Band-gap Renormalization Research Articles

Bandgap renormalization and indirect optical absorption in MgSiN2 at finite temperature

We investigate the temperature effect on the electronic band structure and optical absorption property of wide-bandgap ternary nitride MgSiN2 using first-principles calculations. We find that electron–phonon coupling leads to a sizable reduction in the indirect gap of MgSiN2, which is indispensable in understanding the optoelectronic properties of this material. Taking the bandgap renormalization into account, the bandgap of MgSiN2 determined by the quasiparticle GW0 calculations shows good agreement with recent experimental result. The predicted phonon-assisted indirect optical absorption spectra show that with increasing temperature, the absorption onset undergoes a redshift. Our work provides helpful insights into the nature of the bandgap of MgSiN2 and facilitates its application in ultraviolet optoelectronic devices.

Stimulated Emission through an Electron-Hole Plasma in Colloidal CdSe Quantum Rings.

Colloidal CdSe quantum rings (QRs) are a recently developed class of nanomaterials with a unique topology. In nanocrystals with more common shapes, such as dots and platelets, the photophysics is consistently dominated by strongly bound electron–hole pairs, so-called excitons, regardless of the charge carrier density. Here, we show that charge carriers in QRs condense into a hot uncorrelated plasma state at high density. Through strong band gap renormalization, this plasma state is able to produce broadband and sizable optical gain. The gain is limited by a second-order, yet radiative, recombination process, and the buildup is counteracted by a charge-cooling bottleneck. Our results show that weakly confined QRs offer a unique system to study uncorrelated electron–hole dynamics in nanoscale materials.

Ultrafast Lasing Dynamics in a CsPbBr3 Perovskite Microplate

The perovskite microlaser is a competitive candidate of light source for optical communication and integrated photonic circuits. Understanding the fundamental mechanism of lasing is crucial for the upcoming devices. The ultrafast establishment of lasing modes within a 2D perovskite microplate cavity at room temperature is investigated. The transient red shift of lasing modes can be found. Analysis based on electron–hole plasma (EHP) and a dynamic Drude‐like model are carried out with simulations on the transient dielectric response and the mode shift. In addition, the integrated lasing gain profile have a red shift at high excitation intensity, which is explained with EHP‐induced bandgap renormalization. The conflict between the experimental phenomena and the exciton–polariton theory confirms that under intense excitation, the exciton–polariton is ruled out for the origin of lasing. These results provide a direct understanding of the lasing evolving in a 2D perovskite microcavity. Suppressing the EHP‐related transient shift of cavity modes will advance the lasing applications.

Atomlike interaction and optically tunable giant band-gap renormalization in large-area atomically thin MoS2

Coulomb interactions in atomically thin transition metal dichalcogenides can be dynamically engineered by exploiting the dielectric environment to control the optical and electronic properties. Here we demonstrate an optically tunable giant band-gap renormalization (BGR) $\ensuremath{\sim}1200$ and 850 meV from the edge of the conduction band and complete suppression of the exciton absorption in large-area single-layer (1L) and three-layer (3L) ${\mathrm{MoS}}_{2}$, respectively. The observed giant BGR is two orders of magnitude larger than that in the conventional semiconductors, and it persists for tens of ps. Strikingly, our results demonstrate photoinduced transparency at the electronic band gap using an intense optical field at room temperature. Exciton bleach recovery in 1L and 3L show a contrasting fluence-dependent response, demonstrating the layer-dependent optical tuning of exciton lifetime in a way that would be both reversible and real time. We find that the optical band gap (exciton resonance peak) shows a transient redshift followed by an anomalous blueshift from the lowest energy point as a function of the photo-generated carrier density. The observed exciton energy shift is analogous to atom-atom interactions, and it varies as a Lennard-Jones like potential as a function of the interexciton separation.

Signatures of ultrafast electronic and atomistic dynamics in bulk photoluminescence of CVD and natural diamonds excited by ultrashort laser pulses of variable pulsewidth

Inter-band photoexcitation in bulk natural and synthetic diamonds by tightly focused near-IR (1030 nm) ultrashort laser pulses of variable duration (0.3–6.3 ps) promotes characteristic UV photoluminescence A-band and phonon-mediated free-exciton recombination bands, respectively, with distinct phonon progressions. The photoluminescence yield in these diamonds is very similar and highly-nonlinear versus laser intensity with the power slopes, gradually decreasing at higher intensities for all the laser pulsewidths to indicate varying contributions of multi-photon photoexcitation, free-carrier impact ionization and Auger recombination processes in electron-hole plasma (EHP). The peak position of the main free-excitonic photoluminescence band in the synthetic diamond demonstrates universal, pulsewidth-independent “red” spectral shift as a function of laser intensity, representing the electronic bandgap renormalization at the increasing plasma density. The related phonon progression indicates the predominating interaction of free carriers with near-center-zone optical phonons, exerting distinct dynamic increase in phonon energy at the increasing plasma density. Dynamic photoluminescence micro-spectroscopy appears as a simple, but informative experimental tool, paving the way to clarification and modeling of ultrafast electronic and lattice dynamics, as well as laser energy deposition, in different types of diamonds for their micromarking and tracing.

Dominant Role of Quantum Anharmonicity in the Stability and Optical Properties of Infinite Linear Acetylenic Carbon Chains.

Carbyne, an infinite-length straight chain of carbon atoms, is supposed to undergo a second order phase transition from the metallic bond-symmetric cumulene (═C═C═)∞ toward the distorted insulating polyyne chain (-C≡C-)∞ displaying bond-length alternation. However, recent synthesis of ultra long carbon chains (∼6000 atoms, [Nat. Mater., 2016, 15, 634]) did not show any phase transition and detected only the polyyne phase, in agreement with previous experiments on capped finite carbon chains. Here, by performing first-principles calculations, we show that quantum-anharmonicity reduces the energy gain of the polyyne phase with respect to the cumulene one by 71%. The magnitude of the bond-length alternation increases by increasing temperature, in stark contrast with a second order phase transition, confining the cumulene-to-polyyne transition to extremely high and unphysical temperatures. Finally, we predict that a high temperature insulator-to-metal transition occurs in the polyyne phase confined in insulating nanotubes with sufficiently large dielectric constant due to a giant quantum-anharmonic bandgap renormalization.

Origin of large magnetoresistance in the topological nonsymmorphic semimetal TaSe3

$\mathrm{Ta}{\mathrm{Se}}_{3}$ is a layered van der Waals semimetal with several inverted band gaps throughout the entire Brillouin zone and nontrivial ${Z}_{2}$ topological indices, which place it at the boundary between a strong and a weak topological phase. Our transport experiments reveal a quadratic nonsaturating magnetoresistance (MR) with values reaching ${10}^{4}$% at 1.8 K and 14 T, whose origins have to be searched in the material's band structure. Here we combine angle-resolved photoelectron spectroscopy experiments, also with spin resolution, with ab initio calculations based on density functional theory in order to draw a connection between the Fermi surface topology and the measured transport properties. Simulations based on the calculated Fermi surface clarify that electron-hole compensation plays an important role for the observed MR in the bulk material. At the surface, the position of Fermi level differs, and it can be controlled by alkali metal deposition which accounts not only for the energy shift of the bands but it slightly modifies the dispersion of the valence and conduction bands. We propose that the observed band-gap renormalization might offer a route for engineering the topological phase in $\mathrm{Ta}{\mathrm{Se}}_{3}$, alternative to strain.

Effects of many-body interactions on the transient optical properties of lead halide perovskites

Lead halide perovskites (LHPs) are emerging as promising candidates for use in various high-performance optoelectronic applications, yet their photophysics remains a topic of debate. Here, we theoretically investigated how the ultrafast optical properties of a few prototype LHPs are affected by many-body interactions, including the bandgap renormalization (BGR) effect, the band-filling (BF) effect, the free-carrier absorption effect, and the exciton effect, at carrier densities ranging from 1016 to 1019 cm−3. The results show that the exciton absorption becomes more obvious near the bandgap with increasing exciton energy (as the halogen component of the LHP is varied from I to Cl). Transient reflectivity results indicate that the signal has one peak below the bandgap as a result of the BGR effect at low carrier densities and one valley above the bandgap originating from the BF effect at high carrier densities. In addition, the absorbance decreases with increasing the carrier density as a result of the BF effect because the filled energy levels are observed at 2 meV above the bottom of the conduction band. The results of the present work are expected to promote the application of LHPs in solar cells, light-emitting diodes, and other photoelectric devices.

Nonlinear Optical Properties and Ultrafast Carrier Dynamics of 2D Indium Selenide Nanosheets

AbstractThis work reports the nonlinear optical properties and ultrafast carrier dynamics of indium selenide (InSe) nanosheets obtained via liquid‐phase exfoliation under pulsed excitation with different durations. InSe nanosheets exhibit a better saturable absorption response under 6 ns pulse excitation than that under 380 fs excitation. In addition, the scattering phenomena of InSe dispersions with different mechanisms under various pulse durations are discovered, which are caused by the thermal effect under ns pulse excitation and dynamic spatial self‐phase modulation affected by laser streaming under fs pulse excitation. The pump‐probe measurements reveal that the InSe dispersion has ultrafast saturable absorption and photoinduced absorption processes, which may be caused by free carrier absorption or bandgap renormalization.

Competitive screening and band gap renormalization in n -type monolayer transition metal dichalcogenides

Gate induced carriers impact the many-body interactions in monolayer transition metal dichalcogenides (TMDs) by modifying the screened Coulomb potential and renormalizing the band gap, thus influencing the strong excitonic effects in these materials. Using the $GW$ approximation and a plasmon pole theory to model the carrier induced plasmons in the frequency-dependent part of the screening, we accurately calculate the band gap renormalization of the electron doped monolayer ${\mathrm{MoS}}_{2}$ and ${\mathrm{WS}}_{2}$. The excitonic states of the low doped systems are calculated by solving the Bethe-Salpeter equation. Our results clarify the competition between screening and band gap renormalization. An exact cancellation occurs between the reduced band gap and the exciton binding energy for doped monolayer ${\mathrm{WS}}_{2}$, in good agreement with previous experimental results. In contrast, the exciton energy of doped monolayer ${\mathrm{MoS}}_{2}$ blueshifts by tens of meV. We show the role of the electronic band structure of the monolayers in the calculated exciton energies. Our results could be generally expanded to other monolayer TMDs and are helpful for quantitatively engineering optoelectronic devices with desired features.

Analyzing random lasing spectra of the zinc oxide bulk and the multiple quantum wells by empirical mode decomposition and fast Fourier transform

Empirical mode decomposition (EMD) was used to efficiently distinguish weak random-cavity emission from large broad spontaneous emission of the ZnO bulk and the multiple quantum wells (MQWs) structures. By fast Fourier transforming (FFT) the EMD results, we obtained the optical cavity lengths of random lasing and their corresponding emission intensity. With increasing pumping power, the EMD-FFT method confirms that the nonlinear trend of the random lasing emission in ZnO bulk and the change in optical cavity length is a result of change in refractive index dispersion due to the bandgap renormalization with high excited carrier density in nonpolar a-plane ZnO MQWs.

Quasiparticle band-gap renormalization in doped monolayer MoS2

The quasiparticle band-gap renormalization induced by the doped carriers is an important and well-known feature in two-dimensional semiconductors, including transition-metal dichalcogenides (TMDs), and it is of both theoretical and practical interest. To get a quantitative understanding of this effect, here we calculate the quasiparticle band-gap renormalization of the electron-doped monolayer MoS$_2$, a prototypical member of TMDs. The many-body electron-electron interaction induced renormalization of the self-energy is found within the random phase approximation and to account for the quasi-2D character of the Coulomb interaction in this system a Keldysh-type interaction with a nonlocal dielectric constant is used. Considering the renormalization of both the valence and the conduction bands, our calculations reveal a large and nonlinear band-gap renormalization upon adding free carriers to the conduction band. We find a 410 meV reduction of the band gap for the monolayer MoS$_2$ on SiO$_2$ substrate at the free carrier density $n=4.9\times 10^{12} \rm{cm^{-2}}$ which is in excellent agreement with available experimental results. We also discuss the role of exchange and correlation parts of the self-energy on the overall band-gap renormalization of the system. The strong dependence of the band-gap renormalization on the surrounding dielectric environment is also demonstrated in this work, and a much larger shrinkage of the band gap is predicted for the freestanding monolayer MoS$_2$.

The Schottky-Mott Rule Expanded for Two-Dimensional Semiconductors: Influence of Substrate Dielectric Screening.

A comprehensive understanding of the energy level alignment mechanisms between two-dimensional (2D) semiconductors and electrodes is currently lacking, but it is a prerequisite for tailoring the interface electronic properties to the requirements of device applications. Here, we use angle-resolved direct and inverse photoelectron spectroscopy to unravel the key factors that determine the level alignment at interfaces between a monolayer of the prototypical 2D semiconductor MoS2 and conductor, semiconductor, and insulator substrates. For substrate work function (Φsub) values below 4.5 eV we find that Fermi level pinning occurs, involving electron transfer to native MoS2 gap states below the conduction band. For Φsub above 4.5 eV, vacuum level alignment prevails but the charge injection barriers do not strictly follow the changes of Φsub as expected from the Schottky-Mott rule. Notably, even the trends of the injection barriers for holes and electrons are different. This is caused by the band gap renormalization of monolayer MoS2 by dielectric screening, which depends on the dielectric constant (εr) of the substrate. Based on these observations, we introduce an expanded Schottky-Mott rule that accounts for band gap renormalization by εr -dependent screening and show that it can accurately predict charge injection barriers for monolayer MoS2. It is proposed that the formalism of the expanded Schottky-Mott rule should be universally applicable for 2D semiconductors, provided that material-specific experimental benchmark data are available.

Unusual Temperature Dependence of Bandgap in 2D Inorganic Lead-Halide Perovskite Nanoplatelets.

Understanding the origin of temperature‐dependent bandgap in inorganic lead‐halide perovskites is essential and important for their applications in photovoltaics and optoelectronics. Herein, it is found that the temperature dependence of bandgap in CsPbBr3 perovskites is variable with material dimensionality. In contrast to the monotonous redshift ordinarily observed in bulk‐like CsPbBr3 nanocrystals (NCs), the bandgap of 2D CsPbBr3 nanoplatelets (NPLs) exhibits an initial blueshift then redshift trend with decreasing temperature (290–10 K). The Bose–Einstein two‐oscillator modeling manifests that the blueshift‐redshift crossover of bandgap in the NPLs is attributed to the significantly larger weight of contribution from electron‐optical phonon interaction to the bandgap renormalization in the NPLs than in the NCs. These new findings may gain deep insights into the origin of bandgap shift with temperature for both fundamentals and applications of perovskite semiconductor materials.

Bandgap control in two-dimensional semiconductors via coherent doping of plasmonic hot electrons

Bandgap control is of central importance for semiconductor technologies. The traditional means of control is to dope the lattice chemically, electrically or optically with charge carriers. Here, we demonstrate a widely tunable bandgap (renormalisation up to 550 meV at room-temperature) in two-dimensional (2D) semiconductors by coherently doping the lattice with plasmonic hot electrons. In particular, we integrate tungsten-disulfide (WS2) monolayers into a self-assembled plasmonic crystal, which enables coherent coupling between semiconductor excitons and plasmon resonances. Accompanying this process, the plasmon-induced hot electrons can repeatedly fill the WS2 conduction band, leading to population inversion and a significant reconstruction in band structures and exciton relaxations. Our findings provide an effective measure to engineer optical responses of 2D semiconductors, allowing flexibilities in design and optimisation of photonic and optoelectronic devices.

An excitonic model for the electron\u2013hole plasma relaxation in proton-irradiated insulators

The relaxation of free electron–hole pairs generated after proton irradiation is modelled by means of a simplified set of hydrodynamic equations. The model describes the coupled evolution of the electron–hole pair and self-trapped exciton (STE) densities, along with the electronic and lattice temperatures. The equilibration of the electronic and lattice excitations is based on the two-temperature model, while two mechanisms for the relaxation of free electron–hole pairs are considered: STE formation and Auger recombination. Coulomb screening and band gap renormalisation are also taken into account. Our numerical results show an ultrafast ({ll },{mathrm {1}} ps) free electron–hole pair relaxation time in amorphous {{mathrm {SiO}}_{mathrm {2}}} for initial carrier densities either below or above the exciton Mott transition. Coulomb screening alone is not found to yield the long relaxation time ({mathrm {gg }}{mathrm {10}} ps) experimentally observed in amorphous {{mathrm {SiO}}_{mathrm {2}}} and borosilicate crown glass BK7 irradiated with high-intensity laser pulses or BK7 irradiated by short proton pulses. Another mechanism, e.g. thermal detrapping of STEs, is required to correctly model the long free electron–hole pair relaxation time observed experimentally.Graphical

N - to p -type conductivity transition and band-gap renormalization in ZnO:(Cu+Te) codoped films

The natural conductivity of as-grown ZnO is $n$-type. It has been challenging to produce stable $p$-type material, which has delayed possible technological applications. In this work, the conductivity transformation from $n$- to $p$-type ZnO films deposited by sputtering was followed as a function of copper and tellurium concentrations and of the substrate temperature during growth (room temperature, $150{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}, 250{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$, and $350{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$). The nominal codopant concentrations ranged from 1 to 12 at %. For the minimum concentration, compensation effects yielded highly resistive ZnO. Nonetheless, by tailoring the concentration of Cu and Te, it was possible to vary the resistivity $({10}^{3}--{10}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})$, mobility $(\ensuremath{\sim}{10}^{\ensuremath{-}2}--{10}^{\ensuremath{\circ}}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{V}\phantom{\rule{0.16em}{0ex}}\mathrm{s})$, and free-hole density $({10}^{15}--{10}^{20}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3})$ of $p$-type ZnO grown at $250{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. Besides modifying the electrical properties, codoping changed the host band structure significantly, producing a band-gap renormalization from 3.2 eV (UV) to 1.8 eV (red). This control over the band gap is advantageous for applications where controllable photon absorption or emission are sought. Experimentally, films were stable for a period of at least six months. Band-gap engineered $p$-type ZnO:(Cu+Te) films open the possibility for the fabrication of all-ZnO optoelectronic devices such as homojunction solar cells and/or light-emitting diodes.

Giant Linear and Nonlinear Excitonic Responses in an Atomically Thin Indirect Semiconductor Nitrogen Phosphide

Large linear and nonlinear optical responses can be obtained from two-dimensional semiconductors with an indirect electronic gap. Here, we demonstrate exceptionally large exciton-driven responses such as the fundamental exciton binding energy (2 eV), zero-point band-gap renormalization (200 meV), and nonlinear second and third harmonic coefficients (800 pm/V and 1.4 × 10–18 m2/V2, respectively) from an atomically thin binary group-V nitrogen phosphide (NP) semiconductor. The influence of lattice vibrations on the absorption spectra unfolds strong electronic couplings to both LA and ZO-TO phonon modes. All the linear process analyses were computed using a fully ab initio-based G0W0 + Bethe–Salpeter equation approach that also includes the electron–phonon self-energies. The nonlinear processes were instead obtained using a real-time ab initio process flow after creating a coupling between the time-dependent external electric field and the correlated electrons within the modern theory of polarization and the same electron–hole interaction level.

Polaronic signatures in pristine phosphorene

We investigate polaronic effects in a monolayer black phosphorus (or phosphorene) due to the charge carrier--intrinsic phonons interaction. We employ a microscopic model to describe vibrational spectra and electron-phonon interactions within the tight-binding approach. Our adiabatic solution for polarons suggests the critical coupling constant of ${\ensuremath{\lambda}}_{c}=3.0$ for polaron self-trapping in this anisotropic material. We report nonadiabatic calculations for the band-gap renormalization and the effective mass enhancement as a function of temperature and a range of electron-phonon coupling strengths. Our results demonstrate a surprising large band-gap renormalization, even for the lower bound of the electron-phonon coupling strength reported in the literature. We find that optical phonons give the dominant contributions to the polaronic effect.

Dissecting Interlayer Hole and Electron Transfer in Transition Metal Dichalcogenide Heterostructures via Two-Dimensional Electronic Spectroscopy.

Monolayer transition metal dichalcogenides (ML-TMDs) are two-dimensional semiconductors that stack to form heterostructures (HSs) with tailored electronic and optical properties. TMD/TMD-HSs like WS2/MoS2 have type II band alignment and form long-lived (nanosecond) interlayer excitons following sub-100 fs interlayer charge transfer (ICT) from the photoexcited intralayer exciton. While many studies have demonstrated the ultrafast nature of ICT processes, we still lack a clear physical understanding of ICT due to the trade-off between temporal and frequency resolution in conventional transient absorption spectroscopy. Here, we perform two-dimensional electronic spectroscopy (2DES), a method with both high frequency and temporal resolution, on a large-area WS2/MoS2 HS where we unambiguously time resolve both interlayer hole and electron transfer with 34 ± 14 and 69 ± 9 fs time constants, respectively. We simultaneously resolve additional optoelectronic processes including band gap renormalization and intralayer exciton coupling. This study demonstrates the advantages of 2DES in comprehensively resolving ultrafast processes in TMD-HS, including ICT.