Nonlinear charge transport in strongly coupled semiconductor superlattices is described by Wigner-Poisson kinetic equations involving one or two minibands. Electron-electron collisions are treated within the Hartree approximation whereas other inelastic collisions are described by a modified BGK (Bhatnaghar-Gross-Krook) model. The hyperbolic limit is such that the collision frequencies are of the same order as the Bloch frequencies due to the electric field and the corresponding terms in the kinetic equation are dominant. In this limit, spatially nonlocal drift-diffusion balance equations for the miniband populations and the electric field are derived by means of the Chapman-Enskog perturbation technique. For a lateral superlattice with spin-orbit interaction, electrons with spin up or down have different energies and their corresponding drift-diffusion equations can be used to calculate spin-polarized currents and electron spin polarization. Numerical solutions show stable self-sustained oscillations of the current and the spin polarization through a voltage biased lateral superlattice thereby providing an example of superlattice spin oscillator.
Semiconductor superlattices may display dispersions that are degenerate either at the zone center or zone boundary. We show that they are linear upon the wave-vector in the vicinity of the crossing point. This establishes a realisation of massless Dirac bands within semiconductor materials. We show that the eigenstates and the corresponding Wannier functions of these superlattices have peculiar symmetry properties. We discuss the stability of the properties of such superlattices versus the electron in-plane motion. As a distinct fingerprint, the inter-subband magneto-absorption spectrum for su…
We investigate the coherent dynamics of carriers in semiconductor superlattices driven by ac-dc electric fields. We solve numerically the time-dependent effective-mass equation for the envelope function. We find that carriers undergo Rabi oscillations when the driving frequency is close to the separation between minibands.
We derive simple difference formulas describing a small-signal absorption of THz field in a semiconductor superlattice driven by a microwave pump. We give a transparent geometric interpretation of these formulas that allows a search of optimum conditions for the gain employing only a simple qualitative analysis. Our theoretical approach provides a powerful tool for finding the correspondence between quasistatic and dynamic regimes in ac-driven semiconductor superlattices.
Electron transmission through semiconductor superlattices is studied with transfer matrix method and resonance theory. The formation of electron band-pass transmission is ascribed to the coupling of different modes in those semiconductor superlattices with the symmetric unit cell. Upon Fabry-Pérot resonance condition, Bloch modes and two other resonant modes are identified to be related to the nature of the superlattice and its unit cell, respectively. The bands related to the unit cell and the superlattice overlap spontaneously in the tunneling region due to the shared wells, and the coupling…
Via the numerical analysis on the intraband dynamics of optically excited semiconductor superlattices, we find that time-integrated squared THz emission signals can be used for probing both dynamic localization and multi-photon resonance in the coherent regime. Competition effect between dynamic localization and photon-assisted transport has also been discussed.
Carrier dynamics at energy level anticrossings in biased semiconductor superlattices, was studied in the time domain by solving the time-dependent Schroedinger equation. The resonant nature of interminiband Rabi oscillations has been explicitly demonstrated to arise from interference of intrawell and Bloch oscillations. We also report a simulation of direct Rabi oscillations across three minibands, in the high field regime, due to interaction between three strongly coupled minibands.
An analysis of wavefront motion in weakly coupled doped semiconductor superlattices is presented. If a dimensionless doping is sufficiently large, the superlattice behaves as a discrete system presenting front propagation failure and the wavefronts can be described near the threshold currents $J_i$ ($i=1,2$) at which they depin and move. The wavefront velocity scales with current as $|J-J_i|^{1\over 2}$. If the dimensionless doping is low enough, the superlattice behaves as a continuum system and wavefronts are essentially shock waves whose velocity obeys an equal area rule.
Generation of terahertz harmonics by frequency multiplication with a semiconductor superlattice due to an excitation of relaxation oscillations by incident waves is investigated theoretically. It is shown that the relaxation oscillations excitation becomes feasible if the superlattice dc resistance is low enough in comparison with a characteristic radiation impedance of the external waveguide system. The power of the generated harmonics as a function of the incident wave power demonstrates a threshold-like behavior at a specific input power level dependent on the superlattice peak current. We …
We theoretically show that conditions for THz gain and conditions for formation of destructive electric domains in semiconductor superlattices are fairly different in the case of parametric generation and amplification. Action of an unbiased high-frequency electric field on a superlattice causes a periodic variation of energy and effective mass of miniband electrons. This parametric effect can result in a significant gain at some even harmonic of the pump frequency without formation of electric domains and corruption from pump harmonics.
Time delay in electron propagation through a finite periodic system such as a semiconductor superlattice is studied by direct numerical solution of the time-dependent Schrödinger equation. It is found that addition of an anti-reflection coating significantly reduces the time delay, in addition to increasing the transmissivity.
The system of equations describing an ultrashort optical pulses propagation in semiconductor superlattice with applied magnetic field was obtained based on Boltzmann equation in the relaxation-time approximation for the single electron distribution function and coupled Maxwell equations for the electromagnetic field. It was demonstrated that an original linear-polarized optical pulse initiates an orthogonal polarization in the field of a sample. The propagation dynamics of initiated and initial pulses in the sample was investigated. The effects of the lattice geometry have been elicited.
Physical systems exhibiting fast spontaneous chaotic oscillations are used to generate high-quality true random sequences in random number generators. The concept of using fast practical entropy sources to produce true random sequences is crucial to make storage and transfer of data more secure at very high speeds. While the first high-speed devices were chaotic semiconductor lasers, the discovery of spontaneous chaos in semiconductor superlattices at room temperature provides a valuable nanotechnology alternative. Spontaneous chaos was observed in 1996 experiments at temperatures below liquid…
We study theoretically the dynamical rectification of a terahertz AC electric field, ie. the DC current and voltage response to the incident radiation, in strongly coupled semiconductor superlattices. We address the problem of stability against electric field domains: A spontaneous DC voltage is known to appear exactly for parameters for which a spatially homogeneous electron distribution is unstable. We show that by applying a weak direct current bias the rectifier can be switched from a zero DC voltage state to one with a finite voltage in full absence of domains. The switching occurs near t…
Shot noise affects differently the nonlinear electron transport in semiconductor superlattices depending on the strength of the coupling among the superlattice quantum wells. Strongly coupled superlattices can be described by a miniband Boltzmann-Langevin equation from which a stochastic drift-diffusion equation is derived by means of a consistent Chapman-Enskog method. Similarly, shot noise in weakly coupled, highly doped semiconductor superlattices is described by a stochastic discrete drift-diffusion model. The current-voltage characteristics of the corresponding deterministic model consist…
In weakly coupled, current biased, doped semiconductor superlattices, domain walls may move upstream against the flow of electrons. For appropriate doping values, a domain wall separating two electric field domains moves downstream below a first critical current, it remains stationary between this value and a second critical current, and it moves upstream above. These conclusions are reached by using a comparison principle to analyze a discrete drift-diffusion model, and validated by numerical simulations. Possible experimental realizations are suggested.
The exciton absorption coefficient is determined analytically for a semiconductor superlattice in crossed electric and magnetic fields, for the magnetic field being parallel and the electric field being perpendicular to the superlattice axis. Our investigation applies to the case where the magnetic length, while being much smaller than the exiton Bohr radius, considerably exceeds the superlattice period. The optical absorption in superlattices displays a spectral fine structure related to the sequences of exciton states bound whose energies are adjacent to the Landau energies of the charge car…
A non-equilibrium Green's function method is applied to model high-field quantum transport and electron-phonon resonances in semiconductor superlattices. The field-dependent density of states for elastic (impurity) scattering is found non-perturbatively in an approach which can be applied to both high and low electric fields. I-V curves, and specifically electron-phonon resonances, are calculated by treating the inelastic (LO phonon) scattering perturbatively. Calculations show how strong impurity scattering suppresses the electron-phonon resonance peaks in I-V curves, and their detailed sensi…
Electric transport in semiconductor superlattices is dominated by pronounced negative differential conductivity. In this report the standard transport theories for superlattices, i.e. miniband conduction, Wannier-Stark-hopping, and sequential tunneling, are reviewed in detail. Their relation to each other is clarified by a comparison with a quantum transport model based on nonequilibrium Green functions. It is demonstrated how the occurrence of negative differential conductivity causes inhomogeneous electric field distributions, yielding either a characteristic sawtooth shape of the current-vo…
We investigate the dephasing dynamics of Bloch oscillations in semiconductor superlattices by means of a very simple model including 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 ou…
In a superlattice placed in crossed electric and magnetic fields, under certain conditions, the inversion of electron population can appear at which the average energy of electrons is above the middle of the miniband and the effective mass of the electron is negative. This is the implementation of the negative effective mass amplifier and generator (NEMAG) in the superlattice. It can result in the amplification and generation of terahertz radiation even in the absence of negative differential conductivity.
We consider terahertz absorption and gain in a single miniband of semiconductor superlattice subject to a bichromatic electric field in the most general case of commensurate frequencies of the probe and pump fields. Using an exact solution of Boltzmann transport equation, we show that in the small-signal limit the formulas for absorption always contain two distinct terms related to the parametric and incoherent interactions of miniband electrons with the alternating pump field. It provides a theoretical background for a control of THz gain without switching to the negative differential conduct…
We study electron transport through a semiconductor superlattice subject to an electric field parallel to and a magnetic field perpendicular to the growth axis. Using a single miniband, semiclassical balance equation model with both elastic and inelastic scattering, we find that (1) the current-voltage characteristic becomes multistable in a large magnetic field; and (2) ``hot'' electrons display novel features in their current-voltage characteristics, including absolute negative conductivity (ANC) and, for sufficiently strong magnetic fields, a spontaneous dc current at zero bias. We discuss …
We study the response of low-dimensional semiconductor superlattices to strong terahertz fields on condition of a strong suppression of inelastic scattering processes of electrons caused by the polar-optical phonons. For our study we employ a balance equations approach which allows investigating the response of the superlattices to strong terahertz fields taking account of both the inelastic and the strongly pronounced elastic scattering of electrons. Our approach provides a way to analyze the influence of the Bloch dynamics of electrons in a superlattice miniband side by side with the effects…
We present fully quantum-mechanical magnetotransport calculations for short-period lateral superlattices with one-dimensional electrostatic modulation. A non-perturbative treatment of both magnetic field and modulation potential proves to be necessary to reproduce novel quantum oscillations in the magnetoresistance found in recent experiments in the resistance component parallel to the modulation potential. In addition, we predict oscillations of opposite phase in the component perpendicular to the modulation not yet observed experimentally. We show that the new oscillations originate from the…
We present a detailed study of the dynamics of electronic wavepackets in Fibonacci semiconductor superlattices, both in flat band conditions and subject to homogeneous electric fields perpendicular to the layers. Coherent propagation of electrons is described by means of a scalar Hamiltonian using the effective-mass approximation. We have found that an initial Gaussian wavepacket is filtered selectively when passing through the superlattice. This means that only those components of the wavepacket whose wavenumber belong to allowed subminibands of the fractal-like energy spectrum can propagate …
In two recent Letters [Phys. Rev. Lett. 90, 046806; Phys. Rev. Lett. 94, 057408], Hirakawa et al. investigate the emission of coherent terahertz (THz) radiation from optically excited superlattices. The authors interpret the spectra of the THz transients in terms of a semiclassical transport model and conclude that the data provide evidence for the existence of the so-called Bloch gain. We show that the interpretation of the data in terms of a conductivity is, however, not performed correctly, thus making the conclusions of cited authors void.
We report the experimental study of resonant Rayleigh scattering in GaAs-AlGaAs superlattices with ordered and intentionally disordered potential profiles (correlated and uncorrelated) in the growth direction z. We show that the intentional disorder along z modify markedly the energy dispersion of the dephasing rates of the excitons. The application of an external magnetic field in the same direction allows the continuous tuning of the in plane exciton localization and to study the interplay between the in plane and vertical disorder.
The current (voltage) responsivity of the superlattice-based diode detectors in the terahertz frequency band which includes the region of the polar optical phonon frequencies has been analyzed theoretically. Within the framework of the equivalent circuit approach an electro-dynamical model which allows one to analyze the responsivity taking into account the plasmon polariton excitation both in the substrate and in the contact layers of the diodes has been suggested. It has been shown that the presence of the plasmon polariton excitation gives rise to strong features in the frequency dependence…
A Wigner-Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are supposed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron-electron interaction is treated in the Hartree approximation. There are elastic collisions with impurities and inelastic collisions with phonons, imperfections, etc. The latter are described by a modified BGK (Bhatnagar-Gross-Krook) collision model that allows for energy dissipation while yielding charge continuity. In the hyperbolic limit, nonlocal drift-diffusion equations…
In semiconductor superlattices, when Bragg oscillating electrons interact with an input electromagnetic field, frequency multiplication is possible. An ideal superlattice has a purely antisymmetric voltage current response and can thus produce only odd harmonics. However, real world superlattices can also have even harmonic response and that increases the range of possible output frequencies. These effects have been recently explained with a predictive model that combines an Ansatz solution for the Boltzmann Equation with a Nonequilibrium Green's Functions approach. This predictive tool, coupl…
In twisted homobilayer transition metal dichalcogenides, intra- and inter-layer valley excitons hybridize with the layer configurations spatially varying in the moiré. The ground state valley excitons are trapped at two high-symmetry points with opposite electric dipoles in a moiré supercell, forming a honeycomb superlattice of nearest-neighbor dipolar attraction. We find that the spatial texture of layer configuration results in a luminescence anomaly of the moiré trapped excitons, where a tiny displacement by interactions dramatically increases the brightness and changes polarization from ci…
The charge transfer from an adatom to a semiconductor substrate of one-dimensional quantum dot array is evaluated theoretically. Due to the Van Hove singularity in the density of electron states at the band edges, the charge transfer decay rate is enhanced nonanalytically in terms of the coupling constant $g$ as $g^{4/3}$. The optical absorption spectrum for the ionization of a core level electron of the adatom to the conduction band is also calculated. The reversible non-Markovian process and irreversible Markovian process in the time evolution of the adatom localized state manifest themselve…
We consider the dynamics of electrons in semiconductor superlattices in intense multifrequency electric fields. We examine the conditions for dynamic localization and electromagnetic transparency. We investigate processes of formation, destruction and stabilization of electromagnetic transparency in biharmonic field. The stable dc fields are founded.
A model for charge transport in undoped, photo-excited semiconductor superlattices, which includes the dependence of the electron-hole recombination on the electric field and on the photo-excitation intensity through the field-dependent recombination coefficient, is proposed and analyzed. Under dc voltage bias and high photo-excitation intensities, there appear self-sustained oscillations of the current due to a repeated homogeneous nucleation of a number of charge dipole waves inside the superlattice. In contrast to the case of a constant recombination coefficient, nucleated dipole waves can …
Using an effective medium approach, we describe how by combining mercury-cadmium-telluride semiconductor alloys with band gap energies of opposite signs it may be possible to design a superlattice where the electrons have isotropic zero-effective mass and a single valley linear energy-momentum dispersion. We demonstrate that because of the zero-mass property, the superlattice may have a strong nonlinear response under the action of an external electromagnetic field.
We present the first numerical solutions of a kinetic theory description of self-sustained current oscillations in n-doped semiconductor superlattices. The governing equation is a single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary conditions for the distribution function describe electron injection in the contact regions. These conditions seamlessly become Ohm's law at the injecting contact and the zero charge boundary condition at the receiving contact when integrated over the wave vector. The time-dependent model is nu…
We study the dynamical behavior of disordered quantum-well-based semiconductor superlattices where the disorder is intentional and short-range correlated. We show that, whereas the transmission time of a particle grows exponentially with the number of wells in an usual disordered superlattice for any value of the incident particle energy, for specific values of the incident energy this time increases linearly when correlated disorder is included. As expected, those values of the energy coincide with a narrow subband of extended states predicted by the static calculations of Dom\'ınguez-Adame {…
A numerical study of domain wall relocation during voltage switching with different ramping times is presented for weakly coupled, doped semiconductor superlattices exhibiting multistable domain formation in the first plateau of their current-voltage characteristics. Stable self-oscillations of the current at the end of stable stationary branches of the current-voltage characteristics have been found. These oscillations are due to periodic motion of charge dipoles near the cathode that disappear inside the SL, before they can reach the receiving contact. Depending on the dc voltage step, the t…
We have found experimentally that the shot noise of the tunneling current $I$ through an undoped semiconductor superlattice is reduced with respect to the Poissonian noise value $2eI$, and that the noise approaches 1/3 of that value in superlattices whose quantum wells are strongly coupled. On the other hand, when the coupling is weak or when a strong electric field is applied to the superlattice the noise becomes Poissonian. Although our results are qualitatively consistent with existing theories for one-dimensional mulitple barriers, the theories cannot account for the dependence of the nois…
We develop a mean-field theory of carrier-induced ferromagnetism in diluted magnetic semiconductors. Our approach represents an improvement over standard RKKY model allowing spatial inhomogeneity of the system, free-carrier spin polarization, finite temperature, and free-carrier exchange and correlation to be accounted for self-consistently. As an example, we calculate the electronic structure of a Mn$_x$Ga$_{1-x}$As/GaAs superlattice with alternating ferromagnetic and paramagnetic layers and demonstrate the possibility of semiconductor magnetoresistance systems with designed properties.
In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that convective nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. In this case, numerical solutions show that there are stable Bloch oscillations confined to a region near the collector with inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear when damping due to inelastic collisions becomes sufficiently strong.
Wannier-Mott excitons in a semiconductor layered superlattice (SL) of period much smaller than the 2D exciton Bohr radius in the presence of a longitudinal external dc electric field directed parallel to the SL axis are investigated analytically. The exciton states and the optical absorption coefficient are derived in the tight-binding and adiabatic approximations. Strong and weak electric fields providing spatially localized and extended electron and hole states, respectively, are studied. The dependencies of the exciton states and the exciton absorption spectrum on the SL parameters and the …
The exciton decay rate at a rough interface in type-II semiconductor superlattices is investigated. It is shown that the possibility of recombination of indirect excitons at a plane interface essentially affects kinetics of the exciton photoluminescence at a rough interface. This happens because of strong correlation between the exciton recombination at the plane interface and at the roughness. Expressions that relate the parameters of the luminescence kinetics with statistical characteristics of the rough interface are obtained. The mean height and length of roughnesses in GaAs/AlAs superlatt…
Weakly coupled semiconductor superlattices under dc voltage bias are excitable systems with many degrees of freedom that may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Superlattices with identical periods exhibit current self-oscillations due to the dynamics of charge dipole waves but chaotic oscillations exist on narrow voltage intervals. They disappear easily due to variation in structural growth parameters. Based on numerical simulations, we predict that inserting two identical sufficiently separated wider wells increases superlat…
We discuss an effect of dc current and dc voltage (stopping bias) generation in a semiconductor superlattice subjected by an ac electric field and its phase-shifted n-th harmonic. In the low field limit, we find a simple dependence of dc voltage on a strength, frequency, and relative phase of mixing harmonics for an arbitrary even value of n. We show that the generated dc voltage has a maximum when a frequency of ac field is of the order of a scattering constant of electrons in a superlattice. This means that for typical semiconductor superlattices at room temperature operating in the THz freq…
We study a model describing electronic transport in a weakly-coupled semiconductor superlattice with a shunting side layer. Key parameters include the lateral size of the superlattice, the connectivity between the quantum wells of the superlattice and the shunt layer, and the conduction properties of the shunt layer. For a superlattice with small lateral extent and high quality shunt, static electric field domains are suppressed and a spatially-uniform field configuration is predicted to be stable, a result that may be useful for proposed devices such as a superlattice-based TeraHertz (THz) os…
Electrodynamic properties of the graphene - magnetic semiconductor - graphene superlattice placed in magnetic field have been investigated theoretically in Faraday geometry with taking into account dissipation processes. Frequency and field dependences of the reflectance, transmittance and absorbtance of electromagnetic waves by such superlattice have been calculated for different numbers of periods of the structure and different sizes of the periods with using a transfer matrix method. The possibility of efficient control of electrodynamic properties of graphene - magnetic semiconductor - gra…
We theoretically analyze the influence of magnetic field on small-signal absorption and gain in a superlattice. We predict a very large and tunable THz gain due to nonlinear cyclotron oscillations in crossed electric and magnetic fields. In contrast to Bloch gain, here the superlattice is in an electrically stable state. We also find that THz Bloch gain can be significantly enhanced with a perpendicular magnetic field. If the magnetic field is tilted with respect to the superlattice axis, the usually unstable Bloch gain profile becomes stable in the vicinity of Stark-cyclotron resonances.
We show that space-charge instabilities (electric field domains) in semiconductor superlattices are the attribute of absolute negative conductance induced by small constant and large alternating electric fields. We propose the efficient method for suppression of this destructive phenomenon in order to obtain a generation at microwave and THz frequencies in devices operating at room temperature. We theoretically proved that an unbiased superlattice with a moderate doping subjected to a microwave pump field provides a strong gain at third, fifth, seventh, etc. harmonics of the pump frequency in …
When quantized, traces of classically chaotic single particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single electron chaos influences colle…
We theoretically investigated the scheme allowing to avoid destructive space-charge instabilities and to obtain a strong gain at microwave and THz frequencies in semiconductor superlattice devices. Superlattice is subjected to a microwave field and a generation is achieved at some odd harmonics of the pump frequency. Gain arises because of parametric amplification seeded by harmonic generation. Negative differential conductance (NDC) is not a necessary condition for the generation. For the mode of operation with NDC, a limited space-charge accumulation does not sufficiently reduce the gain.
We describe a limiting case when nonlinear dynamics of an ac-driven semiconductor superlattice in the miniband transport regime is governed by a periodically forced and damped pendulum. We find analytically the conditions for a transition to chaos and consider an influence of temperature on the effect. We also discuss fractional dc voltage states in a superlattice originating from phase-locked states of the pendulum.
Electronic transport is theoretically investigated in laterally confined semiconductor superlattices using the formalism of non-equilibrium Green's functions. The transport properties are calculated for nanowire superlattices of varying diameters, from the quantum dot superlattice regime to the quantum well superlattice regime. Scattering processes due to electron-phonon couplings, phonon anharmonicity, charged impurities, surface and interface roughness and alloy disorder are included on a microscopic basis. Elastic scattering mechanisms are treated in a partial coherent way beyond the self-c…
We study the motion of electrons in a single miniband of a semiconductor superlattice driven by THz electric field polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behaviour and symmetry-breaking. We estimate the magnitudes of dc current and dc voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of modern …
We demonstrate theoretically the coexistence of Dirac semimetal and topological insulator phases in InSb/$α$-Sn conventional semiconductor superlattices, based on advanced first-principles calculations combined with low-energy $k\cdot p$ theory. By proper interfaces designing, a large interface polarization emerges when the growth direction is chosen along {[}111{]}. Such an intrinsic polarized electrostatic field reduces band gap largely and invert the band structure finally, leading to emerge of the topological Dirac semimetal phase with a pair of Dirac nodes appearing along the (111) crysta…
Theories describing electrical transport in semiconductor superlattices can essentially be divided in three disjoint categories: i) transport in a miniband; ii) hopping between Wannier-Stark ladders; and iii) sequential tunneling. We present a quantum transport model, based on nonequilibrium Green functions, which, in the appropriate limits, reproduces the three conventional theories, and describes the transport in the previously unaccessible region of the parameter space.
