Bloch Oscillations In Semiconductor Superlattices Research Articles

Numerical method for hydrodynamic modulation equations describing Bloch oscillations in semiconductor superlattices

We present a finite difference method to solve a new type of nonlocal hydrodynamic equations that arise in the theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices. The hydrodynamic equations describe the evolution of the electron density, electric field and the complex amplitude of the Bloch oscillations for the electron current density and the mean energy density. These equations contain averages over the Bloch phase which are integrals of the unknown electric field and are derived by singular perturbation methods. Among the solutions of the hydrodynamic equations, at a 70K lattice temperature, there are spatially inhomogeneous Bloch oscillations coexisting with moving electric field domains and Gunn-type oscillations of the current. At higher temperature (300K) only Bloch oscillations remain. These novel solutions are found for restitution coefficients in a narrow interval below their critical values and disappear for larger values. We use an efficient numerical method based on an implicit second-order finite difference scheme for both the electric field equation (of drift-diffusion type) and the parabolic equation for the complex amplitude. Double integrals appearing in the nonlocal hydrodynamic equations are calculated by means of expansions in modified Bessel functions. We use numerical simulations to ascertain the convergence of the method. If the complex amplitude equation is solved using a first order scheme for restitution coefficients near their critical values, a spurious convection arises that annihilates the complex amplitude in the part of the superlattice that is closer to the cathode. This numerical artifact disappears if the space step is appropriately reduced or we use the second-order numerical scheme.

Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices

In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. To demonstrate this, a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions is proposed and hydrodynamic equations for electron density, electric field and the complex amplitude of the Bloch oscillations are derived by singular perturbation methods. For appropriate parameter ranges, numerical solutions of these equations show stable Bloch oscillations with spatially inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear as scattering times become sufficiently short. For sufficiently low lattice temperatures, Bloch and Gunn type oscillations mediated by electric field, current and energy domains coexist for a range of voltages. For larger lattice temperatures (300 K), there are only Bloch oscillations with stationary amplitude and electric field profiles.

Acoustic analog of electronic Bloch oscillations and Zener tunneling

The observation of Bloch oscillations in sound propagation through a multilayer of two different fluidlike components is predicted. In order to obtain the equivalent to the acoustic analog of a Wannier-Stark ladder [E. E. Mendez et al., Phys. Rev. Lett. 60, 2426–2429 (1988)], a set of cavities with increasing thickness is employed. Bloch oscillations were theoretically predicted as time-resolved oscillations in transmission in direct analogy to electronic Bloch oscillations in semiconductor superlattices [J. Feldmann et al., Phys. Rev. B 46, R7252–R7255 (1992)]. Finally, an experimental setup is proposed to observe the phenomenon by using arrays of cylindrical rods in air, which acoustically behaves as a fluidlike system with effective sound velocity and density [D. Torrent et al., Phys. Rev. Lett. 96, 204302 (2006)]. For the proposed system, Bloch oscillations and Zener tunneling are confirmed by using multiple scattering simulations. [Work supported by MEC of Spain.]

Chaos-induced orbit delocalization and complex Bloch oscillations in semiconductor superlattices

We show how semiconductor superlattices can be used to provide a new type of quantum chaotic system that is accessible to experiment. When a magnetic field is tilted relative to the superlattice axis, the semiclassical orbits of electrons confined to a single miniband undergo a controllable transition from stable Bloch oscillations to chaotic orbits. The onset of chaos delocalizes the electron paths and generates complex trajectories that extend across many periods of the superlattice. We show that the chaotic motion has a fundamentally different origin to that reported for previous semiconductor structures.

Dephasing effects induced by weak disorder in superlattices

We investigate the dephasing dynamics of Bloch oscillations in semiconductor superlattices by means of a very simple model including weak disorder and applied electric fields. A thorough numerical study of our model allows us to claim that small, unintentional well width fluctuations can be responsible for fast dephasing of Bloch oscillations at low temperatures. We show that the lifetime of Bloch oscillations is controlled by a characteristic time which depends on the degree of disorder and is independent of the electric field. This result is further supported by the excellent agreement between our model calculations and several recent experiments, and leads to specific new predictions.

Influence of LO-Phonon Emission on Bloch Oscillations in Semiconductor Superlattices

The intraband phase coherence of electronic Bloch wavepackets in semiconductor superlattices is partially conserved when electrons undergo energy relaxation by LO-phonon emission. The decay time of the intraband coherence as probed by terahertz-emission spectroscopy is found to be unaffected by excitation below or above the threshold for LO-phonon emission. On the other hand, the population relaxation probed by femtosecond optical transmission spectroscopy is drastically accelerated when the threshold is reached. Electrons which have undergone LO-phonon emission form a more localized distribution in k-space giving rise to a stronger THz signal.

Superradiant emission from Bloch oscillations in semiconductor superlattices.

The superradiant character of submillimeter-wave emission from optically excited electronic Bloch oscillations in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As superlattice is investigated by time-resolved terahertz emission spectroscopy. The intensity of the radiation and its decay time are studied as a function of the density of excited charge carriers. From the measured emission efficiency, the spatial amplitude of the charge oscillations is estimated. \textcopyright{} 1996 The American Physical Society.

Time-resolved optical investigations of bloch oscillations in semiconductor superlattices

We present a complementary study of the interband and intraband dynamics of optically excited Bloch oscillations in GaAs Al xGa 1−xAs superlattices. Distinct differences in the frequency and dephasing of the oscillations give evidence for Bloch oscillations performed by electrons in continuum states and by excitonic wavepackets. The dephasing time of the electronic continuum states is found to be exceptionally long as compared to the excitonic dephasing time under identical excitation conditions. These observations are confirmed by THz emission experiments, where Bloch oscillations are detected under optical excitation well above the fundamental band gap. The experimental observations suggest that the electronic coherence may be partially maintained during relaxation and momentum scattering processes.

Optical investigations of Bloch oscillations in semiconductor superlattices

The progress in growth and understanding of semiconductor hetero-structures made the realization of artificial materials like the semiconductor superlattices possible. In the last few years, optical experiments have unambiguously proven that Bloch oscillations exist in semiconductor superlattices. In this paper, the key experiments and their contributions to the understanding of Bloch oscillations are briefly discussed. Then, open questions and possible experiments to answer them are discussed.

Bloch Oscillations in Semiconductor Superlattices

A brief summary of the time-resolved investigation of Bloch oscillations of electron wave packets in semiconductor superlattices is given. Focussing on the emission of coherent terahertz-frequency electromagnetic radiation by Bloch oscillations, new experimental and theoretical results are presented. In all experiments published so far, Bloch oscillations have been induced by simultaneous impulsive optical excitation of several excitonic Wannier-Stark states at the bandedge of the first electron miniband. Here, we report on the first observation of Bloch oscillations induced by photo-excitation of continuum states as high as 100 meV above the fundamental bandgap. We then address the feasibility of optically pumped Bloch (or Esaki-Tsu) oscillators as a practical source for electromagnetic signals with a frequency continuously tunable from several hundred GHz to at least 6 THz. Advantage is taken of the supperradiant character of the emission process. The emission efficiency is discussed and concepts for an increase of the output power are proposed.

Influence of scattering on the formation of Wannier-Stark ladders and Bloch oscillations in semiconductor superlattices.

We study the critical field for the formation of Wannier-Stark ladders and Bloch oscillations in $\frac{\mathrm{GaAs}}{{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}}$ superlattices at low temperatures. From the results of photocurrent and transient four-wave mixing experiments, we conclude that the critical field is higher for superlattices with wide minibands than for superlattices, with narrow minibands. The explanation for this dependence is that intraminiband scattering due to LO-phonon emission is excluded in minibands narrower than the LO-phonon energy.

Optical investigation of bloch oscillations in semiconductor superlattices

We investigate the dephasing dynamics in semiconductor superlattices using time-resolved four-wave mixing. The signals show a periodic modulation which can be related to Bloch oscillations in the superlattice miniband. The oscillation frequency is strongly dependent on the applied field, in agreement with theoretical expectation. At high fields, the dephasing times become very short due to field-induced scattering.