Electron-hole Coulomb Attraction Research Articles

Anomalous non-equilibrium response in black phosphorus to sub-gap mid-infrared excitation

The competition between the electron-hole Coulomb attraction and the 3D dielectric screening dictates the optical properties of layered semiconductors. In low-dimensional materials, the equilibrium dielectric environment can be significantly altered by the ultrafast excitation of photo-carriers, leading to renormalized band gap and exciton binding energies. Recently, black phosphorus emerged as a 2D material with strongly layer-dependent electronic properties. Here, we resolve the response of bulk black phosphorus to mid-infrared pulses tuned across the band gap. We find that, while above-gap excitation leads to a broadband light-induced transparency, sub-gap pulses drive an anomalous response, peaked at the single-layer exciton resonance. With the support of DFT calculations, we tentatively ascribe this experimental evidence to a non-adiabatic modification of the screening environment. Our work heralds the non-adiabatic optical manipulation of the electronic properties of 2D materials, which is of great relevance for the engineering of versatile van der Waals materials.

Coulomb mechanism of Raman radiation in graphene

The phenomena of single-layer graphene resonant photoluminescence and Raman radiation are discussed taking into account the photo-generated electron–hole Coulomb interaction. On the base of general principles of a many-particle interactions and the interband resonance optical transitions a photon radiation new mechanism (Coulomb mechanism) is proposed. Through Stokes 2D'-mode particular case analysis has shown that the graphene photoluminescence and the resonant Raman radiation are characterized by the same frequency shifts. Probabilities of resonance photo-radiation processes have been presented where the electron–hole Coulomb attraction has been taken into account. The probabilities are the same fourth-order small values. The weak photo-radiation Coulomb mechanism has a common character. It is applicable to both zero and nonzero band gap crystals.

Ballistic photocurrents in semiconductor quantum wells caused by the excitation of asymmetric excitons

We theoretically investigate the generation and dynamics of photocurrents induced by linearly polarized single-frequency light pulses in GaAs quantum wells. Our approach is based on the multiband semiconductor Bloch equations (SBE) formulated in the basis of eigenfunctions on the 14-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model and includes excitonic effects and carrier longitudinal-optical-phonon scattering processes. By solving the SBE, we obtain both shift and ballistic currents. For a particular excitation geometry, we obtain a ballistic current which is absent if the electron-hole attraction is neglected. Whereas in other cases excitonic effects quantitatively modify photocurrents that originate from single-particle properties, here we demonstrate the existence of a ballistic current which is absent in single-particle calculations. This photocurrent is of second order in the light-matter interaction and is purely caused by the asymmetric electron-hole Coulomb attraction that results from the inversion asymmetry of GaAs. Furthermore, we show that the coherent dynamics of excitonic wave packets gives rise to oscillations in the photocurrent transients.

Anisotropic excitons and their contributions to shift current transients in bulk GaAs

Shift current transient are obtained for near band gap excitation of bulk GaAs by numerical solutions of the semiconductor Bloch equations in a basis obtained from a 14 band k.p model of the band structure. This approach provides a transparent description of the optically induced excitations in terms of interband, intersubband, and intraband excitations which enables a clear distinction between different contributions to the shift current transients and fully includes resonant as well as off-resonant processes. Using a geodesic grid in reciprocal space in our numerical solutions, we are able to include the electron-hole Coulomb attraction in combination with our anisotropic three-dimensional band structure. We obtain an excitonic absorption peak and an enhancement of the continuum absorption and demonstrate that the excitonic wave function contains a significant amount of anisotropy. Optical excitation at the excitonic resonance generates shift current transients of significant strength, however, due to the electron-hole attraction the shift distance is smaller than for above band gap excitation. We thus demonstrate that our approach is able to provide important information on the ultrafast electron dynamics on the atomic scale.

Influence of Coulomb-induced band couplings on linear excitonic absorption spectra of semiconducting carbon nanotubes

Starting from the extended Su-Schrieffer-Heeger model, multiband semiconductor Bloch equations are formulated in momentum space and applied to the analysis of the linear optical response of semiconducting carbon nanotubes (SCNTs). This formalism includes the coupling of electron-hole pair excitations between different valence and conduction bands, originating from the electron-hole Coulomb attraction. The influence of these couplings, which are referred to as nondiagonal interband Coulomb interaction (NDI-CI), on the linear excitonic absorption spectra is investigated and discussed for light fields polarized parallel to the tube direction. The results show that the intervalley NDI-CI leads to a significant increase of the band gap and a decrease of the exciton binding energy that results in a blueshift of the lowest-frequency excitonic absorption peak. The strength of these effects depends on the symmetry of the SCNT. Furthermore, for zigzag SCNTs with higher symmetry other nonintervalley NDI-CI terms also affect the spectral positions of excitonic absorption peaks.

Atomistic Calculation of Coulomb Interactions in Semiconductor Nanocrystals: Role of Surface Passivation and Composition Details

We report a theoretical investigation of electronic properties of semiconductor InAs and GaAs nanocrystals. Our calculation scheme starts with the single particle calculation using atomistic tight-binding model including spin orbital interaction and d-orbitals. Then the exciton binding energies are calculated with screened Coulomb interaction. We study the role of surface passivation e ects by varying value of surface passivation potential. We compare results obtained with dot center positioned on di erent lattice sites thus containing di erent number of anion and cations. We conclude that passivation of surface states a ects signi cantly single particle energies and the value of electron hole Coulomb attraction. Interestingly, due to limited screening, the short-range (on-site) contribution to the electron hole Coulomb attraction plays signi cant role for small nanocrystals with radius smaller than 1 nm.

Magnetoexcitons in electron-hole bilayer nanotubes made of rolled-up type-II band aligned quantum wells

A new Aharonov–Bohm (AB) system based on spatially separated electron-hole bilayer nanotubes made of rolled-up type-II band aligned AlAs/GaAs quantum wells for observation of the so-called excitonic AB-effect is theoretically investigated. Our results explain how the AB oscillations are manifested in both the spectrum and optical intensity of the exciton through angular momentum transitions from zero to successive nonzero values and persistent fluctuations, respectively. We attribute the former regular transitions and later undamped oscillations to the radial and axial charge separation appeared in the electron-hole Coulomb attraction, respectively. The impact of the magnetic field on the binding energy, magnetization, and energy-shift in the magnetoexciton is examined as well. Such study lead to the proposal that electron-hole bilayer nanotubes of type-II could be utilized as magneto-optical switching devices based on the AB-effect which may have potential applications in quantum information systems.

Physical theory of excitons in conducting polymers

In this tutorial review, we cover the solid state physics approach to electronic and optical properties of conducting polymers. We attempt to bring together languages and advantages of the solid state theory for polymers and of the quantum chemistry for monomers. We consider polymers as generic one-dimensional semiconductors with features of strongly correlated electronic systems. Our model combines the long range electron-hole Coulomb attraction with a specific effect of strong intra-monomer electronic correlations, which results in effective intra-monomer electron-hole repulsion. Our approach allows to go beyond the single-chain picture and to compare excitons for polymers in solutions and in films. The approach helps connecting such different questions as shallow singlet and deep triplet excitons, stronger binding of interchain excitons in films, crossings of excitons' branches, 1/N energies shifts in oligomers. We describe a strong suppression of the luminescence from free charge carriers by long-range Coulomb interactions. Main attention is devoted to the most requested in applications phenyl based polymers. The specifics of the benzene ring monomer give rise to existence of three possible types of excitons: Wannier-Mott, Frenkel and intermediate ones. We discuss experimental manifestations of various excitons and of their transformations. We touch effects of the time-resolved self-trapping by libron modes leading to formation of torsion polarons.

Impacts of structural asymmetry on the magnetic response of excitons and biexcitons in single self-assembled In(Ga)As quantum rings

The diamagnetic shifts of neutral excitons and biexcitons confined in single self-assembled In(Ga)As/GaAs quantum rings are investigated. Unlike quantum dots, quantum rings reveal a considerably large biexciton diamagnetic shift, about two times larger than that of single excitons. Based on model calculations, we found that the inherent structural asymmetry and imperfection, combined with the interparticle Coulomb interactions, is the fundamental cause of the more extended biexciton wave function in the quantum rings. The exciton wave function tends to be localized in one of the potential valleys induced by structural imperfections of the quantum ring due to the strong localization of hole and the electron-hole Coulomb attraction, resembling the behavior in single dots. Our results suggest that the phase coherence of neutral excitons in quantum rings will be smeared out by such wave function localizations.

Coulomb-interaction effects on the electronic structure of radially polarized excitons in nanorings

The electronic structure of radially polarized excitons in structured nanorings is analyzed, with emphasis in the ground-state properties and their dependence under applied magnetic fields perpendicular to the ring plane. The electron-hole Coulomb attraction has been treated rigorously, through numerical diagonalization of the full exciton Hamiltonian in the non-interacting electron-hole pairs basis. Depending on the relative weight of the kinetic energy and Coulomb contributions, the ground-state of polarized excitons has "extended" or "localized" features. In the first case, corresponding to small rings dominated by the kinetic energy, the ground-state shows Aharonov-Bohm (AB) oscillations due to the individual orbits of the building particles of the exciton. In the localized regime, corresponding to large rings dominated by the Coulomb interaction, the only remaining AB oscillations are due to the magnetic flux trapped between the electron and hole orbits. This dependence of the exciton, a neutral excitation, on the flux difference confirms this feature as a signature of Coulomb dominated polarized excitons. Analytical approximations are provided in both regimens, which accurate reproduce the numerical results.

Size-dependent single-particle energy levels and interparticle Coulomb interactions in CdSe quantum dots measured by scanning tunneling spectroscopy

We report on tunneling spectroscopy measurements on colloidal CdSe quantum dots of different sizes. The size-dependent energy level structure and electron-hole Coulomb attraction in CdSe quantum dots are obtained by a combination of shell-tunneling spectroscopy and optical spectroscopy. The results are in good agreement with tight-binding calculations. The electron-electron interactions are investigated by shell-filling spectroscopy. The tunneling spectra in this regime are analyzed by solving the master equation for the electron and hole occupancy of the quantum dot.

Stability of magnetic polaron states in two-dimensional semimagnetic heterostructures.

The problem of centrosymmetric-heavy-hole-state stability in a quantum well with semimagnetic barriers is considered. We show that the hole state centered in the middle of the well can become unstable during magnetic polaron formation. We found that in the case of an experimentally observed two-dimensional exciton magnetic polaron such a transition is prevented mainly due to the electron-hole Coulomb attraction. We established the fact that the criterion for centrosymmetric-hole-state stability is strongly influenced by value and orientation of the external magnetic fields applied to the system. A heavy-hole transition to the state attributed to one of two heterointerfaces is expected to occur in CdTe/(Cd,Mn)Te quantum wells at liquid-helium temperature in the presence of a magnetic field normal to the quantum-well plane. We found that the sensitivity of the heavy-hole wave function to the external electric field varies dramatically during magnetic polaron formation.

Spin-superlattice formation in a type-II ZnSe/Zn0.96Fe0.04Se multiple-quantum-well structure.

We have investigated the carrier spin segregation process in a ZnSe/${\mathrm{Zn}}_{0.96}$${\mathrm{Fe}}_{0.04}$Se quantum-well structure by studying the energy and relative intensity of the ground-state exciton components as a function of applied magnetic field. The ${\mathit{e}}_{1}$${\mathit{h}}_{1}$ heavy-hole exciton initially tends towards type-II behavior as the field is applied but the trend reverses itself at higher fields as the conduction-band splitting of the magnetic barriers becomes significant. The interplay between the electron-hole Coulomb attraction and the tunable type-II confining potentials is described in the context of a variational model.

Electrons and excitons in an imperfect superlattice in electric fields

We present variational calculations of excitonic states in a superlattice coupled with a wide quantum well in electric fields. The electronic states in the structure are analyzed by using both exact solutions of the one-dimensional Schrödinger equation and the simple tight-binding approximation. We demonstrate the latter method to be well applicable to calculating and designing complicated irregular superlattices. The electron spectrum can be conveniently interpreted as a result of field-induced mixing and anticrossing of electron quantized states in the enlarged quantum well with non-equidistant Stark-ladder states in the semi-infinite ideal superlattice. The electron-hole Coulomb attraction results in a relative redistribution between the extended and the localized states in the exciton. The allowance for this redistribution has a particularly strong influence upon the exciton oscillator strength and radiative lifetime.

Formation of magnetic polarons bound to interfaces in quantum wells with semimagnetic barriers

It is shown that the hole state centred in the middle of the well can become unstable during magnetic polaron formation resulting in a polaron state connected with an interface. The criterion of formation of interface-trapped polarons in a quantum well with semimagnetic barriers is found. We have shown that in the case of the experimentally observed two-dimensional exciton magnetic polaron, interface trapping is prevented mainly due to the electron-hole Coulomb attraction. The effect of an external magnetic field on the stability criterion is also considered.

Confinement of excitons in quantum dots.

A theoretical study of exciton confinement in small CdS and ZnS quantum dots is reported. In our calculational scheme the hole is described by an effective bond-orbital model that accounts for the valence-band degeneracy in bulk semiconductors. The electron is described with a single-band effective-mass approximation. The confining quantum-dot potentials for the hole and electron are modeled as spherically symmetric potential wells with finite barrier heights. The electron-hole Coulomb attraction is included, and exciton energies are obtained variationally in an iterative Hartree scheme. Exciton energies for dot diameters in the range 10--80 \AA{} are calculated and compared with experimental data and other theoretical results.

Optical dephasing in disordered semiconductors

Photon echo experiments in disordered bulk alloy semiconductors yield a remarkably large range of irreversible decay rates of the optical polarization. In particular, the alloys CdSSe and AlGaAs were studied. The interpretation of the experimental findings is based on a theory which simultaneously treats the interaction of excitations, including the electron-hole Coulomb attraction, with static disorder and with phonons. It is pointed out that the influences of disorder and of electron-phonon coupling on optical phase coherence are strongly interrelated.

Influence of Coulomb interaction on the photon echo in disordered semiconductors.

The photon-echo signal in disordered semiconductors is treated including the electron-hole Coulomb attraction. The amplitude of the spontaneous photon echo is calculated up to third order in the external-field amplitude using the semiconductor Bloch equations. Several idealized situations are analyzed showing the significance of a critical correlation of the polarization dynamics in the two time intervals preceding and following the second excitation pulse. Strong photon-echo decay is predicted for short-range disorder without Coulomb interaction. The inclusion of electron-hole attraction leads to a stabilization of the echo signal. For the case of long-range disorder with Coulomb interaction, we predict slow decay in the diffusive limit.

Ge-Aqueous-Electrolyte Interface: Electrical Properties and Electroreflectance at the Fundamental Direct Threshold

Electroreflectance (ER) measurements at the ${\ensuremath{\Gamma}}_{8+}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{7\ensuremath{-}}$ (fundamental direct) threshold are combined with electrical measurements in a detailed investigation of the nearly intrinsic Ge---neutral-aqueous-electrolyte interface. Capacitance and photovoltage (PV) measurements are combined to determine the flat-band potential and the impurity concentration of the space-charge region. These measurements show that no fast surface states are present for moderate modulating voltages for which the surface remains nondegenerate, and they allow the surface field to be calculated accurately over this range of surface potential. The instantaneous PV response shows that the Dember potential obeys quasiequilibrium equations for time intervals as short as 4 \ensuremath{\mu}sec. ER spectra are taken concurrently with measurements of the semiconductor surface field, yielding spectra suitable for quantitative interpretation. The very good agreement between these electrolyte and previously measured field-effect ER spectra indicates that the electrolyte ER spectra originate in the semiconductor, and demonstrates the equivalence of the two measurement techniques for this interface. By direct observation of the instantaneous reflectivity response, it is shown that surface states, generated electrochemically if intrinsic Ge is modulated beyond near-degeneracy (${\ensuremath{\phi}}_{s}\ensuremath{\gtrsim}300$ mV), seriously influence observed ER spectra. The low-field measurements possible with the electrolyte technique indicate that the ER spectra do not vanish identically at flat band (zero surface potential and field) for symmetric modulation of intrinsic material, as expected, but rather reach a minimum for slightly $p$-type surfaces (${\ensuremath{\phi}}_{s}=17$ mV, $\mathcal{E}\ensuremath{\cong}260$ V/cm). The amplitudes of the observed ER spectra exceed the predictions of the Franz-Keldysh theory by over an order of magnitude at all fields, providing strong evidence of enhancement by the electron-hole Coulomb attraction and substantiating previous conclusions obtained primarily on the basis of line-shape arguments. It is shown that sufficient strength to produce the observed low-field ER spectra can come only from the $n=1$ exciton absorption lines which lose their discrete nature at room temperature and behave as continuous states. The qualitative success of the inhomogeneous perturbation theory in describing line-shape evolution with increasing field appears to be due to the similarity of Franz-Keldysh and modulated continuum-exciton line shapes, together with a common dependence on the characteristic energy $\ensuremath{\hbar}\ensuremath{\Omega}$. A lifetime broadening of 1.8 \ifmmode\pm\else\textpm\fi{} 0.5 meV is deduced for this transition.

Ge-Aqueous-Electrolyte Interface: Electrical Properties and Electroreflectance at the Fundamental Direct Threshold

Electroreflectance (ER) measurements at the ${\ensuremath{\Gamma}}_{8+}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{7\ensuremath{-}}$ (fundamental direct) threshold are combined with electrical measurements in a detailed investigation of the nearly intrinsic Ge---neutral-aqueous-electrolyte interface. Capacitance and photovoltage (PV) measurements are combined to determine the flat-band potential and the impurity concentration of the space-charge region. These measurements show that no fast surface states are present for moderate modulating voltages for which the surface remains nondegenerate, and they allow the surface field to be calculated accurately over this range of surface potential. The instantaneous PV response shows that the Dember potential obeys quasiequilibrium equations for time intervals as short as 4 \ensuremath{\mu}sec. ER spectra are taken concurrently with measurements of the semiconductor surface field, yielding spectra suitable for quantitative interpretation. The very good agreement between these electrolyte and previously measured field-effect ER spectra indicates that the electrolyte ER spectra originate in the semiconductor, and demonstrates the equivalence of the two measurement techniques for this interface. By direct observation of the instantaneous reflectivity response, it is shown that surface states, generated electrochemically if intrinsic Ge is modulated beyond near-degeneracy (${\ensuremath{\phi}}_{s}\ensuremath{\gtrsim}300$ mV), seriously influence observed ER spectra. The low-field measurements possible with the electrolyte technique indicate that the ER spectra do not vanish identically at flat band (zero surface potential and field) for symmetric modulation of intrinsic material, as expected, but rather reach a minimum for slightly $p$-type surfaces (${\ensuremath{\phi}}_{s}=17$ mV, $\mathcal{E}\ensuremath{\cong}260$ V/cm). The amplitudes of the observed ER spectra exceed the predictions of the Franz-Keldysh theory by over an order of magnitude at all fields, providing strong evidence of enhancement by the electron-hole Coulomb attraction and substantiating previous conclusions obtained primarily on the basis of line-shape arguments. It is shown that sufficient strength to produce the observed low-field ER spectra can come only from the $n=1$ exciton absorption lines which lose their discrete nature at room temperature and behave as continuous states. The qualitative success of the inhomogeneous perturbation theory in describing line-shape evolution with increasing field appears to be due to the similarity of Franz-Keldysh and modulated continuum-exciton line shapes, together with a common dependence on the characteristic energy $\ensuremath{\hbar}\ensuremath{\Omega}$. A lifetime broadening of 1.8 \ifmmode\pm\else\textpm\fi{} 0.5 meV is deduced for this transition.