Optical Transition Matrix Elements Research Articles

Enhanced LWIR response of InP/InAsP quantum discs-in-nanowire array photodetectors by photogating and ultra-thin ITO contacts

Here we report on an experimental and theoretical investigation of the long-wavelength infrared (LWIR) photoresponse of photodetectors based on arrays of three million InP nanowires with axially embedded InAsP quantum discs. An ultra-thin top indium tin oxide contact combined with a novel photogating mechanism facilitates an improved LWIR normal incidence sensitivity in contrast to traditional planar quantum well photodetectors. The electronic structure of the quantum discs, including strain and defect-induced photogating effects, and optical transition matrix elements were calculated by an 8-band k·p simulation along with solving drift-diffusion equations to unravel the physics behind the generation of narrow linewidth intersubband signals observed from the quantum discs.

Gate tunable linear dichroism in monolayer 1T'-MoS2.

The linear dichroism demonstrates promising applications in the fields of polarization-resolved photodetectors and polarization optical imaging. Herein, we study the optical properties of monolayer 1T'-MoS2 based on a four-band effective k · p Hamiltonian within the framework of linear response theory. Owing to the anisotropic band structure, the k-resolved optical transition matrix elements associated with armchair(x) and zigzag(y) direction polarized light exhibit a staggered pattern. The anisotropy of the optical absorption spectrum is shown to sensitively depend on the photon energy, the light polarization and the gate voltage. A gate voltage can continuously modulate the anisotropy of the optical absorption spectra, rendering it isotropic or even reversing the initial anisotropy. This modulation leads to linear dichroism conversions across multiple wavelengths. Our findings are useful to design polarized photodetectors and sensors based on monolayer 1T'-MoS2. Our results are also applicable to other monolayer transition metal dichalcogenides with 1T' structure.

Spin–orbit effects on the electronic and optical properties of lead iodide

Lead iodide (PbI2) has gained much interest due to its direct electronic gap in the visible range and layered crystal structure. It has thereby been considered as a promising material for applications in atomically thin optoelectronic devices. In this work, we present a detailed investigation of the effect of spin–orbit coupling (SOC) that arises from the presence of heavy atoms on the electronic and optical properties of PbI2 using first-principles calculations based on density-functional theory and many-body perturbation theory. We find that SOC not only alters the bandgap but also induces the mixing of orbital characters, resulting in a significant change in the overall band structure and charge carrier effective masses. Moreover, the band orbital mixing caused by SOC results in the dramatic change in optical transition matrix elements and, correspondingly, the absorption spectrum. Our experimentally measured absorption spectra validate the calculation results and demonstrate the importance of SOC in the optical processes of PbI2. Our findings provide insights that are important for the potential use of PbI2 as a material platform for visible optoelectronic devices.

Topological-insulator nanocylinders

Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy spectrum, the surface states and the dipole matrix elements for optical transitions with in-plane polarization of 3DTI nanocylinders of finite height LL and radius RR. We first derive an effective 2D Hamiltonian by exploiting the cylindrical symmetry of the problem. We develop two approaches: the first one is an exact numerical tight-binding model obtained by discretising the Hamiltonian. The second one, which allows us to obtain analytical results, is an approximated model based on a large-RR expansion and on an effective boundary condition to account for the finite height of the nanocylinder. We find that the agreement between the two models, as far as eigenenergies and eigenfunctions are concerned, is excellent for the lowest absolute value of the longitudinal component of the angular momentum. Finally, we derive analytical expressions for the dipole matrix elements by first considering the lateral surface alone and the bases alone, and then for the whole nanocylinder. In particular, we focus on the two limiting cases of tall and squat nanocylinders. The latter case is compared with the numerical results finding a good agreement.

Shape fluctuations and radiation from thermally excited electronic states of boron clusters

The effect of thermal shape fluctuations on the recurrent fluorescence of boron-cluster cations, ${\mathrm{B}}_{N}{}^{+}$ $(N=9--14)$, has been investigated numerically, with a special emphasis on ${\mathrm{B}}_{13}{}^{+}$. For this cluster, the electronic structures of the ground state and the four lowest electronically excited states were calculated using time-dependent density-functional theory and sampled on molecular dynamics trajectories of the cluster calculated at an experimentally relevant excitation energy. The sampled optical transition matrix elements for ${\mathrm{B}}_{13}{}^{+}$ allowed us to construct its emission spectrum from the thermally populated electronically excited states. The spectrum was found to be broad, reaching down to at least 0.85 eV. This contrasts strongly with the static picture, where the lowest electronic transition happens at 2.3 eV. The low-lying electronic excitations produce a strong increase in the rates of recurrent fluorescence, calculated to peak at $4.6\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, with a time average of $8\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The average value is one order of magnitude higher than the static result, approaching the measured radiation rate. Similar results were found for the other cluster sizes. The results indicate that the effect makes a significant contribution to the radiative cooling, even given the exploratory nature of the study. Furthermore, the radiationless crossing between the ground-state and first-electronic-excited-state surfaces of ${\mathrm{B}}_{13}{}^{+}$ was calculated, found to be very fast compared to experimental timescales, justifying the thermal population assumption.

Benchmarking exchange-correlation potentials with the mstar60 dataset: Importance of the nonlocal exchange potential for effective mass calculations in semiconductors

The accuracy of effective masses predicted by density functional theory depends on the exchange-correlation functional employed, with nonlocal hybrid functionals giving more accurate results than semilocal functionals. In this article, we benchmark the performance of the Perdew-Burke-Ernzerhof (PBE), Tran-Blaha modified Becke-Johnson (TB-mBJ), and the hybrid Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals and potentials for the calculation of effective masses with perturbation theory. We introduce the mstar60 dataset, which contains 60 effective masses derived from 18 semiconductors. The ratio between experimental and calculated effective masses is $1.70 \pm 0.20$ for PBE, $0.76 \pm 0.04$ for TB-mBJ, $0.99 \pm 0.04$ for HSE06. We reveal that the nonlocal exchange in HSE06 enlarges the optical transition matrix elements leading to the superior accuracy of the hybrid functional in the calculation of effective masses. The omission of nonlocal exchange in the transition operator for HSE leads to serious errors. For the semilocal PBE functional, the errors in the bandgap and the optical transition matrix elements partially cancel out in the calculation of effective masses. The TB-mBJ functional yields PBE-like matrix elements paired with realistic bandgaps leading to a consistent overestimation of effective masses. However, if only limited computational resources are available, experimental masses can be estimated by multiplying TB-mBJ masses with the factor of 0.76. We then compare effective masses of transition metal dichalcogenide bulk and monolayer materials: we show that changes in the matrix elements are important in understanding the layer-dependent effective mass renormalization.

Interplay between Auger recombination, carrier leakage, and polarization in InGaAlN multiple-quantum-well light-emitting diodes

In conventional hexagonal InGaAlN multiple-quantum-well (MQW) (h-) light-emitting diodes (LEDs), carrier leakage from QWs is the main source of internal quantum efficiency (IQE) degradation without contributing to the LED efficiency droop. Our analysis based on the newly developed Open Boundary Quantum LED Simulator indicates that radiative recombination is hampered by the poor electron–hole wavefunction overlap induced by strong internal polarization for which QW carriers mostly recombine via Auger scattering rather than by radiative processes. By contrast, in non-polar h-LEDs, the IQE peak doubles its value compared to conventional h-LEDs while quenching the efficiency droop by 70% at current density of 100 A/cm2. Those effects are further enhanced in cubic InGaAlN MQW (c-) LEDs for which the IQE peak increases by an additional 30%, and the efficiency droop is further reduced by 80% compared to non-polar h-LEDs, thanks to the larger optical transition matrix element and the strong electron–hole wavefunction overlap in c-LEDs. Overall, a c-LED with a low efficiency droop of 3% at 100 A/cm2 is anticipated, paving a clear pathway toward ultimate solid-state lighting.

Cation disorder engineering yields AgBiS2 nanocrystals with enhanced optical absorption for efficient ultrathin solar cells

Strong optical absorption by a semiconductor is a highly desirable property for many optoelectronic and photovoltaic applications. The optimal thickness of a semiconductor absorber is primarily determined by its absorption coefficient. To date, this parameter has been considered as a fundamental material property, and efforts to realize thinner photovoltaics have relied on light-trapping structures that add complexity and cost. Here we demonstrate that engineering cation disorder in a ternary chalcogenide semiconductor leads to considerable absorption increase due to enhancement of the optical transition matrix elements. We show that cation-disorder-engineered AgBiS2 colloidal nanocrystals offer an absorption coefficient that is higher than other photovoltaic materials, enabling highly efficient extremely thin absorber photovoltaic devices. We report solution-processed, environmentally friendly, 30-nm-thick solar cells with short-circuit current density of 27 mA cm−2, a power conversion efficiency of 9.17% (8.85% certified) and high stability under ambient conditions.

Length-Gauge Optical Matrix Elements in WIEN2k

Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with the position operator, the momentum matrix elements do not fully capture the oscillator strength, while the length-gauge velocity matrix elements do. So far, length-gauge velocity matrix elements were not accessible in the all-electron full-potential WIEN2k package. We demonstrate the feasibility of computing length-gauge matrix elements in WIEN2k for a hybrid exchange-correlation functional based on a finite difference approach. To illustrate the implementation we determined matrix elements for optical transitions between the conduction and valence bands in GaAs, GaN, (CH3NH3)PbI3 and a monolayer MoS2. The non-locality of the Hartree–Fock exact exchange potential leads to a strong enhancement of the oscillator strength as noticed recently in calculations employing pseudopotentials (Laurien and Rubel: arXiv:2111.14772 (2021)). We obtained an analytical expression for the enhancement factor for the difference in eigenvalues not captured by the kinetic energy. It is expected that these results can also be extended to other non-local potentials, e.g., a many-body GW approximation.

Dark-bright excitons mixing in alloyed InGaAs self-assembled quantum dots

Quantum dots are arguably one of the best platforms for optically accessible spin based qubits. The paramount demand of extended qubit storage time can be met by using quantum-dot-confined dark exciton: a longlived electron-hole pair with parallel spins. Despite its name the dark exciton reveals weak luminescence that can be directly measured. The origins of this optical activity remain largely unexplored. In this work, using the atomistic tight-binding method combined with configuration-interaction approach, we demonstrate that atomic-scale randomness strongly affects oscillator strength of dark excitons confined in self-assembled cylindrical InGaAs quantum dots with no need for faceting or shape-elongation. We show that this process is mediated by two mechanisms: mixing dark and bright configurations by exchange interaction, and equally important appearance of non-vanishing optical transition matrix elements that otherwise correspond to nominally forbidden transitions in a non-alloyed case. The alloy randomness has essential impact on both bright and dark exciton states, including their energy, emission intensity, and polarization angle. We conclude that, due to the atomic-scale alloy randomness, finding dots with desired dark exciton properties may require exploration of a large ensemble, similarly to how dots with low bright exciton splitting are selected for entanglement generation.

ON THE THEORY OF ONE-PHOTON ABSORPTION OF POLARIZED LIGHT IN NARROW-GAP CRYSTALS. EXCLUDING THE EFFECT OF COHERENT SATURATION

In this work, from a microscopic point of view, the linear-circular dichroism of one-photon between band absorption of light in the Kane approximation in narrow-gap crystals is investigated. The matrix elements of onephoton interband optical transitions and the spectral dependence of the light absorption coefficient are calculated.

ON THE THEORY OF ONE-PHOTON ABSORPTION OF POLARIZED LIGHT IN NARROW-GAP CRYSTALS. TAKING INTO ACCOUNT THE EFFECT OF COHERENT SATURATION

In the article, from a microscopic point of view, the linear-circular dichroism of one-photon between band absorption of light in the Kane approximation in narrow-gap crystals is investigated.
 The linear-circular dichroism of one-photon absorption of polarized light is calculated taking into account the effect of coherent saturation in photoexcited charge carriers.
 The matrix elements of one-photon interband optical transitions and the corresponding linear-circular dichroism and the spectral dependence of the light absorption coefficient are calculated.

Optical conductivity of triple point fermions

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian, which is parameterized by an angular parameter λ. We find strong λ dependence in both Drude and interband optical absorption of these systems. The deviation of the T 2 coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particular λ = π/6 point, we find that the ‘helicity’ reversal optical transition matrix element is identically zero. Nevertheless, deviating from this point, the helicity reversal emerges as an absorption channel.

Even-odd-dependent optical transitions of zigzag monolayer black phosphorus nanoribbons

We analytically study the electronic structure and optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) using the tight-binding Hamiltonian and Kubo formula. By directly solving the discrete Schrodinger equation, we obtain the energy spectra and wavefunctions for N-ZPNR (where TV is the number of transverse zigzag atomic chains) and classify the eigenstates according to the lattice symmetry. Then, we obtain the optical transition selection rule of ZPNRs on the basis of symmetry analysis and analytical expressions of optical transition matrix elements. Under incident light that is linearly polarized along the ribbon, we determine that the optical transition selection rule for N-ZPNR with even- or odd-N is qualitatively different. Specifically, for even-N ZPNRs, the inter- (intra-) band selection rule is An =odd (even) because the parity of the wavefunction corresponding to the n-th subband in the conduction (valence) band is (-1)n[(-1)(n+1)] owing to the presence of C2x symmetry. However, the optical transitions between any subbands are possible owing to the absence of C2x symmetry. Our results provide a further understanding on the electronic states and optical properties of ZPNRs, which are useful for explaining the optical experiment data on ZPNR samples.

Effects of Electron-Hole Asymmetry on Electronic Structure of Helical Edge States in HgTe/HgCdTe Quantum Wells

We study the effects of electron-hole asymmetry on the electronic structure of helical edge states in HgTe/HgCdTe quantum wells. In the framework of the four-band kp-model, which takes into account the absence of a spatial inversion centre, we obtain analytical expressions for the energy spectrum and wave functions of edge states, as well as the effective g-factor tensor and matrix elements of electro-dipole optical transitions between the spin branches of the edge electrons. We show that when two conditions are simultaneously satisfied -- electron-hole asymmetry and the absence of an inversion centre -- the spectrum of edge electrons deviates from the linear one, in that case we obtain corrections to the linear spectrum.

Spherical topological insulator nanoparticles: Quantum size effects and optical transitions

We have investigated the interplay between band inversion and size quantization in spherically shaped nanoparticles made from topological-insulator (TI) materials. A general theoretical framework is developed based on a versatile continuum-model description of the TI bulk band structure and the assumption of a hard-wall mass confinement. Analytical results are obtained for the wave functions of single-electron energy eigenstates and the matrix elements for optical transitions between them. As expected from spherical symmetry, quantized levels in TI nanoparticles can be labeled by quantum numbers $j$ and $m=-j, -j+1, \dots, j$ for total angular momentum and its projection on an arbitrary axis. The fact that TIs are narrow-gap materials, where the charge-carrier dynamics is described by a type of two-flavor Dirac model, requires $j$ to assume half-integer values and also causes a doubling of energy-level degeneracy where two different classes of states are distinguished by being parity eigenstates with eigenvalues $(-1)^{j\mp 1/2}$. The existence of energy eigenstates having the same $j$ but opposite parity enables optical transitions where $j$ is conserved, in addition to those adhering to the familiar selection rule where $j$ changes by $\pm 1$. All optical transitions satisfy the usual selection rule $\Delta m = 0, \pm 1$. We treat intra- and inter-band optical transitions on the same footing and establish ways for observing unusual quantum-size effects in TI nanoparticles, including oscillatory dependences of the band gap and of transition amplitudes on the nanoparticle radius. Our theory also provides a unified perspective on multi-band models for charge carriers in semiconductors and Dirac fermions from elementary-particle physics.

Optical response of an inverted InAs/GaSb quantum well in an in-plane magnetic field**Project supported by the National Natural Science Foundation of China (Grant Nos. 61076092 and 61290303).

The optical response of an inverted InAs/GaSb quantum well is studied theoretically. The influence of an in-plane magnetic field that is applied parallel to the quantum well is considered. This in-plane magnetic field will induce a dynamical polarization even when the electric field component of the external optical field is parallel to the quantum well. The electron–electron interaction in the quantum well system will lead to the de-polarization effect. This effect is found to be important and is taken into account in the calculation of the optical response. It is found that the main feature in the frequency dependence of the velocity–velocity correlation function remains when the velocity considered is parallel to the in-plane magnetic field. When the direction of the velocity is perpendicular to the in-plane magnetic field, the de-polarization effect will suppress the oscillatory behavior in the corresponding velocity–velocity correlation function. The in-plane magnetic field can change the band structure of the quantum well drastically from a gapped semiconductor to a no-gapped semi-metal, but it is found that the distribution of the velocity matrix elements or the optical transition matrix elements in the wave vector space has the same two-tadpole topology.

Anisotropic ultrafast optical response of terahertz pumped graphene

We have measured the ultrafast anisotropic optical response of highly doped graphene to an intense single cycle terahertz pulse. The time profile of the terahertz-induced anisotropy signal at 800 nm has minima and maxima repeating those of the pump terahertz electric field modulus. It grows with increasing carrier density and demonstrates a specific nonlinear dependence on the electric field strength. To describe the signal, we have developed a theoretical model that is based on the energy and momentum balance equations and takes into account optical phonons of graphene and the substrate. According to the theory, the anisotropic response is caused by the displacement of the electronic momentum distribution from zero momentum induced by the pump electric field in combination with polarization dependence of the matrix elements of interband optical transitions.

A re-examination of experimental evidence on the spectral dependence of the optical transition matrix element associated with thin-film silicon

We analyze the error associated with the optical transition matrix element spectral dependencies for hydrogenated amorphous silicon and crystalline silicon found by Jackson et al. (Phys Rev B 31:5187–5198, 1985). We find that this error is considerable for photon energies less than 1.5 eV. This suggests that spectral dependencies for the optical transition matrix element, other than those proposed by Jackson et al., are possible for photon energies less than 1.5 eV. With this limitation in mind, we then fit a Lorentzian peak to the crystalline silicon experimental optical transition matrix element result of Jackson et al. Within the framework of the damped harmonic oscillator perspective, plotting the term related to the location of the resonant frequency as a function of the damping coefficient, for a number of thin-film silicon experimental results, we have found a relationship between these model parameters. We suspect that this dependence has important implications for the optical response of various forms of thin-film silicon and related materials.

Optical transitions and localized edge states in skewed zigzag phosphorene nanoribbons

Using the Tight Binding (TB) parameters extracted from Density Functional Theory (DFT) and Recursive Green's Function method, it is shown that skewed-zigzag black phosphorous (phosphorene) nanoribbons obtain large and tuneable bandgap in response to vertical and transverse electric fields. Depending on the direction of the applied field the mid-gap states could possess the localized or metallic nature i.e. non-zero mid-gap density of states. Adjustability of the bandgap and optical dipole transition matrix elements are explained based on the symmetry of involved band edge states. This promises new electronic and optical devices based on phosphorene nanoribbons.