Atomistic Analysis of Room Temperature Quantum Coherence in Two-Dimensional CdSe Nanostructures

Quantum Dynamics of Charge Carriers in Fullerenes Encapsulated by Covalent Organic Polyhedra: Choice of Fullerene Matters

Charge separation is at the heart of solar energy applications, and efficient materials require fast photoinduced electron transfer (ET) and slow charge recombination (CR). Using time-dependent self-consistent charge density functional tight-binding theory combined with nonadiabatic (NA) molecular dynamics, we report a detailed analysis of ET and CR in hybrids composed of photoactive covalent organic polyhedra (COP) and encapsulated fullerenes. The ET occurs on a subpicosecond time scale and accelerates with increasing fullerene diameter, C60 to C70 to C84. As the fullerene size increases, the π-electron system available for interaction with the COP grows, the fullerene-COP separation decreases, and the number of fullerene states available to accept the photoexcited electron increases, accelerating the ET. In comparison, the CR occurs on a nanosecond time scale and correlates with the length of the fullerene shortest axis because the relevant fullerene state is polarized in that direction. The largest and least symmetrical C84 exhibits the fastest ET and the slowest CR, making COP@C84 the most promising hybrid. Both high-frequency bond stretching and bending vibrations and low-frequency breathing modes are involved in the ET and CR processes, with more modes present in the C84 system due its lower symmetry. The 10-20 fs vibrationally induced coherence loss in the electronic subsystem contributes to long lifetimes of the charge-separated states. The comprehensive investigation of the structure-property relationship of the charge carrier dynamics in the COP@fullerene hybrids provides a detailed atomistic understanding of interfacial ET processes and generates guidelines for rational design of high-performance materials for solar energy and related applications.

Decoherence ensures convergence of non-adiabatic molecular dynamics with number of states

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems.

Interfacial Charge Transfer in Photoexcited QD-Molecule Composite of Tetrahedral CdSe Quantum Dot Coupled with Carbazole

Photoexcited charge transfer dynamics in CdSe quantum dots (QDs) coupled with carbazole were explored to model QD-molecule systems for light-harvesting applications. The absorption spectra of QDs with different sizes, i.e., Cd35Se20X30L30 (T1), Cd56Se35X42L42 (T2), and Cd84Se56X56L56 (T3) were simulated with quantum dynamical methods, which qualitatively match the reported experimental spectra. The carbazole is attached with a 3-amino group at the apex position of T1 (namely T1-3A-Cz), establishing proper electronic communication between T1 and carbazole. The spectra of T1-3A-Cz is 0.22 eV red-shifted compared to T1. A time-dependent perturbation was applied in tune with the lowest energy peak (3.63 eV) of T1-3A-Cz to investigate the charge transfer dynamics, which revealed an ultrafast charge separation within the femtosecond time scale. The electronic structure showed a favorable energy alignment between T1 and carbazole in T1-3A-Cz. The LUMO of carbazole was situated below the conduction band of the QD, while the HOMO of carbazole mixed perfectly with the top of the valence band of the QD, developing the interfacial charge transfer states. These states promoted the photoexcited electron transfer directly from the CdSe core to carbazole. A rapid and enhanced charge separation occurred with the laser field strength increasing from 0.001 to 0.005 V/Å. However, T1 connected to the other positions of carbazole did not show charge separation effectively. The photoinduced charge transfer is negligible in the case of T2-carbazole systems due to poor electronic coupling, and it is not observed in T3-carbazole systems. So, the T1-3A-Cz model acts as a perfect donor-acceptor QD-molecule nanocomposite that can harvest photon energy efficiently. Further enhancement of charge transfer can be achieved by coupling more carbazoles to the T1 QD (e.g., T1-3A-Cz2) due to the extension of hole delocalization between T1 and the carbazoles.

Prolonged Exciton Lifetime Is Achieved in Porphyrin Nanoring by Template Engineering: A Nonadiabatic Tight Binding Approach

Porphyrin nanoring has been attracting immense attention due to its light harvesting capacity and potential applications in optical, catalysis, sensor, and electronic devices. We demonstrate by nonadiabatic quantum dynamics simulations that the photovoltaic efficiency can be enhanced by template engineering. Altering the hexadentate template (T6) with two tridentate templates (2T3) within the porphyrin ring (P6) cavity accelerated the electron transfer twice and suppressed the electron-hole recombination by nearly three times. The atomistic tight-binding simulation rationalized the dynamics by different localizations of charge of the band edge states, changes in nonadiabatic coupling, alteration in quantum coherence, and involvement of diverse electron-phonon vibrational modes. Further 2T3 templates more strongly hold the P6 ring than T6, reducing the structural fluctuation. As a result, the nonadiabatic coupling becomes weaker and suppresses the carrier recombination. Current atomistic simulation presents a template engineering strategy to enhance the exciton lifetime along with ultrafast charge separation, crucial factors for photovoltaic applications.

Controlling Charge Carrier Dynamics in Porphyrin Nanorings by Optically Active Templates

Understanding the dynamics of photogenerated charge carriers is essential for enhancing the performance of solar and optoelectronic devices. Using atomistic quantum dynamics simulations, we demonstrate that a short π-conjugated optically active template can be used to control hot carrier relaxation, charge carrier separation, and carrier recombination in light-harvesting porphyrin nanorings. Relaxation of hot holes is slowed by 60% with an optically active template compared to that with an analogous optically inactive template. Both systems exhibit subpicosecond electron transfer from the photoactive core to the templates. Notably, charge recombination is suppressed 6-fold by the optically active template. The atomistic time-domain simulations rationalize these effects by the extent of electron and hole localization, modification of the density of states, participation of distinct vibrational motions, and changes in quantum coherence. Extension of the hot carrier lifetime and reduction of charge carrier recombination, without hampering charge separation, demonstrate a strategy for enhancing efficiencies of energy materials with optically active templates.

Exploration of the origin of the excellent charge-carrier dynamics in Ruddlesden-Popper oxysulfide perovskite Y2Ti2O5S2

Although the efficient separation of electron-hole (e-h) pairs is one of the most sought-after electronic characteristics of materials, due to thermally induced atomic motion and other factors, they do not remain separated during the carrier transport process, potentially leading to rapid carrier recombination. Here, we utilized real-time time-dependent density functional theory in combination with nonadiabatic molecular dynamics (NAMD) to explore the separated dynamic transport path within Ruddlesden-Popper oxysulfide perovskite Y2Ti2O5S2 caused by the dielectric layer and phonon frequency difference. The underlying origin of the efficient overall water splitting in Y2Ti2O5S2 is systematically explored. We report the existence of the bi-directional e-h separate-path transport, in which, the electrons transport in the Ti2O5 layer and the holes diffuse in the rock-salt layer. This is in contrast to the conventional e-h separated distribution with a crowded transport channel, as observed in SrTiO3 and hybrid perovskites. Such a unique feature finally results in a long carrier lifetime of 321 ns, larger than that in the SrTiO3 perovskite (160 ns) with only one carrier transport channel. This work provides insights into the carrier transport in lead-free perovskites and yields a novel design strategy for next-generation functionalized optoelectronic devices.

The sp3 Defect Decreases Charge Carrier Lifetime in (8,3) Single-Walled Carbon Nanotubes

A recent experimental approach introduces sp3 defects into single-walled carbon nanotubes (SWNTs) through controlled functionalization with guanine, resulting in a decrease in charge carrier lifetime. However, the physical mechanism behind this phenomenon remains unclear. We employ nonadiabatic molecular dynamics to systematically model the nonradiative recombination process of electron-hole pairs in SWNTs with sp3 defects generated by a guanine molecule. We demonstrate that the introduction of sp3 defects creates an overlapping channel between the highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO), significantly enhancing the nonadiabatic (NA) coupling and leading to a 4.7-fold acceleration in charge carrier recombination compared to defect-free SWNTs. The charge carrier recombination slows significantly at a lower temperature (50 K) due to the weakening of the NA coupling. Our results rationalize the accelerated recombination of charge carriers in SWNTs with sp3 defects in experiments and contribute to a deeper understanding of the carrier dynamics in SWNTs.

Measuring the Ultrafast Spectral Diffusion and Vibronic Coupling Dynamics in CdSe Colloidal Quantum Wells using Two-Dimensional Electronic Spectroscopy

We measure the ultrafast spectral diffusion, vibronic dynamics, and energy relaxation of a CdSe colloidal quantum wells (CQWs) system at room temperature using two-dimensional electronic spectroscopy (2DES). The energy relaxation of light-hole (LH) excitons and hot carriers to heavy-hole (HH) excitons is resolved with a time scale of ∼210 fs. We observe the equilibration dynamics between the spectroscopically accessible HH excitonic state and a dark state with a time scale of ∼160 fs. We use the center line slope analysis to quantify the spectral diffusion dynamics in HH excitons, which contains an apparent sub-200 fs decay together with oscillatory features resolved at 4 and 25 meV. These observations can be explained by the coupling to various lattice phonon modes. We further perform quantum calculations that can replicate and explain the observed dynamics. The 4 meV mode is observed to be in the near-critically damped regime and may be mediating the transition between the bright and dark HH excitons. These findings show that 2DES can provide a comprehensive and detailed characterization of the ultrafast spectral properties in CQWs and similar nanomaterials.

Symmetrical Linkage in Porphyrin Nanoring Suppressed the Electron-Hole Recombination Demonstrated by Nonadiabatic Molecular Dynamics

Macromolecular porphyrin nanorings are receiving significant attention because of their excellent optoelectronic properties. However, their efficiencies as potential solar materials are significantly affected by nonradiative charge recombination. To understand the recombination mechanism by alternating structural parameters and using tight-binding nonadiabatic molecular dynamics, we demonstrate that charge recombination depends strongly on the mode of the linker in the porphyrin nanoring. The nanoring having all-butadiyne-linkage (pristine-P8) inhibits carrier relaxation. In contrast, a partially fused nanoring (fused-P8) expedites the rate of quantum transition. An extension of the lifetime by a factor of 4 is due to the larger optical gap in pristine-P8 that reduces the NA coupling by decreasing the overlap between band edge states. Additionally, an intense phonon peak in the low-frequency region and rapid coherence loss within the electronic subsystem favors prolonging the carrier lifetime. This study provides an atomistic realization for the design of macromolecular porphyrin nanorings for the potential use in photovoltaic materials.

Enhanced Exciton Quantum Coherence in Single CsPbBr3 Perovskite Quantum Dots using Femtosecond Two-Photon Near-Field Scanning Optical Microscopy

Cesium-halide perovskite quantum dots (QDs) have gained tremendous interest as quantum emitters in quantum information processing applications due to their optical and photophysical properties. However, engineering excitonic states in quantum dots requires a deep knowledge of the coherent dynamics of their excitons at a single-particle level. Here, we use femtosecond time-resolved two-photon near-field scanning optical microscopy (NSOM) to reveal coherences involving a single cesium lead bromide perovskite QD (CsPbBr₃) at room temperature. We show that, compared to other nonperovskite nanoparticles, the electronic coherence on a single perovskite QD has a relatively long lifetime of ca. 150 fs, whereas CdSe QDs have exciton coherence times shorter than 75 fs at room temperature. One possible explanation for the longer coherence time observed for the CsPbBr₃ perovskite system is related to the exciton fine structure of these perovskite QDs compared to other nanoparticles. These perovskite QDs exhibit interesting optical properties that differ from those of the traditional QDs including bright triplet exciton states. In fact, due to the small amplitude of the energy gap fluctuations of dipole-allowed triplet states in perovskite QDs, the coherent superposition could be preserved for longer times. Furthermore, single-particle excitation approach implemented in this work allows us to remove effects of heterogeneity that are usually present in ensemble averaging experiments at room temperature. The realization of quantum-mechanical phase-coherence of a charge carrier that can operate at room temperature is an issue of great importance for the potential application of coherent electronic phenomena in electronic and optoelectronic devices. These interesting findings provide further evidence of the great potential of these perovskite QDs as candidates for quantum computing and information processing applications.

2D Electronic Spectroscopic Techniques for Quantum Technology Applications

2D electronic spectroscopy (2DES) techniques have gained particular interest given their capability of following ultrafast coherent and noncoherent processes in real-time. Although the fame of 2DES is still majorly linked to the investigation of energy and charge transport in biological light-harvesting complexes, 2DES is now starting to be recognized as a particularly valuable tool for studying transport processes in artificial nanomaterials and nanodevices. Particularly meaningful is the possibility of assessing coherent mechanisms active in the transport of excitation energy in these materials toward possible quantum technology applications. The diverse nature of these new target samples poses significant challenges and calls for a critical rethinking of the technique and its different realizations. With the confluence of promising new applications and rapidly developing technical capabilities, the enormous potential of 2DES techniques to impact the field of nanosystems, quantum technologies, and quantum devices is here delineated.

Stochastically Realized Observables for Excitonic Molecular Aggregates

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

MAI Termination Favors Efficient Hole Extraction and Slow Charge Recombination at the MAPbI3/CuSCN Heterojunction

Photoinduced charge separation is the key step determining the efficiency of photon-to-electron conversion in solar cells, while charge carrier lifetimes govern the overall solar cell performance. Experiments report that copper(I) thiocyanate (CuSCN) is a very promising hole extraction layer for perovskite solar cells. Using nonadiabatic molecular dynamics combined with ab initio time-domain density functional theory, we show that termination of CH₃NH₃PbI₃ (MAPbI₃) at MAPbI₃/CuSCN heterojunctions has a strong influence on both charge separation and recombination. Both processes are favored by MAI termination, compared to PbI₂ termination. Because the MAPbI₃ valence band originates from iodine orbitals while the conduction band arises from Pb orbitals, MAI termination places holes close to CuSCN, favoring extraction, and creates an MAI barrier for recombination of electrons in MAPbI₃ and holes in CuSCN. The opposite is true for PbI₂ termination. The origin of these effects is attributed solely to the properties of the MAPbI₃ surfaces, and therefore, the conclusions should apply to other hole-transporting materials and can be generalized to other perovskites. Importantly, the simulations show that the injected hole remains hot for several hundreds of femtoseconds, allowing it to escape the interfacial region and prevent formation of bound excitons. This study suggests that metal halide perovskites should be treated with an organic precursor, such as MAI, prior to the formation of their interfaces with hole-transporting materials. The reported results advance the fundamental understanding of the highly unusual properties of metal halide perovskites and provide specific guidelines for optimizing the performance of perovskite solar cells and other devices.

Atomic fluctuations in electronic materials revealed by dephasing

The microscopic origin and timescale of the fluctuations of the energies of electronic states has a significant impact on the properties of interest of electronic materials, with implication in fields ranging from photovoltaic devices to quantum information processing. Spectroscopic investigations of coherent dynamics provide a direct measurement of electronic fluctuations. Modern multidimensional spectroscopy techniques allow the mapping of coherent processes along multiple time or frequency axes and thus allow unprecedented discrimination between different sources of electronic dephasing. Exploiting modern abilities in coherence mapping in both amplitude and phase, we unravel dissipative processes of electronic coherences in the model system of CdSe quantum dots (QDs). The method allows the assignment of the nature of the observed coherence as vibrational or electronic. The expected coherence maps are obtained for the coherent longitudinal optical (LO) phonon, which serves as an internal standard and confirms the sensitivity of the technique. Fast dephasing is observed between the first two exciton states, despite their shared electron state and common environment. This result is contrary to predictions of the standard effective mass model for these materials, in which the exciton levels are strongly correlated through a common size dependence. In contrast, the experiment is in agreement with ab initio molecular dynamics of a single QD. Electronic dephasing in these materials is thus dominated by the realistic electronic structure arising from fluctuations at the atomic level rather than static size distribution. The analysis of electronic dephasing thereby uniquely enables the study of electronic fluctuations in complex materials.

Structural rigidity accelerates quantum decoherence and extends carrier lifetime in porphyrin nanoballs: a time domain atomistic simulation

Nonradiative electron-hole (e-h) recombination is the primary source of energy loss in photovoltaic cells and inevitably, it competes with the charge transfer process, leading to poor device performance. Therefore, much attention has to be paid for delaying such processes; increasing the excitonic lifetime may be a solution for this. Using the real-time, density functional tight-binding theory (DFTB) combined with nonadiabatic molecular dynamics (NAMD) simulations, we demonstrate the exciton relaxation phenomena of different metal-centered porphyrin nanoballs, which are supposed to be very important for the light-harvesting process. It has been revealed that the carrier recombination rate gradually decreases with the increase in the molecular stiffness by introducing metal-coordinating templating agents into the nanoball. Our simulation demonstrates that the lower atomic fluctuations lead to poorer electron-phonon nonadiabatic coupling in association with weak phonon modes and these as a whole are responsible for shorter quantum coherence and hence delayed recombination events. Our analysis is in good agreement with the recent experimental observation. By replacing the Zn metal center with a heavier Cd atom, a similar trend is observed; however, the rate slows down abruptly. The present simulation study provides the fundamental mechanism in detail behind the undesired energy loss during exciton recombination and suggests a rational design of impressive nanosystems for future device fabrication.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Evidence of Skewness and Sub-Gaussian Character in Temperature-Dependent Distributions of One Million Electronic Excitation Energies in PbS Quantum Dots

Obtaining statistical distributions by sampling a large number of conformations is vital for an accurate description of temperature-dependent properties of chemical systems. However, constructing distributions with 10⁵-10⁶ samples is computationally challenging because of the prohibitively high computational cost of performing first-principles quantum mechanical calculations. In this work, we present a new technique called the effective stochastic potential configuration interaction singles (ESP-CIS) method to obtain excitation energies. The ESP-CIS method uses random matrix theory for the construction of an effective stochastic representation of the Fock operator and combines it with the CIS method. Excited-state energies of PbS quantum dots (0.75-1.75 nm) at temperatures of 10-400 K were calculated using the ESP-CIS method. Results from a total of 27 million excitation energy calculations revealed the distributions to be sub-Gaussian in nature with negative skewness, which progressively became red-shifted with increasing temperature. This study demonstrates the efficacy of the ESP-CIS method as a general-purpose method for efficient excited-state calculations.

Rapid Decoherence Suppresses Charge Recombination in Multi-Layer 2D Halide Perovskites: Time-Domain Ab Initio Analysis

Two-dimensional (2D) Ruddlesden-Popper halide perovskites are appealing candidates for optoelectronics and photovoltaics. Nonradiative electron-hole recombination constitutes a major pathway for charge and energy losses in these materials. Surprisingly, experimental recombination is slower in multilayers than a monolayer, even though multilayer systems have smaller energy gaps and higher frequency phonons that should accelerate the recombination. Focusing on (BA)₂(MA) _n-1Pb _nI_{3 n+1} with n = 1 and 3, BA = CH₃(CH₂)₃NH₃, and MA = CH₃NH₃, we show that it is the enhancement of elastic electron-phonon scattering that suppresses charge recombination for n = 3, by causing rapid loss of electronic coherence. The scattering is enhanced in the multilayer 2D perovskites because, in contrast to the monolayer, they contain MA cations embedded into the inorganic Pb-I lattice. Although MAs do not contribute directly to electron and hole wave functions, they perturb the Pb-I lattice and create strong electric fields that interact with the charges. The rapid loss of coherence explains long excited state lifetimes that extend into nanoseconds. Both electron-hole recombination and coherence times show excellent agreement with the corresponding lifetime and line width measurements. The simulations rationalize the observed dependence of excited state lifetime in 2D layered halide perovskites on layer thickness and advance our understanding of the atomistic mechanisms underlying charge-phonon dynamics in nanoscale materials.

Criticality of Symmetry in Rational Design of Chalcogenide Perovskites

Chalcogenide perovskites constitute an emerging class of promising photovoltaic materials that are stable and less toxic than popular lead-halide perovskites. Transition-metal and chalcogenide doping are the possible strategies for improving the photovoltaic properties of these materials via the band gap engineering. At the same time, doping can facilitate nonradiative charge-carrier recombination in these materials, adversely affecting their photovoltaic properties. We report a systematic study of electronic structure and nonadiabatic dynamics in transition-metal- and chalcogenide-doped barium-zirconium-sulfide-based perovskites. The potential of these doping strategies to modulate the performance of photovoltaic materials is explored. Through the detailed analysis of the factors affecting the dynamics, we illustrate how symmetry (both structural and orbital) and decoherence can be critical to furnishing the most favorable properties. The noted factors of symmetry and decoherence may provide new rational design principles for efficient photovoltaics.

Addressing the exciton fine structure in colloidal nanocrystals: the case of CdSe nanoplatelets

We study the band-edge exciton fine structure and in particular its bright-dark splitting in colloidal semiconductor nanocrystals by four different optical methods based on fluorescence line narrowing and time-resolved measurements at various temperatures down to 2 K. We demonstrate that all these methods provide consistent splitting values and discuss their advances and limitations. Colloidal CdSe nanoplatelets with thicknesses of 3, 4 and 5 monolayers are chosen for experimental demonstrations. The bright-dark splitting of excitons varies from 3.2 to 6.0 meV and is inversely proportional to the nanoplatelet thickness. Good agreement between experimental and theoretically calculated size dependence of the bright-dark exciton splitting is achieved. The recombination rates of the bright and dark excitons and the bright to dark relaxation rate are measured by time-resolved techniques.