to dominate the spectrum of pure water, owing to the scattering that these modes suffer from the sparse nanoparticles in suspension. In perspective, this finding may inspire simple routes to manipulate high-frequency acoustic propagation in hybrid-liquid and solid-materials.

We used a newer, synchrotron-based, spectroscopic technique (nuclear resonance vibrational spectroscopy, NRVS) in combination with a more traditional one (infrared absorption, IR) to obtain a complete, quantitative picture of the metal center vibrational dynamics in a six-coordinated tin porphyrin. From the NRVS (119)Sn site-selectivity and the sensitivity of the IR signal to (112)Sn/(119)Sn isotope substitution, we identified the frequency of the antisymmetric stretching of the axial bonds (290 cm(-1)) and all the other vibrations involving Sn. Experimentally authenticated density functional theory (DFT) calculations aid the data interpretation by providing detailed normal mode descriptions for each observed vibration. These results may represent a starting point toward the characterization of the local vibrational dynamics of the metallic site in tin porphyrins and compounds with related structures. The quantitative complementariness between IR, NRVS, and DFT is emphasized.

Flexibility is an important property of porphyrins, both natural and synthetic. We applied two synchrotron-based techniques, nuclear resonance vibrational spectroscopy and inelastic X-ray scattering, to quantify this property by measuring the bulk modulus of a protein active-site mimic [chloro(octaethylporphyrinato)iron(III)] and the resilience of the iron environment. Their values are 6.95 ± 0.24 GPa and 15.4 ± 0.5 N/m, respectively.

Nuclear resonance vibrational spectroscopy (NRVS) and Raman spectroscopy on (54)Fe- and (57)Fe-enriched cytochrome c (cyt c) identify multiple bands involving vibrations of the heme Fe. Comparison with predictions from Fe isotope shifts reveals that 70% of the NRVS signal in the 300-450 cm(-1) frequency range corresponds to vibrations resolved in Soret-enhanced Raman spectra. This frequency range dominates the "stiffness", an effective force constant determined by the Fe vibrational density of states (VDOS), which measures the strength of nearest-neighbor interactions with Fe. The stiffness of the low-spin Fe environment in both oxidation states of cyt c significantly exceeds that for the high-spin Fe in deoxymyoglobin, where the 200-300 cm(-1) frequency range dominates the VDOS. This situation is reflected in the shorter Fe-ligand bond lengths in the former with respect to the latter. The longer Fe-S(Met80) in oxidized cyt c with respect to reduced cyt c leads to a decrease in the stiffness of the iron environment upon oxidation. Comparison with NRVS measurements allows us to assess assignments for vibrational modes resolved in this region of the heme Raman spectrum. We consider the possibility that the 372 cm(-1) band in reduced cyt c involves the Fe-S(Met80) bond.

We use nuclear resonance vibrational spectroscopy (NRVS) to identify the Fe-NO stretching frequency in the NO adduct of myoglobin (MbNO) and in the related six-coordinate porphyrin Fe(TPP)(1-MeIm)(NO). Frequency shifts observed in MbNO Raman spectra upon isotopic substitution of Fe or the nitrosyl nitrogen confirm and extend the NRVS results. In contrast with previous assignments, the Fe-NO frequency of these six-coordinate complexes lies 70-100 cm-1 lower than in the analogous five-coordinate nitrosyl complexes, indicating a significant weakening of the Fe-NO bond in the presence of a trans imidazole ligand. This result supports proposed mechanisms for NO activation of heme proteins and underscores the value of NRVS as a direct probe of metal reactivity in complex biomolecules.

We use quantitative experimental and theoretical approaches to characterize the vibrational dynamics of the Fe atom in porphyrins designed to model heme protein active sites. Nuclear resonance vibrational spectroscopy (NRVS) yields frequencies, amplitudes, and directions for 57Fe vibrations in a series of ferrous nitrosyl porphyrins, which provide a benchmark for evaluation of quantum chemical vibrational calculations. Detailed normal mode predictions result from DFT calculations on ferrous nitrosyl tetraphenylporphyrin Fe(TPP)(NO), its cation [Fe(TPP)(NO)]+, and ferrous nitrosyl porphine Fe(P)(NO). Differing functionals lead to significant variability in the predicted Fe-NO bond length and frequency for Fe(TPP)(NO). Otherwise, quantitative comparison of calculated and measured Fe dynamics on an absolute scale reveals good overall agreement, suggesting that DFT calculations provide a reliable guide to the character of observed Fe vibrational modes. These include a series of modes involving Fe motion in the plane of the porphyrin, which are rarely identified using infrared and Raman spectroscopies. The NO binding geometry breaks the four-fold symmetry of the Fe environment, and the resulting frequency splittings of the in-plane modes predicted for Fe(TPP)(NO) agree with observations. In contrast to expectations of a simple three-body model, mode energy remains localized on the FeNO fragment for only two modes, an N-O stretch and a mode with mixed Fe-NO stretch and FeNO bend character. Bending of the FeNO unit also contributes to several of the in-plane modes, but no primary FeNO bending mode is identified for Fe(TPP)(NO). Vibrations associated with hindered rotation of the NO and heme doming are predicted at low frequencies, where Fe motion perpendicular to the heme is identified experimentally at 73 and 128 cm-1. Identification of the latter two modes is a crucial first step toward quantifying the reactive energetics of Fe porphyrins and heme proteins.