Nonlinear dynamics and band transport in a superlattice driven by a plane wave

A quantum particle transport induced in a spatially-periodic potential by a propagating plane wave has a number important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices and cold atoms in optical crystal. Here we apply kinetic description of the directed transport in a superlattice beyond standard linear approximation, and utilize exact path-integral solutions of the semiclassical transport equation. We show that the particle drift and average velocities have non-monotonic dependence on the wave amplitude with several prominent extrema. Such nontrivial kinetic behaviour is related to global bifurcations developing with an increase of the wave amplitude. They cause dramatic transformations of the system phase space and lead to changes of the transport regime. We describe different types of phase trajectories contributing to the directed transport and analyse their spectral content

Control of charge transports in semiconductor superlattices using an acoustic wave

In this work, we describe the electron dynamics in semiconductor superlattices (SLs) when driven by an acoustic wave. First, we discuss the physical features and structure of SLs. Then we describe semiclassical transport in periodic potential driven by a plane wave, and the dynamics of ultracold atoms in the periodic potentials. Secondly, we explore single electron dynamics in superlattices driven by an acoustic wave, then present and analyse the types of electron trajectories according to the strength of the acoustic wave amplitude. The two dynamical regimes obtained depend on the wave amplitude strength and the initial position of electrons in the acoustic wave. The frequency range of the oscillation produced can be as large as terahertz. Lastly, we discuss the effect of applying a static electric field to the acoustically driven SLs. When the acoustic wave and electric fields were applied together along the axis of SLs, we obtained a higher peak drift velocity than when the acoustic wave or electric fields were applied alone. We use the phase portrait to explain the electron trajectory and the path of the electrons. The global state associated with the drastic change in the drift velocity of the electrons depends on the varied parameters in the dynamical systems. We numerically calculate the electron trajectories while we varied the strength of electric field and wave amplitude to investigate the role of interactions in the system. When very high electric field and very high wave amplitude are applied together along the axis of SL, global catastrophe occurs. This is the discontinuous bifurcation in dynamical system

High-frequency acoustoelectronic phenomena in miniband superlattices

The motion of a quantum particle in a periodic potential can generate rich dynamics in the presence of a driving field. Such systems include, but are not limited to, semiconductor superlattices which exhibit a very anisotropic band structure that results into pronounced nonlinearities and high carrier mobility. In this thesis, we investigate the semiclassical dynamics and electron transport in a spatially periodic potential driven by a propagating wave. Firstly, we examine the transport features of an electron in a single miniband superlattice driven by a high-frequency acoustic plane wave. In this system, the nonlinear electron dynamics crucially depends on the amplitude of the acoustic wave. The transport characteristics are studied by means of a non-linearised kinetic model. In particular, to provide a realistic description of the directed transport, we employ the exact path-integral solutions of the Boltzmann transport equation. The calculated electron drift velocity and the time-averaged velocity show a nonmonotonic dependence upon the amplitude of the acoustic wave with multiple pronounced extrema. We found out that the changes in the velocity-amplitude characteristics are directly associated with a series of global bifurcations due to topological rearrangements of the phase space of the system. These dramatic transformations are connected with superlattice intraminiband transitions, and accompanied by inelastic emission (absorption) of the quantum particle. The bifurcations also signify the transitions between different dynamical regimes, involving unconfined electron motion, wave-dragging and phonon-assisted Bloch oscillations. Each regime has a characteristic spectral fingerprint, which manifests itself in appearance of specific high-frequency components in the spectra of the corresponding averaging trajectory. Secondly, we consider to use the acoustically pumped superlattices for an amplification of THz electromagnetic waves, involving the mechanisms similar to the Bloch gain in electrically biased superlattices. In particular, we predict the tunable THz gain due to nonlinear oscillations which are associated with the localised motion of electrons confined by a propagating potential wave. Traditionally, one of the key issues which emerges from considering different schemes for achieving small signal gain in superlattices, is the control of electric stability. Here, it is shown that for our case of the fast miniband electrons driven by an acoustic wave, terahertz gain can occur without the electric instability. Additionally, we find that the characteristic changes in the averaged velocities are connected to the shape of gain profiles. Consequently, the analytic findings, which determine the transitions between different dynamical regimes at the bifurcations, hold up for the behaviour of amplification of high-frequency electromagnetic waves. The increase of the miniband width, results in an enhancement of the effect of phase space restructuring on the drift velocity and high-frequency gain. Finally, we analyse the case for a superlattice device utilising acoustic waves with a very slow propagation speed. Benefiting from a simple solution of the Boltzmann equation, here we clarify the role of spatial nonlinearity both in miniband electron dynamics and in amplification of an electromagnetic wave. We show that nonlinear Bloch oscillations occur at a single critical value of the wave amplitude, inducing high negative differential drift velocity. Within this model, we also explain how the amplification of a high-frequency signal can arise below the threshold for an excitation of Bloch oscillations

Progress towards terahertz acoustic phonon generation in doping superlattices

Progress is described in experiments to generate coherent terahertz acoustic phonons in silicon doping superlattices by the resonant absorption of nanosecond-pulsed far-infrared laser radiation. Future experiments are proposed that would use the superlattice as a transducer in a terahertz cryogenic acoustic reflection microscope with sub-nanometer resolution

Progress towards terahertz acoustic phonon generation in doping superlattices

Progress is described in experiments to generate coherent terahertz acoustic phonons in silicon doping superlattices by the resonant absorption of nanosecond-pulsed far-infrared laser radiation. Future experiments are proposed that would use the superlattice as a transducer in a terahertz cryogenic acoustic reflection microscope with sub-nanometer resolution

A weakly coupled semiconductor superlattice as a harmonic hypersonic-electrical transducer

We study experimentally and theoretically the effects of high-frequency strain pulse trains on the charge transport in a weakly coupled semiconductor superlattice. In a frequency range of the order of 100 GHz such excitation may be considered as single harmonic hypersonic excitation. While travelling along the axis of the SL, the hypersonic acoustic wavepacket affects the electron tunnelling, and thus governs the electrical current through the device. We reveal how the change of current depends on the parameters of the hypersonic excitation and on the bias applied to the superlattice. We have found that the changes in the transport properties of the superlattices caused by the acoustic excitation can be largely explained using the current-voltage relation of the unperturbed system. Our experimental measurements show multiple peaks in the dependence of the transferred charge on the repetition rate of the strain pulses in the train. We demonstrate that these resonances can be understood in terms of the spectrum of the applied acoustic perturbation after taking into account the multiple reflections in the metal film serving as a generator of hypersonic excitation. Our findings suggest an application of the semiconductor superlattice as a hypersonic-electrical transducer, which can be used in various microwave devices

Using acoustic waves to induce high-frequency current oscillations in superlattices

We show that GHz acoustic waves in semiconductor superlattices can induce THz electron dynamics that depend critically on the wave amplitude. Below a threshold amplitude, the acoustic wave drags electrons through the superlattice with a peak drift velocity overshooting that produced by a static electric field. In this regime, single electrons perform drifting orbits with THz frequency components. When the wave amplitude exceeds the critical threshold, an abrupt onset of Bloch-like oscillations causes negative differential velocity. The acoustic wave also affects the collective behavior of the electrons by causing the formation of localised electron accumulation and depletion regions, which propagate through the superlattice, thereby producing self-sustained current oscillations even for very small wave amplitudes. We show that the underlying single-electron dynamics, in particular the transition between the acoustic wave dragging and Bloch oscillation regimes, strongly influence the spatial distribution of the electrons and the form of the current oscillations. In particular, the amplitude of the current oscillations depends non-monotonically on the strength of the acoustic wave, reflecting the variation of the single-electron drift velocity.Comment: 10 pages, 8 figure

Generating coherent phonon waves in narrow-band materials: a twisted bilayer graphene phaser

Twisted bilayer graphene (TBG) exhibits extremely low Fermi velocities for electrons, with the speed of sound surpassing the Fermi velocity. This regime enables the use of TBG for amplifying vibrational waves of the lattice through stimulated emission, following the same principles of operation of free-electron lasers. Our work proposes a lasing mechanism relying on the slow-electron bands to produce a coherent beam of acoustic phonons. We propose a device based on undulated electrons in TBG, which we dub the phaser. The device generates phonon beams in a terahertz (THz) frequency range, which can then be used to produce THz electromagnetic radiation. The ability to generate coherent phonons in solids breaks new ground in controlling quantum memories, probing quantum states, realizing non-equilibrium phases of matter, and designing new types of THz optical devices.Comment: 5 pages, 3 figures + supplementary materia

Theoretical and computational studies of nano-structures and nanomaterials

Theoretical analysis and computer simulations have proven to be cost-effective and powerful tools in scientific studies of materials, particularly at nano-scale where synthesis of nano-structures, interpretation of their observed character and exploration of new structures are not always straightforward. We present here fundamental principles of techniques used today for computational simulations of materials, their capabilities and limitations. We then illustrate efficacy of such studies through review of their applications to nano-structures of oxide materials, carbon and boron nitride based nano-tubes and mechanical behavior of nano-structured materials. We finally present a wish-list of new tools and augmentation of existing tools that would allow expansion of the range of applications of computer simulations to nano-structures and materials