Valence Band Coupling Research Articles

Coherent electron dynamics in monolayer MoS2 under ultrashort optical pulse

A theoretical investigation on the coherent Dirac-like quasiparticle dynamics in monolayer $\text{MoS}_2$ under an ultrashort optical pulse irradiation is presented. Particularly, we remain specific features of ML-MDS associated with the mass asymmetry $\alpha$ and topological aspect $\beta$ parameters resulting in Schr$\stackrel{..}{\text{o}}$dinger type wavevector of charge carriers. The direct band gap, spin-resolved valence band spilitting and valley degeneracy breaking due to strong spin-orbit coupling affect ultrafast dynamics of Dirac fermions. Because the duration of the optical pulse is less than the electron scattering time, which is $\sim 10-100\ fs$, the electron dynamics in electric field of the optical pulse is coherent, and consequently, we can describe the coupling of electron with strong electromagnetic field by the time-dependent Schr$\stackrel{..}{\text{o}}$dinger equation. The conduction band and valence band coupling via the strong electric field of pulse ($0.2-2.5 \ V/\text{\AA}$) gives rise to appearance of a dipole moment during the pulse is applied. We find that the dipole is complex, originating from the existence of band gap. We show an asymmetric singularities in Dirac points for absolute of dipole moment. We solve the resulting coupled evolution equations for the expansion coefficient of valence and conduction bands to obtain probability of population transition between valence and conduction bands. The irreversible electron dynamics as a key feature of two-dimensional Dirac matters in interacting with an ultrashort pulse strongly depends on the electronic structure of $\text{MoS}_2$. Furthermore, we present conduction band population distribution with an asymmetric exhibition at the each pair of Dirac points ($K$ and $K'$), when the pulse ends. This leads to valley polarization effect.

Inversion of Zeeman splitting of exciton states in InGaAs quantum wells

Zeeman splitting of quantum-confined states of excitons in InGaAs quantum wells (QWs) is experimentally found to depend strongly on quantization energy. Moreover, it changes sign when the quantization energy increases with a decrease in the QW width. In the 87-nm QW, the sign change is observed for the excited quantum-confined states, which are above the ground state only by a few meV. A two-step approach for the numerical solution of the two-particle Schroedinger equation, taking into account the Coulomb interaction and valence-band coupling, is used for a theoretical justification of the observed phenomenon. The calculated variation of the g-factor convincingly follows the dependencies obtained in the experiments.

Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides

We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides $MX_2$ ($M$=Mo, W; $X$=S, Se, Te). As the conduction and valence band edges are predominantly contributed by the $d_{z^{2}}$, $d_{xy}$, and $d_{x^{2}-y^{2}}$ orbitals of $M$ atoms, the TB model is constructed using these three orbitals based on the symmetries of the monolayers. Parameters of the TB model are fitted from the first-principles energy bands for all $MX_2$ monolayers. The TB model involving only the nearest-neighbor $M$-$M$ hoppings is sufficient to capture the band-edge properties in the $\pm K$ valleys, including the energy dispersions as well as the Berry curvatures. The TB model involving up to the third-nearest-neighbor $M$-$M$ hoppings can well reproduce the energy bands in the entire Brillouin zone. Spin-orbit coupling in valence bands is well accounted for by including the on-site spin-orbit interactions of $M$ atoms. The conduction band also exhibits a small valley-dependent spin splitting which has an overall sign difference between Mo$X_{2}$ and W$X_{2}$. We discuss the origins of these corrections to the three-band model. The three-band TB model developed here is efficient to account for low-energy physics in $MX_2$ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.

Optical effects of spin currents in semiconductors

A spin current has novel linear and second-order nonlinear optical effects due to its symmetry properties. With the symmetry analysis and the eight-band microscopic calculation we have systematically investigated the interaction between a spin current and a polarized light beam (or the "photon spin current") in direct-gap semiconductors. This interaction is rooted in the intrinsic spin-orbit coupling in valence bands and does not rely on the Rashba or Dresselhaus effect. The light-spin current interaction results in an optical birefringence effect of the spin current. The symmetry analysis indicates that in a semiconductor with inversion symmetry, the linear birefringence effect vanishes and only the circular birefringence effect exists. The circular birefringence effect is similar to the Faraday rotation in magneto-optics but involves no net magnetization nor breaking the time-reversal symmetry. Moreover, a spin current can induce the second-order nonlinear optical processes due to the inversion-symmetry breaking. These findings form a basis of measuring a pure spin current where and when it flows with the standard optical spectroscopy, which may provide a toolbox to explore a wealth of physics connecting the spintronics and photonics.

Direct Optical Detection of a Pure Spin Current in Semiconductor

We predict that a pure spin current in a semiconductor may induce Faraday birefringence even without magnetization. The theory is based on a derived effective interaction between the spin current and a polarized light beam, where the helicity of a photon is mapped to spin 1/2. The effective coupling between the polarized light beam and electron spin current can be realized in direct-gap semiconductors such as GaAs with inherent spin–orbit coupling in valence bands, but it involves neither the Rashba nor the Dresselhaus effect of samples. We estimate the amplitude of the Faraday rotation due to a pure spin current, and we present its incident-beam-angle dependence. We show that this Faraday birefringence can be directly measured.

Proposal for Direct Measurement of a Pure Spin Current by a Polarized Light Beam

The photon helicity may be mapped to a spin-1/2, whereby we put forward an intrinsic interaction between a polarized light beam as a "photon spin current" and a pure spin current in a semiconductor, which arises from the spin-orbit coupling in valence bands as a pure relativity effect without involving the Rashba or the Dresselhaus effect due to inversion asymmetries. The interaction leads to linear and circular optical birefringence, which are similar to the Voigt effect and the Faraday rotation in magneto-optics but nevertheless involve no net magnetization. The birefringence effects provide a direct, nondemolition measurement of pure spin currents.

Size-dependent interband three-photon absorption properties of spherical CdTe quantumdots

The degenerate three-photon absorption coefficient and cross section associated with the interbandtransition 1S3/2(h)–1S(e) for CdTe spherical quantum dots have been calculated within the two-levelmodel. The band structure and wavefunctions are derived from the8 × 8 k·p Hamiltonian which takes into account the conduction–valence band coupling and themixing of the valence states. The transition selection rules for three-photon absorption inthe case of linearly polarized incident light are discussed in detail. The size-dependentthree-photon absorption spectra versus incident photon energy have been obtained andanalyzed.

Polarization of gain and symmetry breaking by interband coupling in quantum well lasers

We have studied the influence of conduction band–valence band coupling on the polarization of gain in quantum well (QW) lasers. As a reference we used the eight-band k∙p description of the gain polarization. Our eight-band k∙p model accounts for the crystal orientation, lack of inversion symmetry, strain induced deformation potentials, and piezoelectricity. We have studied both strained and unstrained (001) and (111) QWs. The results are compared with the transition dipole model of the gain polarization [M. Asada et al., IEEE J. Quantum Electron. 20, 745 (1984)], which is based on a phenomenological generalization of Kane’s [J. Phys. Chem. Solids 1, 249 (1957)] linear k∙p model of bulk crystals. We found a quantitative difference between our multiband model and the transition dipole model of Asada et al. The difference is addressed to lack of orthogonality between the transition dipole and the electron wave vectors. The orthogonality is broken outside the Γ point by both the QW heterostructure geometry and the interband coupling. Results obtained by the complete eight-band model are also compared with restricted multiband models excluding the conduction band.

Photon Green’s functions theory for Coulomb correlated quantum well lasers

A photon Green's function theory is used to incorporate Bethe-Salpeter-like many body corrections in the computations of output spectra of semiconductor quantum well lasers. Coulomb, quantum-confinement, multiple valence band coupling and cavity resonator effects are consistently included in the theory. Numerical results are presented for multiple quantum wells, under different design, and excitation conditions.

Magneto-optical properties of nanocrystals: Zeeman splitting

We discuss different aspects of the Zeeman splitting in optical properties of II-VI spherical quantum dots in presence of a external magnetic field B. A systematic study of the energy eigenvalues, wave functions, and their dominant symmetries within the $8\ifmmode\times\else\texttimes\fi{}8$ $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Kane-Weiler formalism, allowing the inclusion of the conduction- valence-band coupling, nonparabolicity, and mixing of the electronic and spin states, is presented. The analysis of symmetries inherent in the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Hamiltonian leads to sets of basis functions that can be separated into two independent Hilbert subspaces. The linear and quadratic Zeeman splitting in the quantum dot have been studied in the strong confinement regime. A detailed discussion of the symmetries associated with the electronic levels and the magneto-optical selection rules for interband transitions are derived. We also calculated the optical oscillator strengths and their corresponding magnetoabsorption coefficient for Faraday and Voigt configurations. It shows that the effective Land\'e g factor, obtained theoretically, and diamagnetic shift can be tested experimentally by complementary optical spectra measured in Faraday and Voigt geometries.

Effects of exciton–acoustic-phonon scattering on optical line shapes and exciton dephasing in semiconductors and semiconductor quantum wells

The interaction of excitons with acoustic phonons in direct band-gap semiconductors gives the dominant contribution to the temperature-dependent part of the exciton homogeneous linewidths and to dephasing rates at lower temperatures, e.g., below 150 K in bulk GaAs. Experimental results have shown that this contribution increases substantially in going from GaAs quantum wells to bulk GaAs. A perturbation treatment of acoustic phonon scattering in a simple band exciton model---i.e., neglecting valence-band coupling and anisotropy of exciton dispersion---agrees with experimental results in narrow quantum wells. On the other hand, it fails by an order of magnitude for bulk GaAs and by a large factor for other materials. Here we give a thorough theoretical discussion of this problem. The exciton linewidth is calculated to lowest order in the exciton--acoustic-phonon coupling including valence-band interactions and anisotropic exciton dispersion. The effects of multiple scatterings of phonons in higher orders of the exciton-phonon interactions are calculated and previous work on these effects are discussed. The effects of impurity motion from acoustic phonons on the exciton linewidths are evaluated. We conclude that the temperature-dependent exciton linewidth is given reasonably well by the lowest-order phonon scatterings provided that the full anisotropic exciton dispersion is included. Higher-order phonon scatterings give a small contribution to the linewidth and can affect the line shape. These results agree well with available experimental results for the low-temperature exciton linewidths in bulk GaAs and ZnSe and in quantum wells from these materials.

Modeling of Sb-based type-II quantum cascade lasers

The interband Sb-based quantum cascade lasers at mid-IR range are studied. A self-consistent method that solves the Schr\odinger's equation and Poisson's equation simultaneously to obtain the band structure and calculate the optical gain for type-II quantum cascade lasers is presented for the first time to the best of our knowledge. We start with the formulation of band structure based on the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ method with the inclusion of the conduction-band--valence-band coupling effect. The 8\ifmmode\times\else\texttimes\fi{}8 Hamiltonian for the k\ensuremath{\cdot}p method is block diagonalized into two 4\ifmmode\times\else\texttimes\fi{}4 blocks under the axial approximation. Explicit expressions for momentum-matrix elements for interband transitions are given. The optical gain formulation including many-body effects is then presented. The carrier accumulation in different layers and its screening effects are shown. For the lasers of our study, the carrier screening affects the peak gain wavelength by about 0.3 \ensuremath{\mu}m and the peak gain magnitude by 10%. The self-consistent model is shown to be important to give a good agreement with experimental data. The temperature dependence of the optical gain is also examined for the regular and the W-shaped type-II quantum-well structures. The optical gain for the W-shaped type-II quantum well is found to have a 50% enhancement over the regular type-II quantum well. Our model is important for designing high-power, high-efficiency, and high-temperature type-II interband cascade lasers.

Electronic states in a quantum lens

We present a model to find analytically the electronic states in self-assembled quantum dots with a truncated spherical cap (``lens'') geometry. A conformal analytical image is designed to map the quantum dot boundary into a dot with semispherical shape. The Hamiltonian for a carrier confined in the quantum lens is correspondingly mapped into an equivalent operator and its eigenvalues and eigenfunctions for the corresponding Dirichlet problem are analyzed. A modified Rayleigh-Schr\"odinger perturbation theory is presented to obtain analytical expressions for the energy levels and wave functions as a function of the spherical cap height b and radius a of the circular cross section. Calculations for a hard wall confinement potential are presented, and the effect of decreasing symmetry on the energy values and eigenfunctions of the lens-shape quantum dot is studied. As the degeneracies of a semicircular geometry are broken for $b\ensuremath{\ne}a,$ our perturbation approach allows tracking of the split states. Energy states and electronic wave functions with $m=0$ present the most pronounced influence on the reduction of the lens height. The method and expressions presented here can be straightforwardly extended to deal with more general Hamiltonians, including strains and valence-band coupling effects in Group III--V and Group II--VI self-assembled quantum dots.

The valence-band coupling effect on Fano profiles of magnetoexcitons in semiconductor quantum wells

The Fano profile of a magnetoexciton in a quantum well is investigated, based on the diabatic three-channel model. Both the Coulomb coupling and the valence-band coupling have conspicuous effects on the line-profile. The former coupling is responsible for the prominent asymmetric profile, having both a peak and a dip characteristic of the Fano resonance, whereas the latter one blurs the asymmetry and eventually smears the peak- and-dip structure. Such an effect of the valence-band coupling is analyzed in terms of the multi-channel resonant scattering theory.

Exchange-correlation energy of a hole gas including valence band coupling

We have calculated an accurate exchange-correlation energy of a hole gas, including the complexities related to the valence band coupling as occurring in semiconductors like GaAs, but excluding the band warping. A parametrization for the dependence on the density and the ratio between light- and heavy-hole masses is given. We apply our results to a hole gas in an ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}$As quantum well and calculate the two-dimensional band structure and the band-gap renormalization. The inclusion of the valence band coupling in the calculation of the exchange-correlation potentials for holes and electrons leads to a much better agreement between theoretical and experimental data than when it is omitted.

Magnetoluminescence from strain-induced quantum dots

We have calculated the effects of valence-band coupling on the magnetoluminescence spectra from an ${\mathrm{In}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As/GaAs quantum-well dot induced by an InP stressor island. The theory is based on the single-particle Luttinger-Kohn Hamiltonian using a realistic confinement potential. The band coupling strongly influences the calculated spectra. The numerical results were compared with experiments and a good agreement was obtained. Numerical results predict a reversal of the mesoscopic Zeeman splitting for the ground state and an avoided crossing of excited states.

Effect of disorder-induced band mixing on the conduction-band effective mass of InAlGaAs alloys lattice matched to InP

It is found that the calculation of the effective mass for InAlGaAs alloys obtained from the five-band k⋅p theory is smaller than the measured value from the optically detected cyclotron resonance reported recently. We point out that the effect of disorder-induced conduction valence band mixing must be considered. This disorder effect which creates potential fluctuations is to reduce the matrix element P2 for the conduction valence band coupling in the k⋅p theoretical expression. The strength of the potential fluctuations can be described in terms of the electronegativity difference related to chemical disorder. The inclusion of the disorder effect in the (In0.53Al0.47As)x(In0.53Ga0.47As)1−x quaternary system gives a very good fit to the measured data.

Size dependence of lateral quantum-confinement effects of the optical response in In0.53Ga0.47As/InP quantum wires.

The size dependence of various aspects of quantum-confinement effects in ${\mathrm{In}}_{0.53}$${\mathrm{Ga}}_{0.47}$As/InP quantum wires was quantitatively examined through photoluminescence experiments with and without magnetic field, along with theoretical calculation. The wires were fabricated by combining electron-beam lithography and reverse-mesa wet etching, thus enabling us to easily control the lateral size independently of the vertical size. Photoluminescence experiments showed distinct peak shifts with changes in the lateral size and showed a shoulder structure that is attributed to laterally quantized second subbands. The energy shift of both levels is explained by a detailed theoretical calculation that incorporates conduction-band nonparabolicity, valence-band coupling, and excitonic correction. The lateral quantum confinement is also demonstrated by the magnetic-field effect on the luminescence spectrum, in which we can distinguish the lateral quantum effects from other factors. As magnetic-field strength increases, a transition from quantum-confined subbands to Landau subbands was clearly observed for first and second subbands. At high excitation levels, the quenching of higher Landau levels was observed. In-plane and perpendicular-to-plane anisotropy of polarization in luminescence was also investigated and the size dependence of this anisotropy in both directions is largely explained by the calculated lateral confinement effect of the optical-transition matrix elements. The phenomenon observed for narrower wires, however, cannot be explained by our theory and is thought to be due to wave-function localization.

Hot carrier dynamics near the Fermi edge of n-doped GaAs

Femtosecond bleaching measurements are performed in n-doped GaAs at both 300 K and 14 K using low densities of carriers injected at 2 eV. The dwell time of electrons excited far above the Fermi sea is reduced because of hot-electron/cold-electron interactions. The response at 14 K is much stronger and slower than that at 300 K. This is attributed to: (i) the proximity to the Fermi level of the conduction band states probed via split-off valence band coupling; (ii) slow Landau damping of non-equilibrium plasmons, primarily by the minority holes which then heat the majority electrons.

Valence-band coupling in thin (Ga,In)As-AlAs strained quantum wells.

Model representations of varying complexity are used to describe the band structure of semiconductor quantum wells and superlattices. However, the physics of valence-band-confined states is usually restricted to the upper ${\mathrm{\ensuremath{\Gamma}}}_{8}^{\mathit{v}}$ band. We report spectroscopic measurements of the light- to heavy-hole splitting in (Ga,In)As-AlAs strained multiple quantum wells. The results are compared to two types of theoretical calculations: (i) within the framework of the usual approximations, and (ii) taking account of the ${\mathrm{\ensuremath{\Gamma}}}_{7}^{\mathit{v}}$ split-off states, which are mixed with the light-hole ones. We demonstrate the crucial influence of the valence-band coupling, by a significant improvement of the agreement between theory and experiments. Competitive effects of thicknesses, potential-well depths, and magnitude of the ${\mathrm{\ensuremath{\Gamma}}}_{8}^{\mathit{v}\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\Gamma}}}_{7}^{\mathit{v}}$ splitting are detailed and discussed.