Energy Funneling in a Noninteger Two-Dimensional Perovskite

Energy funneling is a phenomenon that has been exploited in optoelectronic devices based on low-dimensional materials to improve their performance. Here, we introduce a new class of two-dimensional semiconductor, characterized by multiple regions of varying thickness in a single confined nanostructure with homogeneous composition. This "noninteger 2D semiconductor" was prepared via the structural transformation of two-octahedron-layer-thick (n = 2) 2D cesium lead bromide perovskite nanosheets; it consisted of a central n = 2 region surrounded by edge-lying n = 3 regions, as imaged by electron microscopy. Thicker noninteger 2D CsPbBr3 nanostructures were obtained as well. These noninteger 2D perovskites formed a laterally coupled quantum well band alignment with virtually no strain at the interface and no dielectric barrier, across which unprecedented intramaterial funneling of the photoexcitation energy was observed from the thin to the thick regions using time-resolved absorption and photoluminescence spectroscopy.

The Effect of Monomer Size on Fusion and Coupling in Colloidal Quantum Dot Molecules

The fusion step in the formation of colloidal quantum dot molecules, constructed from two core/shell quantum dots, dictates the coupling strength and hence their properties and enriched functionalities compared to monomers. Herein, studying the monomer size effect on fusion and coupling, we observe a linear relation of the fusion temperature with the inverse nanocrystal radius. This trend, similar to that in nanocrystal melting, emphasizes the role of the surface energy. The suggested fusion mechanism involves intraparticle ripening where atoms diffuse to the reactive connecting neck region. Moreover, the effect of monomer size and neck filling on the degree of electronic coupling is studied by combined atomistic-pseudopotential calculations and optical measurements, uncovering strong coupling effects in small QD dimers, leading to significant optical changes. Understanding and controlling the fusion and hence coupling effect allows tailoring the optical properties of these nanoscale structures, with potential applications in photonic and quantum technologies.

Polaritonic Bottleneck in Colloidal Quantum Dots

Controlling the relaxation dynamics of excitons is key to improving the efficiencies of semiconductor-based applications. Confined semiconductor nanocrystals (NCs) offer additional handles to control the properties of excitons, for example, by changing their size or shape, resulting in a mismatch between excitonic gaps and phonon frequencies. This has led to the hypothesis of a significant slowing-down of exciton relaxation in strongly confined NCs, but in practice due to increasing exciton-phonon coupling and rapid multiphonon relaxation channels, the exciton relaxation depends only weakly on the size or shape. Here, we focus on elucidating the nonradiative relaxation of excitons in NCs placed in an optical cavity. We find that multiphonon emission of carrier governs the decay, resulting in a polariton-induced phonon bottleneck with relaxation time scales that are slower by orders of magnitude compared to the cavity-free case, while the photon fraction plays a secondary role.

Detecting, Distinguishing, and Spatiotemporally Tracking Photogenerated Charge and Heat at the Nanoscale

Since dissipative processes are ubiquitous in semiconductors, characterizing how electronic and thermal energy transduce and transport at the nanoscale is vital for understanding and leveraging their fundamental properties. For example, in low-dimensional transition metal dichalcogenides (TMDCs), excess heat generation upon photoexcitation is difficult to avoid since even with modest injected exciton densities exciton-exciton annihilation still occurs. Both heat and photoexcited electronic species imprint transient changes in the optical response of a semiconductor, yet the distinct signatures of each are difficult to disentangle in typical spectra due to overlapping resonances. In response, we employ stroboscopic optical scattering microscopy (stroboSCAT) to simultaneously map both heat and exciton populations in few-layer MoS2 on relevant nanometer and picosecond length- and time scales and with 100-mK temperature sensitivity. We discern excitonic contributions to the signal from heat by combining observations close to and far from exciton resonances, characterizing the photoinduced dynamics for each. Our approach is general and can be applied to any electronic material, including thermoelectrics, where heat and electronic observables spatially interplay, and it will enable direct and quantitative discernment of different types of coexisting energy without recourse to complex models or underlying assumptions.

Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

Theory of Photoluminescence Spectral Line Shapes of Semiconductor Nanocrystals

Single-molecule photoluminescence (PL) spectroscopy of semiconductor nanocrystals (NCs) reveals the nature of exciton-phonon interactions in NCs. Understanding the homogeneous spectral line shapes and their temperature dependence remains an open problem. Here, we develop an atomistic model to describe the PL spectrum of NCs, accounting for excitonic effects, phonon dispersion relations, and exciton-phonon couplings. We validate our model using single-NC measurements on CdSe/CdS NCs from T = 4 to 290 K, and we find that the slightly asymmetric main peak at low temperatures is comprised of a narrow zero-phonon line (ZPL) and acoustic phonon sidebands. Furthermore, we identify the specific phonon modes that give rise to the optical phonon sidebands. At temperatures above 200 K, the spectral line width shows a stronger dependence upon the temperature, which we demonstrate to be correlated with higher order exciton-phonon couplings. We also identify the line width dependence upon reorganization energy, NC core sizes, and shell thicknesses.

Composition-Defined Optical Properties and the Direct-to-Indirect Transition in Core-Shell In1-xGaxP/ZnS Colloidal Quantum Dots

Semiconductors are commonly divided into materials with direct or indirect band gaps based on the relative positions of the top of the valence band and the bottom of the conduction band in crystal momentum (k) space. It has, however, been debated if k is a useful quantum number to describe the band structure in quantum-confined nanocrystalline systems, which blur the distinction between direct and indirect gap semiconductors. In bulk III-V semiconductor alloys like In_1-xGa_xP, the band structure can be tuned continuously from the direct- to indirect-gap by changing the value of x. The effect of strong quantum confinement on the direct-to-indirect transition in this system has yet to be established because high-quality colloidal nanocrystal samples have remained inaccessible. Herein, we report one of the first systematic studies of ternary III-V nanocrystals by utilizing an optimized molten-salt In-to-Ga cation exchange protocol to yield bright In_1-xGa_xP/ZnS core-shell particles with photoluminescence quantum yields exceeding 80%. We performed two-dimensional solid-state NMR studies to assess the alloy homogeneity and the extent of surface oxidation in In_1-xGa_xP cores. The radiative decay lifetime for In_1-xGa_xP/ZnS monotonically increases with higher gallium content. Transient absorption studies on In_1-xGa_xP/ZnS nanocrystals demonstrate signatures of direct- and indirect-like behavior based on the presence or absence, respectively, of excitonic bleach features. Atomistic electronic structure calculations based on the semi-empirical pseudopotential model are used to calculate absorption spectra and radiative lifetimes and evaluate band-edge degeneracy; the resulting calculated electronic properties are consistent with experimental observations. By studying photoluminescence characteristics at elevated temperatures, we demonstrate that a reduced lattice mismatch at the III-V/II-VI core-shell interface can enhance the thermal stability of emission. These insights establish cation exchange in molten inorganic salts as a viable synthetic route to nontoxic, high-quality In_1-xGa_xP/ZnS QD emitters with desirable optoelectronic properties.

Incoherent nonadiabatic to coherent adiabatic transition of electron transfer in colloidal quantum dot molecules

Electron transfer is a fundamental process in chemistry, biology, and physics. One of the most intriguing questions concerns the realization of the transitions between nonadiabatic and adiabatic regimes of electron transfer. Using colloidal quantum dot molecules, we computationally demonstrate how the hybridization energy (electronic coupling) can be tuned by changing the neck dimensions and/or the quantum dot sizes. This provides a handle to tune the electron transfer from the incoherent nonadiabatic regime to the coherent adiabatic regime in a single system. We develop an atomistic model to account for several states and couplings to the lattice vibrations and utilize the mean-field mixed quantum-classical method to describe the charge transfer dynamics. Here, we show that charge transfer rates increase by several orders of magnitude as the system is driven to the coherent, adiabatic limit, even at elevated temperatures, and delineate the inter-dot and torsional acoustic modes that couple most strongly to the charge transfer dynamics.

Size-Dependent Lattice Symmetry Breaking Determines the Exciton Fine Structure of Perovskite Nanocrystals

The order of bright and dark excitonic states in lead-halide perovskite nanocrystals is debated. It has been proposed that the Rashba effect, driven by lattice-induced symmetry breaking, causes a bright excitonic ground state. Direct measurements of excitonic spectra, however, show the signatures of a dark ground state, bringing the role of the Rashba effect into question. We use an atomistic theory to model the exciton fine structure of perovskite nanocrystals, accounting for realistic lattice distortions. We calculate optical gaps and excitonic features that compare favorably with experimental works. The exciton fine structure splittings show a nonmonotonic size dependence due to a structural transition between cubic and orthorhombic phases. Additionally, the excitonic ground state is found to be dark with spin triplet character, exhibiting a small Rashba coupling. We additionally explore the effects of nanocrystal shape on the fine structure, clarifying observations on polydisperse nanocrystals.

Anomalous thickness dependence of photoluminescence quantum yield in black phosphorous

Black phosphorus has emerged as a unique optoelectronic material, exhibiting tunable and high device performance from mid-infrared to visible wavelengths. Understanding the photophysics of this system is of interest to further advance device technologies based on it. Here we report the thickness dependence of the photoluminescence quantum yield at room temperature in black phosphorus while measuring the various radiative and non-radiative recombination rates. As the thickness decreases from bulk to ~4 nm, a drop in the photoluminescence quantum yield is initially observed due to enhanced surface carrier recombination, followed by an unexpectedly sharp increase in photoluminescence quantum yield with further thickness scaling, with an average value of ~30% for monolayers. This trend arises from the free-carrier to excitonic transition in black phosphorus thin films, and differs from the behaviour of conventional semiconductors, where photoluminescence quantum yield monotonically deteriorates with decreasing thickness. Furthermore, we find that the surface carrier recombination velocity of black phosphorus is two orders of magnitude lower than the lowest value reported in the literature for any semiconductor with or without passivation; this is due to the presence of self-terminated surface bonds in black phosphorus.

Remembering the Work of Phillip L. Geissler: A Coda to His Scientific Trajectory

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective we celebrate his work at these frontiers. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 74 is April 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Structure optimization with stochastic density functional theory

Linear-scaling techniques for Kohn-Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden-Fletcher-Goldfarb-Shanno algorithm. We further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.

A Pair of 2D Quantum Liquids: Investigating the Phase Behavior of Indirect Excitons

Long-lived indirect excitons (IXs) exhibit a rich phase diagram, including a Bose-Einstein condensate (BEC), a Wigner crystal, and other exotic phases. Recent experiments have hinted at a "classical" liquid of IXs above the BEC transition. To uncover the nature of this phase, we use a broad range of theoretical tools and find no evidence of a driving force toward classical condensation. Instead, we attribute the condensed phase to a quantum electron-hole liquid (EHL), first proposed by Keldysh for direct excitons. Taking into account the association of free carriers into bound excitons, we study the phase equilibrium between a gas of excitons, a gas of free carriers, and an EHL for a wide range of electron-hole separations, temperatures, densities, and mass ratios. Our results agree reasonably well with recent measurements of GaAs/AlGaAs coupled quantum wells.

Hybridization and deconfinement in colloidal quantum dot molecules

The structural, electronic, and optical properties of CdSe/CdS core-shell colloidal quantum dot molecules, a new class of coupled quantum dot dimers, are explored using atomistic approaches. Unlike the case of dimers grown by molecular beam epitaxy, simulated strain profile maps of free-standing colloidal dimers show negligible additional strain resulting from the attachment. The electronic properties of the relaxed dimers are described within a semiempirical pseudopotential model combined with the Bethe-Salpeter equation within the static screening approximation to account for electron-hole correlations. The interplay of strain, hybridization (tunneling splitting), quantum confinement, and electron-hole binding energies on the optical properties is analyzed and discussed. The effects of the dimensions of the neck connecting the two quantum dot building blocks, as well as the shell thickness, are studied.

Time-Dependent Second-Order Green's Function Theory for Neutral Excitations

We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.

Simulations of nonradiative processes in semiconductor nanocrystals

The description of carrier dynamics in spatially confined semiconductor nanocrystals (NCs), which have enhanced electron-hole and exciton-phonon interactions, is a great challenge for modern computational science. These NCs typically contain thousands of atoms and tens of thousands of valence electrons with discrete spectra at low excitation energies, similar to atoms and molecules, that converge to the continuum bulk limit at higher energies. Computational methods developed for molecules are limited to very small nanoclusters, and methods for bulk systems with periodic boundary conditions are not suitable due to the lack of translational symmetry in NCs. This perspective focuses on our recent efforts in developing a unified atomistic model based on the semiempirical pseudopotential approach, which is parameterized by first-principle calculations and validated against experimental measurements, to describe two of the main nonradiative relaxation processes of quantum confined excitons: exciton cooling and Auger recombination. We focus on the description of both electron-hole and exciton-phonon interactions in our approach and discuss the role of size, shape, and interfacing on the electronic properties and dynamics for II-VI and III-V semiconductor NCs.

Tagged particle dynamics in supercooled quantum liquids

We analyze the dynamics of quantum supercooled liquids in terms of tagged particle dynamics. Unlike the classical case, uncertainty in the position of a particle in quantum liquid leads to qualitative changes. We demonstrate these effects in the dynamics of the first two moments of displacements, namely, the mean-squared displacement, 〈Δr^{2}(t)〉, and 〈Δr^{4}(t)〉. Results are presented for a hard-sphere liquid using mode-coupling theory formulation and simulation on a binary Lennard-Jones liquid. As the quantumness (controlled by the de Broglie thermal wavelength) is increased, a nonzero value of the moments at zero time leads to significant deviations from the classical behavior in the initial dynamics. Initial displacement shows ballistic behavior 〈Δr^{2}(t)〉∼t^{2}, but, as a result of large uncertainty in the position, the dynamical effects become weaker with increasing quantumness over this timescale.

Forces from Stochastic Density Functional Theory under Nonorthogonal Atom-Centered Basis Sets

We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis set representation (Fabian et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci.2019, 9, e1412, 10.1002/wcms.1412) and apply it to the Tryptophan Zipper 2 (Trp-zip2) peptide solvated in water. We use an embedded-fragment approach to reduce the statistical errors (fluctuation and systematic bias), where the entire peptide is the main fragment and the remaining 425 water molecules are grouped into small fragments. We analyze the magnitude of the statistical errors in the forces and find that the systematic bias is of the order of 0.065 eV/Å (∼1.2 × 10^–3E_h/a₀) when 120 stochastic orbitals are used, independently of system size. This magnitude of bias is sufficiently small to ensure that the bond lengths estimated by stochastic DFT (within a Langevin molecular dynamics simulation) will deviate by less than 1% from those predicted by a deterministic calculation.

Stochastic Vector Techniques in Ground-State Electronic Structure

We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss highly effective techniques to reduce statistical errors. Finally, we review the use of stochastic vector techniques for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Engineering Exciton Recombination Pathways in Bilayer WSe2 for Bright Luminescence

Exciton-exciton annihilation (EEA) in counterdoped monolayer transition metal dichalcogenides (TMDCs) can be suppressed by favorably changing the band structure with strain. The photoluminescence (PL) quantum yield (QY) monotonically approaches unity with strain at all generation rates. In contrast, here in bilayers (2L) of tungsten diselenide (WSe₂) we observe a nonmonotonic change in EEA rate at high generation rates accompanied by a drastic enhancement in their PL QY at low generation rates. EEA is suppressed at both 0% and 1% strain, but activated at intermediate strains. We explain our observation through the indirect to direct transition in 2L WSe₂ under uniaxial tensile strain. By strain and electrostatic counterdoping, we attain ∼50% PL QY at all generation rates in 2L WSe₂, originally an indirect semiconductor. We demonstrate transient electroluminescence from 2L WSe₂ with ∼1.5% internal quantum efficiency for a broad range of carrier densities by applying strain, which is ∼50 times higher than without strain. The present results elucidate the complete optoelectronic photophysics where indirect and direct excitons are simultaneously present and expedite exciton engineering in a TMDC multilayer beyond indirect-direct bandgap transition.

Tempering stochastic density functional theory

We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the warm component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction in the statistical fluctuations and systematic deviation compared to sDFT for the same computational effort. We demonstrate the method's performance on large hydrogen-passivated silicon nanocrystals, finding a reduction in the systematic deviation in the energy by more than an order of magnitude, while the systematic deviation in the forces is also quenched. Similarly, the statistical fluctuations are reduced by factors of ≈4-5 for the total energy and ≈1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.

Interplay of Surface and Interior Modes in Exciton-Phonon Coupling at the Nanoscale

Exciton-phonon coupling (EXPC) plays a key role in the optoelectronic properties of semiconductor nanocrystals (NCs), but a microscopic picture of EXPC is still lacking, particularly regarding the magnitude and scaling with NC size, the dependence on phonon frequency, and the role of the NC surface. The computational complexity associated with accurately describing excitons and phonons has limited previous theoretical studies of EXPC to small NCs, noninteracting electron-hole models, and/or a small number of phonon modes. Here, we develop an atomistic approach for describing EXPC in NCs of experimentally relevant sizes. We validate our approach by calculating the reorganization energies, a measure of EXPC, for CdSe and CdSe-CdS core-shell NCs, finding good agreement with experimental measurements. We demonstrate that exciton formation distorts the NC lattice primarily along the coordinates of low-frequency acoustic modes. Modes at the NC surface play a significant role in smaller NCs while interior modes dominate for larger systems.

Nonuniqueness of generalized quantum master equations for a single observable

When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. However, obtaining a reduced description does not always need to be achieved through projections-one can also use conservation laws for this purpose. Such an operation should be considered as distinct from any kind of projection; that is, projection onto a single observable yields a different form of master equation compared to that resulting from a projection followed by the application of a constraint. We give a simple example to show this point and give relationships that the different memory kernels must satisfy to yield the same dynamics.

Inhibited nonradiative decay at all exciton densities in monolayer semiconductors

Most optoelectronic devices operate at high photocarrier densities, where all semiconductors suffer from enhanced nonradiative recombination. Nonradiative processes proportionately reduce photoluminescence (PL) quantum yield (QY), a performance metric that directly dictates the maximum device efficiency. Although transition metal dichalcogenide (TMDC) monolayers exhibit near-unity PL QY at low exciton densities, nonradiative exciton-exciton annihilation (EEA) enhanced by van-Hove singularity (VHS) rapidly degrades their PL QY at high exciton densities and limits their utility in practical applications. Here, by applying small mechanical strain (less than 1%), we circumvented VHS resonance and markedly suppressed EEA in monolayer TMDCs, resulting in near-unity PL QY at all exciton densities despite the presence of a high native defect density. Our findings can enable light-emitting devices that retain high efficiency at all brightness levels.

Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction

Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground-state properties of extended materials. The computational complexity of describing the Kohn-Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observables at the account of introducing a statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT. Recently, we have introduced two embedding schemes to mitigate the statistical fluctuations in the electron density and resultant forces on the nuclei. Both techniques were based on fragmenting the system either in real space or slicing the occupied space into energy windows, allowing for a significant reduction in the statistical fluctuations. For chemical accuracy, further reduction of the noise is required, which could be achieved by increasing the number of stochastic orbitals. However, the convergence is relatively slow as the statistical error scales as 1/N_χ according to the central limit theorem, where N_χ is the number of random orbitals. In this paper, we combined the embedding schemes mentioned above and introduced a new approach that builds on overlapped fragments and energy windows. The new approach significantly lowers the noise for ground-state properties, such as the electron density, total energy, and forces on the nuclei, as demonstrated for a G-center in bulk silicon.

Frequency-dependent specific heat in quantum supercooled liquids: A mode-coupling study

Frequency-dependence of specific heat in supercooled hard sphere liquid is computed using quantum mode-coupling theory (QMCT). Mode-coupling equations are solved using a recently proposed perturbative method that allows us to study relaxation in the moderate quantum regime where quantum effects assist liquid to glass transition. Zwanzig's formulation is used to compute the frequency-dependent specific heat in the supercooled state using dynamical information from QMCT. Specific heat shows strong variation as the quantumness of the liquid is changed, which becomes more significant as density is increased. It is found that, near the transition point, different dynamical modes contribute to specific heat in classical and quantum liquids.

Uncovering the Role of Hole Traps in Promoting Hole Transfer from Multiexcitonic Quantum Dots to Molecular Acceptors

Understanding electronic dynamics in multiexcitonic quantum dots (QDs) is important for designing efficient systems useful in high power scenarios, such as solar concentrators and multielectron charge transfer. The multiple charge carriers within a QD can undergo undesired Auger recombination events, which rapidly annihilate carriers on picosecond time scales and generate heat from absorbed photons instead of useful work. Compared to the transfer of multiple electrons, the transfer of multiple holes has proven to be more difficult due to slower hole transfer rates. To probe the competition between Auger recombination and hole transfer in CdSe, CdS, and CdSe/CdS QDs of varying sizes, we synthesized a phenothiazine derivative with optimized functionalities for binding to QDs as a hole accepting ligand and for spectroscopic observation of hole transfer. Transient absorption spectroscopy was used to monitor the photoinduced absorption features from both trapped holes and oxidized ligands under excitation fluences where the averaged initial number of excitons in a QD ranged from ∼1 to 19. We observed fluence-dependent hole transfer kinetics that last around 100 ps longer than the predicted Auger recombination lifetimes, and the transfer of up to 3 holes per QD. Theoretical modeling of the kinetics suggests that binding of hole acceptors introduces trapping states significantly different from those in native QDs passivated with oleate ligands. Holes in these modified trap states have prolonged lifetimes, which promotes the hole transfer efficiency. These results highlight the beneficial role of hole-trapping states in devising hole transfer pathways in QD-based systems under multiexcitonic conditions.

Colloidal Synthesis Path to 2D Crystalline Quantum Dot Superlattices

By combining colloidal nanocrystal synthesis, self-assembly, and solution phase epitaxial growth techniques, we developed a general method for preparing single dot thick atomically attached quantum dot (QD) superlattices with high-quality translational and crystallographic orientational order along with state-of-the-art uniformity in the attachment thickness. The procedure begins with colloidal synthesis of hexagonal prism shaped core/shell QDs (e.g., CdSe/CdS), followed by liquid subphase self-assembly and immobilization of superlattices on a substrate. Solution phase epitaxial growth of additional semiconductor material fills in the voids between the particles, resulting in a QD-in-matrix structure. The photoluminescence emission spectra of the QD-in-matrix structure retains characteristic 0D electronic confinement. Importantly, annealing of the resulting structures removes inhomogeneities in the QD-QD inorganic bridges, which our atomistic electronic structure calculations demonstrate would otherwise lead to Anderson-type localization. The piecewise nature of this procedure allows one to independently tune the size and material of the QD core, shell, QD-QD distance, and the matrix material. These four choices can be tuned to control many properties (degree of quantum confinement, quantum coupling, band alignments, etc.) depending on the specific applications. Finally, cation exchange reactions can be performed on the final QD-in-matrix, as demonstrated herein with a CdSe/CdS to HgSe/HgS conversion.

Universal Inverse Scaling of Exciton-Exciton Annihilation Coefficient with Exciton Lifetime

Be it for essential everyday applications such as bright light-emitting devices or to achieve Bose-Einstein condensation, materials in which high densities of excitons recombine radiatively are crucially important. However, in all excitonic materials, exciton-exciton annihilation (EEA) becomes the dominant loss mechanism at high densities. Typically, a macroscopic parameter named EEA coefficient (C_EEA) is used to compare EEA rates between materials at the same density; higher C_EEA implies higher EEA rate. Here, we find that the reported values of C_EEA for 140 different materials is inversely related to the single-exciton lifetime. Since during EEA one exciton must relax to ground state, C_EEA is proportional to the single-exciton recombination rate. This leads to the counterintuitive observation that the exciton density at which EEA starts to dominate is higher in a material with larger C_EEA. These results broaden our understanding of EEA across different material systems and provide a vantage point for future excitonic materials and devices.

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.

Area and thickness dependence of Auger recombination in nanoplatelets

The ability to control both the thickness and the lateral dimensions of colloidal nanoplatelets offers a test-bed for area and thickness dependent properties in 2D materials. An important example is Auger recombination, which is typically the dominant process by which multiexcitons decay in nanoplatelets. Herein, we uncover fundamental properties of biexciton decay in nanoplatelets by comparing the Auger recombination lifetimes based on interacting and noninteracting formalisms with measurements based on transient absorption spectroscopy. Specifically, we report that electron-hole correlations in the initial biexcitonic state must be included in order to obtain Auger recombination lifetimes in agreement with experimental measurements and that Auger recombination lifetimes depend nearly linearly on the lateral area and somewhat more strongly on the thickness of the nanoplatelet. We also connect these scalings to those of the area and thickness dependencies of single exciton radiative recombination lifetimes, exciton coherence areas, and exciton Bohr radii in these quasi-2D materials.

Dielectric Confinement and Excitonic Effects in Two-Dimensional Nanoplatelets

Quasi-two-dimensional (2D) semiconductor nanoplatelets manifest strong quantum confinement with exceptional optical characteristics of narrow photoluminescence peaks with energies tunable by thickness with monolayer precision. We employed scanning tunneling spectroscopy (STS) in conjunction with optical measurements to probe the thickness-dependent band gap and density of excited states in a series of CdSe nanoplatelets. The tunneling spectra, measured in the double-barrier tunnel junction configuration, reveal the effect of quantum confinement on the band gap taking place mainly through a blue-shift of the conduction band edge, along with a signature of 2D electronic structure intermixed with finite lateral-size and/or defects effects. The STS fundamental band gaps are larger than the optical gaps as expected from the contributions of exciton binding in the absorption, as confirmed by theoretical calculations. The calculations also point to strong valence band mixing between the light- and split-off hole levels. Strikingly, the energy difference between the heavy-hole and light-hole levels in the tunneling spectra are significantly larger than the corresponding values extracted from the absorption spectra. Possible explanations for this, including an interplay of nanoplatelet charging, dielectric confinement, and difference in exciton binding energy for light and heavy holes, are analyzed and discussed.

Auger Recombination Lifetime Scaling for Type I and Quasi-Type II Core/Shell Quantum Dots

Having already achieved near-unity quantum yields, with promising properties for light-emitting diode, lasing, and charge separation applications, colloidal core/shell quantum dots have great technological potential. The shell thickness and band alignment of the shell and core materials are known to influence the efficiency of these devices. In many such applications, improving the efficiency requires a deep understanding of multiexcitonic states. Herein, we elucidate the shell thickness and band alignment dependencies of the biexciton Auger recombination lifetime for quasi-type II CdSe/CdS and type I CdSe/ZnS core/shell quantum dots. We find that the biexciton Auger recombination lifetime increases with the total nanocrystal volume for quasi-type II CdSe/CdS core/shell quantum dots and is independent of the shell thickness for type I CdSe/ZnS core/shell quantum dots. To perform these calculations and compute Auger recombination lifetimes, we developed a low-scaling approach based on the stochastic resolution of identity. The numerical approach provided a framework for studying the scaling of the biexciton Auger recombination lifetimes in terms of the shell thickness dependencies of the exciton radii, Coulomb couplings, and density of final states in quasi-type II CdSe/CdS and type I CdSe/ZnS core/shell quantum dots.

Resilient Pathways to Atomic Attachment of Quantum Dot Dimers and Artificial Solids from Faceted CdSe Quantum Dot Building Blocks

The goal of this work is to identify favored pathways for preparation of defect-resilient attached wurtzite CdX (X = S, Se, Te) nanocrystals. We seek guidelines for oriented attachment of faceted nanocrystals that are most likely to yield pairs of nanocrystals with either few or no electronic defects or electronic defects that are in and of themselves desirable and stable. Using a combination of in situ high-resolution transmission electron microscopy (HRTEM) and electronic structure calculations, we evaluate the relative merits of atomic attachment of wurtzite CdSe nanocrystals on the {11̅00} or {112̅0} family of facets. Pairwise attachment on either facet can lead to perfect interfaces, provided the nanocrystal facets are perfectly flat and the angles between the nanocrystals can adjust during the assembly. Considering defective attachment, we observe for {11̅00} facet attachment that only one type of edge dislocation forms, creating deep hole traps. For {112̅0} facet attachment, we observe that four distinct types of extended defects form, some of which lead to deep hole traps whereas others only to shallow hole traps. HRTEM movies of the dislocation dynamics show that dislocations at {11̅00} interfaces can be removed, albeit slowly. Whereas only some extended defects at {112̅0} interfaces could be removed, others were trapped at the interface. Based on these insights, we identify the most resilient pathways to atomic attachment of pairs of wurtzite CdX nanocrystals and consider how these insights can translate to the creation of electronically useful materials from quantum dots with other crystal structures.

Stochastic embedding DFT: Theory and application to p-nitroaniline in water

Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT.

Energy window stochastic density functional theory

Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for N_χ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as N_χ ^-1/2) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density.

Determination of the In-Plane Exciton Radius in 2D CdSe Nanoplatelets via Magneto-optical Spectroscopy

Colloidal, two-dimensional semiconductor nanoplatelets (NPLs) exhibit quantum confinement in only one dimension, which results in an electronic structure that is significantly altered compared to that of other quantum-confined nanomaterials. Whereas it is often assumed that the lack of quantum confinement in the lateral plane yields a spatially extended exciton, reduced dielectric screening potentially challenges this picture. Here, we implement absorption spectroscopy in pulsed magnetic fields up to 60 T for three different CdSe NPL thicknesses and lateral areas. Based on diamagnetic shifts, we find that the exciton lateral extent is comparable to NPL thickness, indicating that the quantum confinement and reduced screening concomitant with few-monolayer thickness strongly reduces the exciton lateral extent. Atomistic electronic structure calculations of the exciton size for varying lengths, widths, and thicknesses support the substantially smaller in-plane exciton extent.

Stochastic resolution of identity second-order Matsubara Green's function theory

We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N⁵) to O(N³) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 10³ electrons and more.

Ultrahigh Hot Carrier Transient Photocurrent in Nanocrystal Arrays by Auger Recombination

In this report, we show that a new mechanism for carrier transport in solution-processed colloidal semiconductor nanocrystal arrays exists at high excitation intensity on ultrafast time scales and allows for facile intrinsic transport between as-prepared nanocrystals over long distances. By combining a high speed photoconductive switch with an ultrafast laser excitation in a sub-40 ps photoconductor, we observed transient photocurrents with peak densities of 3 × 10⁴ - 10⁶ mA/cm² in self-assembled PbSe nanocrystals capped with long native oleic acid ligands. The ratio between the transient photocurrent peak and the steady-state dark current is 10 orders of magnitude. The transient mobility at the peak current is estimated to range between 0.5-17.5 cm²/(V s) for the various nanocrystal sizes studied, which is 6 to 9 orders of magnitude higher than the dark current steady-state mobility in PbSe, CdSe, and CdTe nanocrystals capped with native ligands. The results are analyzed using a kinetic model which attributes the ultrahigh transient photocurrent to multiple photogenerated excitons undergoing on-particle Auger recombination, followed by rapid tunneling at high energies. This mechanism is demonstrated for a wide range of PbSe nanocrystals sizes (diameters from 2.7 to 7.1 nm) and experimental parameters. Our observations indicate that native ligand-capped nanocrystal arrays are promising for optoelectronics applications wherein multiple carriers are photoinjected to interband states.