Colloidal semiconductor nanoplatelets, in which carriers are strongly confined only along one dimension, present fundamentally different excitonic properties than quantum dots, which support strong confinement in all three dimensions. In particular, multiple excitons strongly confined in just one dimension are free to re-arrange in the lateral plane, reducing the probability for multi-body collisions. Thus, while simultaneous multiple photon emission is typically quenched in quantum dots, in nanoplatelets its probability can be tuned according to size and shape. Here, we focus on analyzing multi-exciton dynamics in individual CdSe/CdS nanoplatelets of various sizes through the measurement of second-, third-, and fourth-order photon correlations. Thus, for the first time, we can directly probe the dynamics of the two, three and four exciton states in the single nanocrystal level. Remarkably, although higher orders of correlation vary substantially among the synthesis products, they strongly correlate with the value of second order antibunching. The scaling of the higher order moments with the degree of antibunching presents a small yet clear deviation from the accepted model of Auger recombination through binary collisions. Such a deviation suggests that many-body contributions are present already at the level of triexcitons. These findings highlight the benefit of high-order photon correlation spectroscopy as a technique to study multi-exciton dynamics in colloidal semiconductor nanocrystals.
The surface of nominally diamagnetic colloidal CdSe nanoplatelets can demonstrate paramagnetism owing to the uncompensated spins of dangling bonds (DBSs). We reveal that by optical spectroscopy in high magnetic fields up to 15 Tesla using the exciton spin as probe of the surface magnetism. The strongly nonlinear magnetic field dependence of the circular polarization of the exciton emission is determined by the DBS and exciton spin polarization as well as by the spin-dependent recombination of dark excitons. The sign of the exciton-DBS exchange interaction can be adjusted by the nanoplatelet gr…
We investigated the nonlinear optical properties of CdSe/CdS nanoplatelets in the vicinity of heavy hole and light hole exciton resonances. The two color pump-probe technique was applied. The first intense pulse created non-equilibrium exciton population, which was detected as a decrease of probe light absorption. We observed intense scattering of excitons between heavy- and light-hole excitonic states. We also studied experimentally saturation of absorption in nanoplatelets. Theoretical description of these phenomena allowed us to determine parameters of exciton dynamics in nanoplatelets.
Colloidal semiconductor nanoplatelets exhibit quantum size effects due to their thickness of only few monolayers, together with strong optical band-edge transitions facilitated by large lateral extensions. In this article we demonstrate room temperature strong coupling of the light and heavy hole exciton transitions of CdSe nanoplatelets with the photonic modes of an open planar microcavity. Vacuum Rabi splittings of $66 \pm 1$ meV and $58 \pm 1$ meV are observed for the heavy and light hole excitons respectively, together with a polariton-mediated hybridisation of both transitions. By measuri…
We measured the intrinsic ground-state exciton dephasing and population dynamics in colloidal quasi two-dimensional (2D) CdSe nanoplatelets at low temperature (5-50K) using transient resonant four-wave mixing in heterodyne detection. Our results indicate that below 20K the exciton dephasing is lifetime limited, with the exciton population lifetime being as fast as 1ps. This is consistent with an exciton lifetime given by a fast radiative decay due to the large in-plane coherence area of the exciton center-of-mass motion in these quasi 2D systems compared to spherical nanocrystals.
Two-dimensional electron-hole gases in colloidal semiconductors have a wide variety of applications. Therefore, a proper physical understanding of these materials is of great importance. In this paper we present a detailed theoretical analysis of the recent experimental results by Tomar et al., that show an unexpected stability of excitons in CdSe nanoplatelets at high photoexcitation densities. Including the screening effects by free charges on the exciton properties, our analysis shows that CdSe nanoplatelets behave very differently from bulk CdSe, and in particular do not show a crossover t…
We report on the experimental and theoretical studies of optical alignment and optical orientation effects in an ensemble of core/shell CdSe/CdS colloidal nanoplatelets. The dependences of three Stokes parameters on the magnetic field applied in the Faraday geometry are measured under continuous wave resonant excitation of the exciton photoluminescence. Theoretical model is developed to take into account both bright and dark exciton states in the case of strong electron and hole exchange interaction and random in-plane orientation of the nanoplatelets in ensemble. The data analysis allows us t…
Exciton-exciton annihilation (EEA) and Auger recombination are detrimental processes occurring in semiconductor optoelectronic devices at high carrier densities. Despite constituting one of the main obstacles for realizing lasing in semiconductor nanocrystals (NCs), the dependencies on NC size are not fully understood, especially for those with both weakly and strongly confined dimensions. Here, we use differential transmission spectroscopy to investigate the dependence of EEA on the physical dimensions of thickness-controlled 2D halide perovskite nanoplatelets (NPls). We find the EEA lifetime…
We address spin properties and spin dynamics of carriers and charged excitons in CdSe/CdS colloidal nanoplatelets with thick shells. Magneto-optical studies are performed by time-resolved and polarization-resolved photoluminescence, spin-flip Raman scattering and picosecond pump-probe Faraday rotation in magnetic fields up to 30 T. We show that at low temperatures the nanoplatelets are negatively charged so that their photoluminescence is dominated by radiative recombination of negatively charged excitons (trions). Electron g-factor of 1.68 is measured and heavy-hole g-factor varying with incr…
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 optoelectronic properties of metal chalcogenide colloidal nanoplatelets are often interpreted in terms of excitonic states. However, recent spectroscopic experiments evidence the presence of trion states, enabled by the slow Auger recombination in these structures. We analyze how the presence of an additional charge in trions modifies the emission energy and oscillator strength as compared to neutral excitons. These properties are very sensitive to dielectric confinement and electronic correlations, which we describe accurately using image-charge and variational Quantum Monte Carlo methods…
We present the phase diagram of free charges (electrons and holes), excitons, and biexcitons in highly excited CdSe nanoplatelets that predicts a crossover to a biexciton-dominated region at easily attainable low temperatures or high photoexcitation densities. Our findings extend previous work describing only free charges and excitons by introducing biexcitons into the equation of state, while keeping the exciton and biexciton binding energies constant in view of the relatively low density of free charges in this material. Our predictions are experimentally testable in the near future and offe…
Excitons in diluted magnetic semiconductors represent excellent probes for studying the magnetic properties of these materials. Various magneto-optical effects, which depend sensitively on the exchange interaction of the excitons with the localized spins of the magnetic ions can be used for probing. Here, we study core/shell CdSe/(Cd,Mn)S colloidal nanoplatelets hosting diluted magnetic semiconductor layers. The inclusion of the magnetic Mn$^{2+}$ ions is evidenced by three magneto-optical techniques using high magnetic fields up to 15 T: polarized photoluminescence, optically detected magneti…
We experimentally investigated for the first time the lowest four band structure of Cd Se nanoplatelets at the r point of Brillouin zone [heavy-hole (hh), light-hole (lh) and two spin-orbital bands] and its modification due to the changing of the CdS shell thickness. The results of an experimental and theoretical study of exciton dynamics in colloidal CdSe/CdS nanoplateles are presented in the case of stationary laser excitation. The excitation was performed by means of the powerful nanosecond laser and the pump and probe technique was utilized. The differential transmission spectra peculiarit…
Using semi-analytical models we calculate the energy, effective Bohr radius and radiative lifetime of neutral excitons confined in CdSe colloidal nanoplatelets (NPLs). The excitonic properties are largely governed by the electron-hole in-plane correlation, which in NPLs is enhanced by the quasi-two-dimensional motion and the dielectric mismatch with the organic environment. In NPLs with lateral size $L \gtrsim 20$ nm the exciton behavior is essentially that in a quantum well, with superradiance leading to exciton lifetimes of 1 ps or less, only limited by the NPL area. However, for $L < 20$ nm…
We show that the finite lateral sizes of ultrathin CdSe nanoplatelets strongly affect both their photoluminescence and optical absorption spectra. This is in contrast to the situation in quantum wells, in which the large lateral sizes may be assumed to be infinite. The lateral sizes of the nanoplatelets are varied over a range of a few to tens of nanometers. For these sizes excitons experience in-plane quantum confinement, and their center-of-mass motion becomes quantized. Our direct experimental observation of the discretization of the exciton center-of-mass states can be well understood on t…
A theory of electron spin-flip Raman scattering (SFRS) is presented that describes the Raman spectral signals shifted by both single and twice the electron Zeeman energy under nearly resonant excitation of the heavy hole excitons in semiconductor nanoplatelets. We analyze the spin structure of photoexcited intermediate states, derive compound matrix elements of the spin-flip scattering and obtain polarization properties of the one- and two-electron SFRS common for all the intermediate states. We show that, in the resonant scattering process under consideration, the complexes "exciton plus loca…
We report excited state emission from p-states at excitation fluences well below ground state saturation in CdSe nanoplatelets. Size dependent exciton ground state-excited state energies and dynamics are determined by three independent methods, time-resolved photoluminescence (PL), time-integrated PL and Hartree renormalized k$\cdot$p calculations -- all in very good agreement. The ground state-excited state energy spacing strongly increases with the lateral platelet quantization. Our results suggest that the PL decay of CdSe platelets is governed by an LO-phonon bottleneck, related to the rep…
Colloidal semiconductor nanoplatelets (NPLs) with electronic structure as quantum wells have recently emerged as exciting materials for optoelectronic applications. Here we investigate how morphology affects important photoluminescence (PL) properties of single CdSe and core/shell CdSe/CdZnS nanoplatelets. By analyzing PL intensity-lifetime correlation and second-order photon correlation results, we demonstrate that, irrespective of morphology, Auger recombination cannot be responsible for PL blinking of single NPLs. We propose that hot carrier trapping plays a significant role in blinking and…
Strongly quantum-confined 2D colloidal PbS nanoplatelets (NPLs) are highly interesting materials for near-infrared optoelectronic applications. Here, we use ultrafast transient optical absorption spectroscopy to study the characteristics and dynamics of photoexcited excitons in ultrathin PbS NPLs with a cubic (rock-salt) structure. The NPLs are synthesized at near room temperature from lead oleate and thiourea precursors and show an optical absorption onset at 680 nm (1.8 eV) as well as photoluminescence at 720 nm (1.7 eV). By treating PbS NPLs with CdCl2 in a post-synthetic step, their photol…
For high-speed optoelectronic applications relying on fast relaxation or energy transfer mechanisms, understanding of carrier relaxation and recombination dynamics is critical. Here, we compare the differences in photoexcited carrier dynamics in 2D and quasi-3D colloidal methylammonium lead iodide perovskite nanoplatelets via differential transmission spectroscopy. We find that the cooling of excited electron-hole pairs by phonon emission progresses much faster and is intensity-independent in the 2D-case. This is due to the low dielectric surrounding of the thin perovskite layers, for which th…
Semiconductor nanoparticles of cadmium chalcogenides are known to exhibit pronounced thickness-dependent $E_0$ series of exciton transitions at the $Γ$ point of the Brillouin zone (BZ). In this work, we report an experimental evidence for high-energy series of exciton transitions, which originates from BZ points different from the $Γ$ point, in the family of cadmium chalcogenide quasi-2D nanoplatelets (NPLs). Intensive UV absorption bands demonstrating a pronounced size effect are observed for CdTe, CdSe, and CdS NPLs in addition to the $E_0$ exciton bands in the visible region. These new band…
The in-plane coefficient of thermal expansion (CTE) for CdSe nanoplatelets with the zinc-blende structure containing from two to five monolayers is calculated from first principles within the quasiharmonic approximation. A comparison of the obtained results with those for bulk CdSe with both the zinc-blende and wurtzite structures finds a significant increase in the magnitude of negative CTE and the temperature range of its observation in nanoplatelets. The main contribution to the negative thermal expansion in CdSe nanoplatelets is given by the out-of-plane flexural ZA mode and in-plane optic…
We propose correlated yet extremely simple single-parameter-dependent wave-functions with a Slater-type correlation factor, to describe excitons in 0D, quasi-1D and quasi-2D semiconductor quantum dots. We provide closed-form formulas for the wave-function normalization factor, electron/hole single-particle density and the expectation value of the kinetic energy. We additionally supply fast integration procedures for the Coulomb interaction in the presence of dielectric mismatch with the surrounding medium for nanoplatelets (quasi-2D systems), and for the bare-Coulomb integral in long nanorods …
Charge carrier dynamics essentially determine the performance of various optoelectronic applications of colloidal semiconductor nanocrystals. Among them, two-dimensional nanoplatelets provide new adjustment freedom for their unique core/crown heterostructure. Herein, we demonstrate that by fine-tuning the core size and the lateral quantum confinement, the charge carrier transfer rate from the crown to the core can be varied by one order of magnitude in CdSe/CdSeS core/alloy-crown nanoplatelets. In addition, the transfer can be affected by a carrier blocking mechanism, i.e., the filled carriers…
Colloidal Cadmium Selenide (CdSe) nanoplatelets (NPLs) are a recently developed class of efficient luminescent nanomaterial suitable for optoelectronic device applications. A change in temperature greatly affects their electronic bandstructure and luminescence properties. It is important to understand how-and-why the characteristics of NPLs are influenced, particularly at elevated temperature, where both reversible and irreversible quenching processes come into picture. Here we present a study on the effect of elevated temperature on the characteristics of colloidal CdSe NPLs. We used an effec…
We review the existing and present the new results of $\bf kp$ calculations of the electron, hole, and exciton effective $g$-factors in semiconductor nanocrystals of different shape and symmetry. We propose a simple yet accurate method for calculation of electron $g$-factor size dependence in bare nanocrystals within the eight-band Kane model. Using the spherical approximation for Luttinger Hamiltonian we find the dependence of hole $g$-factor on light to heavy hole effective mass ratio in semiconductor nanostructures with spherical, axial, and cubically symmetric shape. We show that the non-e…
We show that electron-hole correlation can be used to tune interband and intraband optical transition rates in semiconductor nanostructures with at least one weakly confined direction. The valence-to-conduction band transition rate can be enhanced by a factor $(L/a_B)^{N}$ -- with $L$ the length of the weakly confined direction, $a_B$ the exciton Bohr radius and $N$ the dimensionality of the nanostructure -- while the rate of intraband and inter-valence-band transitions can be slowed down by the inverse factor, $(a_B/L)^{N}$. Adding a hitherto underexplored degree of freedom to engineer excito…
The dynamic Fano resonance (DFR) between discrete quasienergy excitons and sidebands of their ionization continua is predicted and investigated in dc- and ac-driven semiconductor superlattices. This DFR, well controlled by the ac field, delocalizes the excitons and opens an intrinsic decay channel in nonlinear four-wave mixing signals.
A quasi-exciton condensate is a phase characterized by quasi-long range order of an exciton (electron-hole pair) order parameter. Such a phase can arise naturally in a system of two parallel oppositely doped quantum wires, coupled by repulsive Coulomb interactions. We show that the quasi-exciton condensate phase can be stabilized in an extended range of parameters, in both spinless and spinful systems. For spinful electrons, the exciton phase is shown to be distinct from the usual quasi-long range ordered Wigner crystal phase characterized by power-law density wave correlations. The two phases…
An analytical expression is obtained for the biexciton binding energy as a function of the inter-exciton distance and binding energy of constituent quasi-one-dimensional excitons in carbon nanotubes. This allows one to trace biexciton energy variation and relevant non-linear absorption under external conditions whereby the exciton binding energy varies. The non-linear absorption lineshapes calculated exhibit characteristic asymmetric (Rabi) splitting as the exciton energy is tuned to the nearest interband plasmon resonance. These results are useful for tunable optoelectronic device application…
The strong Coulomb forces in monolayer transition metal dichalcogenides ensure that optical excitation of band electrons gives rise to Wannier-Mott excitonic states, each of which can be conceptualized as a composite of a Gaussian wavepacket corresponding to center-of-mass motion and an orbital state corresponding to the motion of the electron and hole about the center-of-mass. Here, we show that at low temperature in monolayer MoS2, given quasi-localized excitons and consequently a significant inter-exciton spacing, the excitons undergo dipole-dipole interaction and annihilate one another in …
Moiré superlattices provide a powerful way to engineer properties of electrons and excitons in two-dimensional van der Waals heterostructures. The moiré effect can be especially strong for interlayer excitons, where electrons and holes reside in different layers and can be addressed separately. In particular, it was recently proposed that the moiré superlattice potential not only localizes interlayer exciton states at different superlattice positions, but also hosts an emerging moiré quasi-angular momentum (QAM) that periodically switches the optical selection rules for interlayer excitons at …
We perform a polarization-resolved magnetoluminescence study of excitons in ReS$_2$. We observe that two linearly polarized Rydberg series of excitons are accompanied by two other Rydberg series of dark excitons, brightened by an in-plane magnetic field. All series extrapolate to the same single-electron bandgap, indicating that the observed excitons originate either from the same valley or from two valleys related by the inversion symmetry, and are split by exchange interaction. To interpret our observations of the magnetic brightening, we have to assume the dominant spin-orbit coupling to be…
We discuss neutral and charged complexes (biexciton and trion) formed by indirect excitons in layered quasi-two-dimensional semiconductor heterostructures. Indirect excitons -- long-lived neutral Coulomb-bound pairs of electrons and holes of different layers -- have been known for semiconductor coupled quantum wells and are recently reported for van der Waals heterostructures such as bilayer graphene and transition metal dichalcogenides. Using the configuration space approach, we derive the analytical expressions for the trion and biexciton binding energies as functions of the interlayer dista…
We propose and analyze a k-filtering effect which gives rise to the drastic difference between the actual spatial coherence length of quasi-two-dimensional (quasi-2D) excitons or microcavity (MC) polaritons in planar nanostructures and that inferred from far-field optical measurements. The effect originates from the conservation of in-plane wavevector k in the optical decay of the particles in outgoing bulk photons. The k-filtering effect explains the large coherence lengths recently observed for indirect excitons in coupled quantum wells (QWs), but is less pronounced for MC polaritons at low …
We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for the quasi-relativistic dispersion of electrons and holes. Exact analytical solutions of the quantum relativistic two-body problem are obtain for several limiting cases. We show that the binding energy scales with the band gap, and conclude on the basis of the data available for semiconductor nanotubes that there is no transition to an excitonic insulator in quasi-metallic nanotubes and that their THz applications are feasible.
Optically detected resonance spectroscopy has been used to investigate effects of weak random lateral potential energy fluctuations on internal transitions of charged magneto-excitons (trions) in quasi two-dimensional GaAs/AlGaAs quantum-well (QW) structures. Resonant changes in the ensemble photoluminescence induced by far-infrared radiation were studied as a function of magnetic field for samples having: 1) no growth interrupts (short range well-width fluctuations), and 2) intentional growth interrupts (long range monolayer well-width differences). Only bound-to-continuum internal transition…
Exciton-polaritons are mixed light-matter quasiparticles. We have developed a statistical model describing stochastic exciton-photon transitions within a condensate of exciton polaritons. We show that the exciton-photon correlator depends on the "hidden variable" which characterizes the rate of exciton-photon transformations in the condensate. We discuss implications of this effect for the quantum statistics of photons emitted by polariton lasers.
It is shown that quantum interference can be employed to create an exciton transistor. An applied potential gates the quasi-particle motion and also discriminates between quasi-particles of differing binding energy. When implemented within nanoscale assemblies, such control elements could mediate the flow of energy and information. Quantum interference can also be used to dissociate excitons as an alternative to using heterojunctions. A finite molecular setting is employed to exhibit the underlying discrete, two-particle, mesoscopic analog to Fano anti-resonance. Selected entanglement measures…
We present a time-resolved study of energy relaxation and trapping dynamics of polariton condensates in a semiconductor microcavity ridge. The combination of two non-resonant, pulsed laser sources in a GaAs ridge-shaped microcavity gives rise to profuse quantum phenomena where the repulsive potentials created by the lasers allow the modulation and control of the polariton flow. We analyze in detail the dependence of the dynamics on the power of both lasers and determine the optimum conditions for realizing an all-optical polariton condensate transistor switch. The experimental results are inte…
We unravel the influence of quasiparticle screening in the non-equilibrium exciton dynamics of monolayer WS$_2$. We report pump photon energy-dependent exciton blue and red-shifts from time-resolved-reflectance contrast measurements. Based on a phenomenological model, we isolate the effective impact of excitons and free carriers on the renormalization of the quasi-free particle band gap, exciton binding energy and linewidth broadening. By this, our work does not only provide a comprehensive picture of the competing phenomena governing the exciton dynamics in WS$_2$ upon photoexcitation, but al…
We report a comprehensive experimental study and detailed model analysis of the terahertz dielectric response and density kinetics of excitons and unbound electron-hole pairs in GaAs quantum wells. A compact expression is given, in absolute units, for the complex-valued terahertz dielectric function of intra-excitonic transitions between the 1s and higher-energy exciton and continuum levels. It closely describes the terahertz spectra of resonantly generated excitons. Exciton ionization and formation are further explored, where the terahertz response exhibits both intra-excitonic and Drude feat…
Two-dimensional correlation spectroscopy (2DCS) based on the nonlinear optical response of excitons to sequences of ultrafast pulses, has the potential to provide some unique insights into carrier dynamics in semiconductors. The most prominent feature of 2DCS, cross peaks, can best be understood using a sum-over-states picture involving the many-body eigenstates. However, the optical response of semiconductors is usually calculated by solving truncated equations of motion for dynamical variables, which result in a quasiparticle picture. In this work we derive Green's function expressions for t…
There have been extensive experimental search for possible exciton superfluid in semiconductor electron-hole bilayer systems below liquid Helium temperature. However, exciton superfluid are meta-stable and will eventually decay through emitting photons. Here we show that the light emitted from the excitonic superfluid has unique and unusual features not shared by any other atomic or condensed matter systems. We evaluate angle resolved photon spectrum, momentum distribution curve, energy distribution curve and quasiparticle excitation spectrum in the exciton superfluid and comment on relevant e…
Quasi-equilibrium relaxational thermodynamics is developed to understand LA-phonon-assisted thermalization of Bose-Einstein distributed excitons in quantum wells. We study the quantum-statistical effects in the relaxational dynamics of the effective temperature of excitons $T = T(t)$. When $T$ is less than the degeneracy temperature $T_0$, well-developed Bose-Einstein statistics of quantum well excitons leads to nonexponential and density-dependent thermalization. At low bath temperatures $T_b \to 0$ the thermalization of quantum-statistically degenerate excitons effectively slows down and $T(…
