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Register a new userExcitons in InP, GaP, GaInP quantum dots: Insights from time-dependent density functional theory
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Colloidal quantum dots (QDs) of group III-V are considered as promising candidates for next-generation environmentally friendly light emitting devices, yet there appears to be only limited understanding of the underlying electronic and excitonic properties. Using large-scale density functional theory with the hybrid B3LYP functional solving the single-particle states and time-dependent density functional theory accounting for the many-body excitonic effects, we have identified the structural, electronic and excitonic optical properties of InP, GaP and GaInP QDs containing up to a thousand atoms or more. The calculated optical gap of InP QD appears in excellent agreement with available experiments, and it scales nearly linearly with the inverse diameter. The radiative exciton decay lifetime is found to increase surprisingly linearly with increasing the dot size. For GaP QDs, we predict an unusual electronic state crossover at diameter around 1.5 nm whereby the nature of the lowest unoccupied molecular orbital (LUMO) state switches its symmetry from $Gamma_{5}$-like at larger diameter to $Gamma_{1}$-like at smaller diameter. After the crossover, the absorption intensity of the band-edge exciton states is significantly enhanced. Finally, we find that Vegards law holds very well for GaInP random alloyed quantum dots down to ultra-small sizes with less than a hundred atoms. The obtained energy gap bowing parameter of this common-cation compound in QD regime appears positive, size-dependent and much smaller than its bulk parentage. The volume deformation, dominating over the charge exchange and structure relaxation effects, is mainly responsible for the QD energy gap bowing. The present work provides a road map for a variety of electronic and optical properties of colloidal QDs in group III-V that can guide spectroscopic studies.
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The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the role of the long spatial range and the frequency dependence of the xc kernel $f_{rm xc}$ for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional Kronig-Penney model and simple approximate xc kernels, which allows us to address these questions in a transparent manner. Depending on the system, it is found that adiabatic xc kernels can produce a single bound exciton, and sometimes two bound excitons, where the long spatial range of $f_{rm xc}$ is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.
We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose, we derive the nonlinear (third-order) TDDFT equation for the excitonic polarization. In this equation, the nonlinear time-dependent effects are described by the time-dependent (non-adiabatic) part of the effective exciton-exciton interaction, which depends on the exchange-correlation (XC) kernel. We apply the approach to study the nonlinear optical response of a GaAs quantum well. In particular, we calculate the 2D Fourier spectra of the system and compare it with experimental data. We find that it is necessary to use a non-adiabatic XC kernel to describe excitonic bound states - biexcitons, which are formed due to the retarded TDDFT exciton-exciton interaction.
Sizable nuclear spin polarization is pumped in individual InP/GaInP dots in a wide range of external magnetic fields B_ext=0-5T by circularly polarized optical excitation. We observe nuclear polarization of up to ~40% at Bext=1.5T and corresponding to an Overhauser field of ~1.2T. We find a strong feedback of the nuclear spin on the spin pumping efficiency. This feedback, produced by the Overhauser field, leads to nuclear spin bi-stability at low magnetic fields of Bext=0.5-1.5T. We find that the exciton Zeeman energy increases markedly, when the Overhauser field cancels the external field. This counter-intuitive result is shown to arise from the opposite contribution of the electron and hole Zeeman splittings to the total exciton Zeeman energy.
Time-dependent density-functional theory (TDDFT) is a computationally efficient first-principles approach for calculating optical spectra in insulators and semiconductors, including excitonic effects. We show how exciton wave functions can be obtained from TDDFT via the Kohn-Sham transition density matrix, both in the frequency-dependent linear-response regime and in real-time propagation. The method is illustrated using one-dimensional model solids. In particular, we show that our approach provides insight into the formation and dissociation of excitons in real time. This opens the door to time-resolved studies of exciton dynamics in materials by means of real-time TDDFT.
The optical spectra of two-dimensional (2D) periodic systems provide a challenge for time-dependent density-functional theory (TDDFT) because of the large excitonic effects in these materials. In this work we explore how accurately these spectra can be described within a pure Kohn-Sham time-dependent density-functional framework, i.e., a framework in which no theory beyond Kohn-Sham density-functional theory, such as $GW$, is required to correct the Kohn-Sham gap. To achieve this goal we adapted a recent approach we developed for the optical spectra of 3D systems [Cavo, Berger, Romaniello, Phys. Rev. B 101, 115109 (2020)] to those of 2D systems. Our approach relies on the link between the exchange-correlation kernel of TDDFT and the derivative discontinuity of ground-state density-functional theory, which guarantees a correct quasi-particle gap, and on a generalization of the polarization functional [Berger, Phys. Rev. Lett., 115, 137402 (2015)], which describes the excitonic effects. We applied our approach to two prototypical 2D monolayers, $h$-BN and MoS$_2$. We find that our protocol gives a qualitative good description of the optical spectrum of $h$-BN, whereas improvements are needed for MoS$_2$ to describe the intensity of the excitonic peaks.
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