Wannier-Stark Regime Research Articles

Low-field onset of Wannier-Stark localization in a polycrystalline hybrid organic inorganic perovskite

Methylammonium lead iodide perovskite (MAPbI3) is renowned for an impressive power conversion efficiency rise and cost-effective fabrication for photovoltaics. In this work, we demonstrate that polycrystalline MAPbI3s undergo drastic changes in optical properties at moderate field strengths with an ultrafast response time, via transient Wannier Stark localization. The distinct band structure of this material - the large lattice periodicity, the narrow electronic energy bandwidths, and the coincidence of these two along the same high-symmetry direction – enables relatively weak fields to bring this material into the Wannier Stark regime. Its polycrystalline nature is not detrimental to the optical switching performance of the material, since the least dispersive direction of the band structure dominates the contribution to the optical response, which favors low-cost fabrication. Together with the outstanding photophysical properties of MAPbI3, this finding highlights the great potential of this material in ultrafast light modulation and novel photonic applications.

Signatures of transient Wannier-Stark localization in bulk gallium arsenide

Many properties of solids result from the fact that in a periodic crystal structure, electronic wave functions are delocalized over many lattice sites. Electrons should become increasingly localized when a strong electric field is applied. So far, this Wannier–Stark regime has been reached only in artificial superlattices. Here we show that extremely transient bias over the few-femtosecond period of phase-stable mid-infrared pulses may localize electrons even in a bulk semiconductor like GaAs. The complicated band structure of a three-dimensional crystal leads to a strong blurring of field-dependent steps in the Wannier–Stark ladder. Only the central step emerges strongly in interband electro-absorption because its energetic position is dictated by the electronic structure at an atomic level and therefore insensitive to the external bias. In this way, we demonstrate an extreme state of matter with potential applications due to e.g., its giant optical non-linearity or extremely high chemical reactivity.

Dephasing of Bloch oscillating electrons in GaAs-based superlattices due to interface roughness scattering

We have investigated dephasing mechanisms of Bloch oscillating electrons in GaAs-based superlattices (SLs) by time-domain terahertz electro-optic sampling method. It was found that dephasing time τr for GaAs∕AlAs SLs in the Wannier-Stark regime rapidly becomes shorter with decreasing well width Lw as τr∝Lw3−5. The observed strong Lw dependence of τr indicates that the dominant dephasing mechanism is interface roughness scattering, which was indeed confirmed by quantitative comparison between theory and experiment. It was also found that alloy disorder scattering is negligibly weak even in the case of GaAs∕Al0.3Ga0.7As SLs.

Monte Carlo investigation of drift and diffusion in semiconductor superlattices in the Wannier-Stark regime

Monte Carlo investigation of drift and diffusion in semiconductor superlattices in the Wannier-Stark regime

Scattering-assisted electric current in semiconductor superlattices in the Wannier-Stark regime

We have used the Monte Carlo technique to investigate the mechanism of scattering-assisted charge transport in semiconductor superlattices under a strong applied electric field in the Wannier-Stark (WS) regime. The distribution function of quasi-two-dimensional carriers localized in each WS level is calculated, and the contributions of different scattering mechanisms to the total scattering probability are analyzed. Based on these results, the drift velocity is derived as a function of the applied electric field. Due to the LO-phonon-induced resonant transfer of electrons between different spatially localized WS states, our calculated I-V characteristics oscillates with clear negative differential velocity behavior. At the electric field strength such that the Bloch oscillation energy is equal to an integer multiple of the LO phonon energy, a peak appears in the I-V curve. Our theoretical result agrees with the experimental data which was obtained from analyzing the terahertz response of superlattices to picosecond optical pulse excitation. (Less)

Time-resolved terahertz emission spectroscopy of wide miniband GaAs/AlGaAs superlattices

We have investigated terahertz (THz) emission due to dynamical electron transport in wide miniband GaAs/Al0.3Ga0.7As superlattices by time-resolved THz emission spectroscopy. Quasiautocorrelation measurements were performed on the emitted THz electromagnetic waves by using a bolometer as a wideband detector. The bias-field dependence of the emitted THz radiation intensity clearly showed a crossover from the miniband transport to the formation of Wannier–Stark ladder. In the Wannier–Stark regime, a few cycle Bloch oscillations were observed even at 300 K in a superlattice whose miniband width is greater than the longitudinal optical phonon energy. Furthermore, it has been found that clear Bloch oscillations are visible only when the bottom of the miniband is photoexcited.

Triple-, double-, and fractionally-spaced Wannier–Stark ladders

The concept of Wannier–Stark (WS) quantization literally refers to infinite crystals or bulk electron states. In real finite crystals, the bulk and edge or surface states always coexist. Moreover, when the surface states are already considerably localized due to the presence of a constant electric field, the WS ladder (WSL) and hence the WS localization may not yet come into play, at least, in the canonical form of WS quantization Ej=const±jϵ, j=0,1,2,… (Ej is the one-electron energy, and the parameter ϵ is associated with the electric field strength). We show that at certain voltages Vm, m=3,4,…, which are lower than V∞ needed for the WS band opening (the sub-WS regime), the mid-spectrum levels can form triple-, double-, and fractional-spaced WSLs, where El=±l[1+2/(m−2)]ϵm. It is also found that in the WS regime, the quantization of surface localized states (sls) smoothly changes from the Airy type (at the spectrum edges) to the WS type with a pronounced energy interval in between, where the level spacing doubles that of canonical WSL. Possible experimental manifestations of predicted effects are also outlined.

Excitonic influences on the anticrossing gap of Wannier–Stark levels in a wide well superlattice

In this paper we compare different theoretical calculations with experimental data of anticrossings of a wide well semiconductor superlattice in the Wannier–Stark regime. Calculations have been performed by using a variation method and a numerical method. For the variation method we used different approaches to minimize energy. With the numerical model, continuum states were calculated and anticrossing of 1s states with continuum states were found. Calculations have been performed for h1e1(0)–h1e2(−1) and h1e1(1)–h1e2(0) anticrossings and are compared with data from photocurrent experiments.

Transitions between Wannier-Stark States of a Superlattice at High Magnetic Field

Conduction of electrons through the quantum wells of a Landau level-quantised superlattice in the Wannier-Stark regime is investigated. We observe features in the current–voltage characteristics which arise from quasi-elastic processes in which electrons tunnel (hop) across as many as four superlattice periods. These transitions occur with a change of Landau level index and are observed together with the previously-studied nearest-neighbour well transitions. We investigate the temperature dependence of these processes.

Excitons in superlattices: Absorption asymmetry, dimensionality transition, and exciton localization

We calculate the field-dependent excitonic absorption spectra of semiconductor superlattices by diagonalizing the full Hamiltonian of the problem. Our model therefore includes both bound and continuum states of the excitons. The theoretical results are compared with experiments. We first show that the Coulomb interaction does not destroy the field-induced transition from the Franz-Keldysh to the Wannier-Stark regime, but causes an absorption asymmetry in the spectra, i.e., a dominance of Wannier-Stark transitions with negative indices. This effect, which has been observed before, is explained by a Coulomb-induced shift of oscillator strength from higher to lower energies in a simple model involving an effective Coulomb potential. We further address the problem of the transformation of the quasi-two-dimensional excitons of the Wannier-Stark levels to the three-dimensional miniband excitons obtained for zero field. For finite electric fields the quasibound miniband exciton states are explained as resonant states of the various Wannier-Stark excitons. We show that in contradiction to previous assumptions the Wannier-Stark ladder transitions are never suppressed by exciton localization. The observability of the transitions only depends on the relation between the zero-field miniband width and the linewidth of the transitions, but not on the ratio between miniband width and exciton binding energy.

Electro-optic detection of Bloch oscillations.

The coherent motion of electronic wave packets in the Wannier-Stark regime of extemally biased GaAs/AIxGal _xAs superlattices is investigated by a time-resolved electro-optic technique. As predicted by the semiclassical theory, electronic wave packets undergo Bloch oscillations. They are observed via anisotropie changes in the refractive index associated with a intraband polarization, which is set up by the coherent spatial motion of electronic wave packets relative to localized holes. The oscillation amplitude depends strongly on the initial excitation conditions. Frequency, amplitude, and dephasing of Bloch oscillations are investigated over a wide range of electric fields. Complementary results to four-wave mixing and THz emission experiments are obtained.

Rigorous excitonic theory of field dependent superlattice absorption

We have performed calculations of the field dependent excitonic absorption spectra of semiconductor superlattices in a model which is capable of fully taking into account the Coulomb interaction and both bound and continuum excitonic states. Results are obtained for the complete range of fields from the Franz-Keldysh to the Wannier-Stark regime. The lineshapes of the excitonic spectra are shown to resemble the derivative of the corresponding single particle spectra with respect to the wavelength. In addition characteristic excitonic features have been found, which also have been observed in photocurrent spectra

Miniband and Wannier-Stark states in GaAsAlAs superlattices investigated by differential photocurrent spectroscopy

We used a new modulation technique, the wavelength modulated photocurrent spectroscopy, to study the field dependent transition from the miniband to the Wannier-Stark regime in GaAsAlAs-superlattices. In the zero field limit the edges of the joint miniband density of states between electrons and heavy as well as light holes create characteristic features in our modulated spectra. Applying small electric fields bulk-like Franz-Keldysh-Oscillations appear at the lower and upper miniband edges. At large electric fields the well known Wannier-Stark-Levels are observable.