Bright Excitonic Fine Structure in Metal-Halide Perovskites: From Two-Dimensional to Bulk.

The optical response of two-dimensional (2D) perovskites, often referred to as natural quantum wells, is primarily governed by excitons, whose properties can be readily tuned by adjusting the perovskite layer thickness. We have investigated the exciton fine structure splitting in the archetypal 2D perovskite (PEA)2(MA)n-1PbnI3n+1 with varying numbers of inorganic octahedral layers n = 1, 2, 3, and 4. We demonstrate that the in-plane excitonic states exhibit splitting and orthogonally oriented dipoles for all confinement regimes. The evolution of the exciton states in an external magnetic field provides further insights into the g-factors and diamagnetic coefficients. With increasing n, we observe a gradual evolution of the excitonic parameters characteristic of a 2D to three-dimensional transition. Our results provide valuable information concerning the evolution of the optoelectronic properties of 2D perovskites with the changing confinement strength.

Polaron Vibronic Progression Shapes the Optical Response of 2D Perovskites.

The optical response of 2D layered perovskites is composed of multiple equally-spaced spectral features, often interpreted as phonon replicas, separated by an energy Δ ≃ 12 - 40 meV, depending upon the compound. Here the authors show that the characteristic energy spacing, seen in both absorption and emission, is correlated with a substantial scattering response above ≃ 200 cm-1 (≃ 25 meV) observed in resonant Raman. This peculiar high-frequency signal, which dominates both Stokes and anti-Stokes regions of the scattering spectra, possesses the characteristic spectral fingerprints of polarons. Notably, its spectral position is shifted away from the Rayleigh line, with a tail on the high energy side. The internal structure of the polaron consists of a series of equidistant signals separated by 25-32 cm-1 (3-4 meV), depending upon the compound, forming a polaron vibronic progression. The observed progression is characterized by a large Huang-Rhys factor (S > 6) for all of the 2D layered perovskites investigated here, indicative of a strong charge carrier - lattice coupling. The polaron binding energy spans a range ≃ 20-35 meV, which is corroborated by the temperature-dependent Raman scattering data. The investigation provides a complete understanding of the optical response of 2D layered perovskites via the direct observation of polaron vibronic progression. The understanding of polaronic effects in perovskites is essential, as it directly influences the suitability of these materials for future opto-electronic applications.

Unveiling the double-peak structure of quantum oscillations in the specific heat.

Quantum oscillation phenomenon is an essential tool to understand the electronic structure of quantum matter. Here we report a systematic study of quantum oscillations in the electronic specific heat Cel in natural graphite. We show that the crossing of a single spin Landau level and the Fermi energy give rise to a double-peak structure, in striking contrast to the single peak expected from Lifshitz-Kosevich theory. Intriguingly, the double-peak structure is predicted by the kernel term for Cel/T in the free electron theory. The Cel/T represents a spectroscopic tuning fork of width 4.8kBT which can be tuned at will to resonance. Using a coincidence method, the double-peak structure can be used to accurately determine the Landé g-factors of quantum materials. More generally, the tuning fork can be used to reveal any peak in fermionic density of states tuned by magnetic field, such as Lifshitz transition in heavy-fermion compounds.

Approaching the Intrinsic Properties of Moiré Structures Using Atomic Force Microscopy Ironing.

Stacking monolayers of transition metal dichalcogenides (TMDs) has led to the discovery of a plethora of new exotic phenomena, resulting from moiré pattern formation. Due to the atomic thickness and high surface-to-volume ratio of heterostructures, the interfaces play a crucial role. Fluctuations in the interlayer distance affect interlayer coupling and moiré effects. Therefore, to access the intrinsic properties of the TMD stack, it is essential to obtain a clean and uniform interface between the layers. Here, we show that this is achieved by ironing with the tip of an atomic force microscope. This post-stacking procedure dramatically improves the homogeneity of the interfaces, which is reflected in the optical response of the interlayer exciton. We demonstrate that ironing improves the layer coupling, enhancing moiré effects and reducing disorder. This is crucial for the investigation of TMD heterostructure physics, which currently suffers from low reproducibility.

Thickness-Dependent Dark-Bright Exciton Splitting and Phonon Bottleneck in CsPbBr3-Based Nanoplatelets Revealed via Magneto-Optical Spectroscopy.

The optimized exploitation of perovskite nanocrystals and nanoplatelets as highly efficient light sources requires a detailed understanding of the energy spacing within the exciton manifold. Dark exciton states are particularly relevant because they represent a channel that reduces radiative efficiency. Here, we apply large in-plane magnetic fields to brighten optically inactive states of CsPbBr3-based nanoplatelets for the first time. This approach allows us to access the dark states and directly determine the dark-bright splitting, which reaches 22 meV for the thinnest nanoplatelets. The splitting is significantly less for thicker nanoplatelets due to reduced exciton confinement. Additionally, the form of the magneto-PL spectrum suggests that dark and bright state populations are nonthermalized, which is indicative of a phonon bottleneck in the exciton relaxation process.

Quantification of Exciton Fine Structure Splitting in a Two-Dimensional Perovskite Compound.

Applications of two-dimensional (2D) perovskites have significantly outpaced the understanding of many fundamental aspects of their photophysics. The optical response of 2D lead halide perovskites is dominated by strongly bound excitonic states. However, a comprehensive experimental verification of the exciton fine structure splitting and associated transition symmetries remains elusive. Here we employ low temperature magneto-optical spectroscopy to reveal the exciton fine structure of (PEA)2PbI4 (here PEA is phenylethylammonium) single crystals. We observe two orthogonally polarized bright in-plane free exciton (FX) states, both accompanied by a manifold of phonon-dressed states that preserve the polarization of the corresponding FX state. Introducing a magnetic field perpendicular to the 2D plane, we resolve the lowest energy dark exciton state, which although theoretically predicted, has systematically escaped experimental observation (in Faraday configuration) until now. These results corroborate standard multiband, effective-mass theories for the exciton fine structure in 2D perovskites and provide valuable quantification of the fine structure splitting in (PEA)2PbI4.

Brightening of dark excitons in 2D perovskites.

Optically inactive dark exciton states play an important role in light emission processes in semiconductors because they provide an efficient nonradiative recombination channel. Understanding the exciton fine structure in materials with potential applications in light-emitting devices is therefore critical. Here, we investigate the exciton fine structure in the family of two-dimensional (2D) perovskites (PEA)2SnI4, (PEA)2PbI4, and (PEA)2PbBr4. In-plane magnetic field mixes the bright and dark exciton states, brightening the otherwise optically inactive dark exciton. The bright-dark splitting increases with increasing exciton binding energy. Hot photoluminescence is observed, indicative of a non-Boltzmann distribution of the bright-dark exciton populations. We attribute this to the phonon bottleneck, which results from the weak exciton­acoustic phonon coupling in soft 2D perovskites. Hot photoluminescence is responsible for the strong emission observed in these materials, despite the substantial bright-dark exciton splitting.

Nonradiative Energy Transfer and Selective Charge Transfer in a WS2/(PEA)2PbI4 Heterostructure.

van der Waals heterostructures are currently the focus of intense investigation; this is essentially due to the unprecedented flexibility offered by the total relaxation of lattice matching requirements and their new and exotic properties compared to the individual layers. Here, we investigate the hybrid transition-metal dichalcogenide/2D perovskite heterostructure WS2/(PEA)2PbI4 (where PEA stands for phenylethylammonium). We present the first density functional theory (DFT) calculations of a heterostructure ensemble, which reveal a novel band alignment, where direct electron transfer is blocked by the organic spacer of the 2D perovskite. In contrast, the valence band forms a cascade from WS2 through the PEA to the PbI4 layer allowing hole transfer. These predictions are supported by optical spectroscopy studies, which provide compelling evidence for both charge transfer and nonradiative transfer of the excitation (energy transfer) between the layers. Our results show that TMD/2D perovskite (where TMD stands for transition-metal dichalcogenides) heterostructures provide a flexible and convenient way to engineer the band alignment.

Tuning the Excitonic Properties of the 2D (PEA)2(MA)n-1PbnI3n+1 Perovskite Family via Quantum Confinement.

In atomically thin two-dimensional (2D) crystals, the excitonic properties and band structure scale strongly with the thickness, providing a new playground for the investigation of exciton physics in the ultimate confinement regime. Here, we demonstrate the evolution of the fundamental excitonic properties, such as reduced mass, wave function extension, and exciton binding energy, in the 2D perovskite (PEA)2(MA)n-1PbnI3n+1, for n = 1, 2, 3. These parameters are experimentally determined using optical spectroscopy in a high magnetic field up to 65 T. The observation of the interband Landau level transitions provides direct access to the reduced effective mass µ and band gap Eg. We show that µ increases with the number of inorganic sheets n, reaching the value of three-dimensional (3D) MAPbI3 already for n = 3. Our experimental observations contradict the general expectation that quantum confinement leads to an enhanced carrier mass, showing another aspect of the unprecedented flexibility in the design of the electronic properties of 2D perovskites.

Excitation efficiency determines the upconversion luminescence intensity of ß-NaYF4:Er3+,Yb3+ nanoparticles in magnetic fields up to 70 T.

Lanthanide-doped nanoparticles enable conversion of near-infrared photons to visible ones. This property is envisioned as a basis of a broad range of applications: from optoelectronics, via energy conversion, to bio-sensing and phototherapy. The spectrum of applications can be extended if magnetooptical properties of lanthanide dopants are well understood. However, at present, there are many conflicting reports on the influence of the magnetic field on the upconverted luminescence. In this work, we resolve this discrepancy by performing a comprehensive study of ß-NaYF4:Er3+,Yb3+ nanoparticles. Crucially, we show that the magnetic field impacts the luminescence only via a Zeeman-driven detuning between the excitation laser and the absorption transition. On the other hand, the energy transfer and multiphonon relaxation rates are unaffected. We propose a phenomenological model, which qualitatively reproduces the experimental results. The presented results are expected to lead to design of novel, dual-mode opto-magnetic upconverting nanomaterials.

Revealing Excitonic Phonon Coupling in (PEA)2(MA)n-1PbnI3n+1 2D Layered Perovskites.

The family of 2D Ruddlesden-Popper perovskites is currently attracting great interest of the scientific community as highly promising materials for energy harvesting and light emission applications. Despite the fact that these materials are known for decades, only recently has it become apparent that their optical properties are driven by the exciton-phonon coupling, which is controlled by the organic spacers. However, the detailed mechanism of this coupling, which gives rise to complex absorption and emission spectra, is the subject of ongoing controversy. In this work we show that the particularly rich, absorption spectra of (PEA)2(CH3NH3)n-1PbnI3n+1 (where PEA stands for phenylethylammonium and n = 1, 2, 3), are related to a vibronic progression of excitonic transition. In contrast to other two-dimensional perovskites, we observe a coupling to a high-energy (40 meV) phonon mode probably related to the torsional motion of the NH3+ head of the organic spacer.

Symmetry Breakdown in Franckeite: Spontaneous Strain, Rippling, and Interlayer Moiré.

Franckeite is a naturally occurring layered mineral with a structure composed of alternating stacks of SnS2-like and PbS-like layers. Although this superlattice is composed of a sequence of isotropic two-dimensional layers, it exhibits a spontaneous rippling that makes the material structurally anisotropic. We demonstrate that this rippling comes hand in hand with an inhomogeneous in-plane strain profile and anisotropic electrical, vibrational, and optical properties. We argue that this symmetry breakdown results from a spatial modulation of the van der Waals interaction between layers due to the SnS2-like and PbS-like lattices incommensurability.

Determining Interaction Enhanced Valley Susceptibility in Spin-Valley-Locked MoS2.

Two-dimensional transition metal dichalcogenides (TMDCs) are recently emerged electronic systems with various novel properties, such as spin-valley locking, circular dichroism, valley Hall effect, and superconductivity. The reduced dimensionality and large effective masses further produce unconventional many-body interaction effects. Here we reveal strong interaction effects in the conduction band of MoS2 by transport experiment. We study the massive Dirac electron Landau levels (LL) in high-quality MoS2 samples with field-effect mobilities of 24 000 cm2/(V·s) at 1.2 K. We identify the valley-resolved LLs and low-lying polarized LLs using the Lifshitz-Kosevitch formula. By further tracing the LL crossings in the Landau fan diagram, we unambiguously determine the density-dependent valley susceptibility and the interaction enhanced g-factor from 12.7 to 23.6. Near integer ratios of Zeeman-to-cyclotron energies, we discover LL anticrossings due to the formation of quantum Hall Ising ferromagnets, the valley polarizations of which appear to be reversible by tuning the density or an in-plane magnetic field. Our results provide evidence for many-body interaction effects in the conduction band of MoS2 and establish a fertile ground for exploring strongly correlated phenomena of massive Dirac electrons.

The impact of hexagonal boron nitride encapsulation on the structural and vibrational properties of few layer black phosphorus.

The encapsulation of two-dimensional layered materials such as black phosphorus is of paramount importance for their stability in air. However, the encapsulation poses several questions, namely, how it affects, via the weak van der Waals forces, the properties of the black phosphorus and whether these properties can be tuned on demand. Prompted by these questions, we have investigated the impact of hexagonal boron nitride encapsulation on the structural and vibrational properties of few layer black phosphorus, using a first-principles method in the framework of density functional theory. We demonstrate that the encapsulation with hexagonal boron nitride imposes biaxial strain on the black phosphorus material, flattening its puckered structure, by decreasing the thickness of the layers via the increase of the puckered angle and the intra-layer P-P bonds. This work exemplifies the evolution of structural parameters in layered materials after the encapsulation process. We find that after encapsulation, phosphorene (single layer black phosphorous) contracts by 1.1% in the armchair direction and stretches by 1.3% in the zigzag direction, whereas few layer black phosphorus mainly expands by up to 3% in the armchair direction. However, these relatively small strains induced by the hexagonal BN, lead to significant changes in the vibrational properties of black phosphorus, with the redshifts of up to 10 cm-1 of the high frequency optical mode A g 1. In general, structural changes induced by the encapsulation process open the door to substrate controlled strain engineering in two-dimensional crystals.

Moiré Intralayer Excitons in a MoSe2/MoS2 Heterostructure.

Spatially periodic structures with a long-range period, referred to as a moiré pattern, can be obtained in van der Waals bilayers in the presence of a small stacking angle or of lattice mismatch between the monolayers. Theoretical predictions suggest that the resulting spatially periodic variation of the band structure modifies the optical properties of both intra- and interlayer excitons of transition metal dichalcogenide heterostructures. Here, we report on the impact of the moiré pattern formed in a MoSe2/MoS2 heterobilayer encapsulated in hexagonal boron nitride. The periodic in-plane potential results in a splitting of the MoSe2 exciton and trion in emission and (for the exciton) absorption spectra. The observed energy difference between the split peaks is fully consistent with theoretical predictions.

Intervalley Scattering of Interlayer Excitons in a MoS2/MoSe2/MoS2 Heterostructure in High Magnetic Field.

Degenerate extrema in the energy dispersion of charge carriers in solids, also referred to as valleys, can be regarded as a binary quantum degree of freedom, which can potentially be used to implement valleytronic concepts in van der Waals heterostructures based on transition metal dichalcogenides. Using magneto-photoluminescence spectroscopy, we achieve a deeper insight into the valley polarization and depolarization mechanisms of interlayer excitons formed across a MoS2/MoSe2/MoS2 heterostructure. We account for the nontrivial behavior of the valley polarization as a function of the magnetic field by considering the interplay between exchange interaction and phonon-mediated intervalley scattering in a system consisting of Zeeman-split energy levels. Our results represent a crucial step toward the understanding of the properties of interlayer excitons with strong implications for the implementation of atomically thin valleytronic devices.

Defect Healing and Charge Transfer-Mediated Valley Polarization in MoS2/MoSe2/MoS2 Trilayer van der Waals Heterostructures.

Monolayer transition metal dichalcogenides (TMDCs) grown by chemical vapor deposition (CVD) are plagued by a significantly lower optical quality compared to exfoliated TMDCs. In this work, we show that the optical quality of CVD-grown MoSe2 is completely recovered if the material is sandwiched in MoS2/MoSe2/MoS2 trilayer van der Waals heterostructures. We show by means of density functional theory that this remarkable and unexpected result is due to defect healing: S atoms of the more reactive MoS2 layers are donated to heal Se vacancy defects in the middle MoSe2 layer. In addition, the trilayer structure exhibits a considerable charge-transfer mediated valley polarization of MoSe2 without the need for resonant excitation. Our fabrication approach, relying solely on simple flake transfer technique, paves the way for the scalable production of large-area TMDC materials with excellent optical quality.

Unraveling the Exciton Binding Energy and the Dielectric Constant in Single-Crystal Methylammonium Lead Triiodide Perovskite.

We have accurately determined the exciton binding energy and reduced mass of single crystals of methylammonium lead triiodide using magneto-reflectivity at very high magnetic fields. The single crystal has excellent optical properties with a narrow line width of ∼3 meV for the excitonic transitions and a 2s transition that is clearly visible even at zero magnetic field. The exciton binding energy of 16 ± 2 meV in the low-temperature orthorhombic phase is almost identical to the value found in polycrystalline samples, crucially ruling out any possibility that the exciton binding energy depends on the grain size. In the room-temperature tetragonal phase, an upper limit for the exciton binding energy of 12 ± 4 meV is estimated from the evolution of 1s-2s splitting at high magnetic field.

The Impact of Phase Retention on the Structural and Optoelectronic Properties of Metal Halide Perovskites.

The extent to which the soft structural properties of metal halide perovskites affect their optoelectronic properties is unclear. X-ray diffraction and micro-photoluminescence measurements are used to show that there is a coexistence of both tetragonal and orthorhombic phases through the low-temperature phase transition, and that cycling through this transition can lead to structural changes and enhanced optoelectronic properties.

Magnetotransport in two-dimensional electron gas in helical nanomembranes.

Heterostructures containing high-mobility two-dimensional electron gas were rolled into freestanding helically shaped contacted Hall bars. Magnetotransport measurements in these structures at high magnetic fields revealed minima in the longitudinal magnetoresistance corresponding to integer and fractional filling factors. A strong asymmetry of the longitudinal magnetoresistance with respect to the external magnetic field direction was observed. For this new type of structures, an edge state picture was considered, and calculations based on the Landauer-Büttiker formalism are performed.