Terahertz magnetospectroscopy of high electron mobility CdTe/CdMgTe quantum wells

The extent of Terahertz (THz) radiation applications during last two decades has grown extensively as it was found to be useful in the fields such as medical imaging, security or drugs control to name just a few. However, despite a tremendous work already done, the compact system of THz imaging operating at room temperature is still an issue. Up to now, GaAs or GaN-based heterostructures and Si electron inversion layers were mostly used in solid-state THz optoelectronics. There, such a resonant phenomena as collective oscillations in a two-dimensional (2D) electron plasma and a free electron cyclotron resonance (CR) were observed. When it comes about THz magnetospectroscopy in a high electron mobility CdTe-based QWs, not many reports in the literature can be found. Due to a polar nature of the crystal lattice bonds and relatively low optical phonon energies the influence of a polaron effect on cyclotron resonance as well as a plasmon-phonon interaction are much larger in CdTe than in the materials mentioned before. Better understanding of these fundamental effects is extremely important for the operation of the devices based on CdTe such as frequency tunable THz detectors, for example. The goal of this work was to investigate the THz radiation induced effects in 2D electron plasma in CdTe-based QWs, concentrating an attention on the 2D plasmon excitation and peculiarities resulting from the polar nature of the material. The experiments were done on a high electron mobility CdTe/CdMgTe quantum wells, modulation doped with n-type impurity at one of the barriers (closer to the surface). All measurements were done at liquid helium temperature. A set of samples with a different parameters such as doping density and quantum well width were investigated in a photocurrent experiments. Also, transmission on samples containing a photo-lithographically formed metal grid-gate on the top was measured. A photocurrent induced in a quantum point contact (QPC) device defined by an electron beam lithography was also investigated. In order to characterize the samples, magnetotransport experiments were done at first. The 2DEG concentration was found as well as electron effective mass and quantum scattering time by analyzing the oscillation period and amplitude of Shubnikov-de Haas oscillations. Also, the feature at Landau level filling factor $\nu$ =4/3 was observed which might arise due to a Fractional Quantum Hall Effect (FQHE). Photocurrent spectra as a function of magnetic field (B) and exciting the sample with a constant frequency radiation taken from THz laser were recorded. In some samples only a narrow cyclotron resonance (CR) peak was observed ($\Delta B_{\text{{FWHM}}}\sim0.2$ T), while in the others optically induced SdH oscillations were present together with CR peak. The absence of SdH oscillations can be explained by the 2DEG heating due to bias current through the sample. An interesting phenomenon was observed, when optically induced SdH oscillations were analyzed. The additional splitting at Landau level filling factors $\nu$ = 1, 2 and 4 was observed. This phenomena might arise to the breaking of an Integer Quantum Hall (IQH) state due to THz radiation induced bolometric effect. However deeper investigation of the phenomenon is needed. The next topic of the investigation was THz detection with a gated 2D electron plasma in CdTe/CdMgTe quantum wells. For this purpose a few samples with a deposited gold gate electrode allowing for the 2DEG concentration control with a voltage, were prepared. Here the SdH oscillations and a CR transition were observed and a non-monotonical dependence of CR peak magnitude on $V_{\text{g}}$ was found. In general, changing the $V_{\text{g}}$ it is possible to reduce the CR peak magnitude to the level of SdH oscillations, or to increase it to exceed SdH magnitude more than 20 times. Also, sample response at a few laser lines was measured as a function of the gate voltage at a constant magnetic field $B=B_{\text{CR}}$. The above described CR peak magnitude dependence on $V_{\text{g}}$ or, in other words, a possibility to switch on and off the resonant detection was demonstrated. Another sample used for these experiments had a Hall bar geometry with a gated conduction channel. Experimental results also showed a non-monotonical CR peak magnitude dependence on the gate polarization. However, in this case the CR magnitude dependence on $V_{\text{g}}$ showed well developed plateau regions. Photocurrent spectra as a function of $B$ were measured on a QPC sample. The device has a lateral gate and the conduction channel with the constriction of the form of a bottle-neck. Spectra were measured for a few laser frequencies and for a few gate voltage values. In both cases, CR maxima with a spectral features at low-$B$ shoulder were registered. The spectral structures were found to represent the first and higher harmonics of electron plasma oscillations in magnetic field, also known as magnetoplasmons. It was found that plasmon frequency does not depend on the gate voltage, suggesting that detected plasma resonances form at the wide part of the channel, and not at the bottle-neck. Data analysis showed that plasmons observed are of ungated type and are confined in the conduction channel (width $W=2.4 \mu$m). In transmission spectra recorded on the grid-gated samples using the Fourier interferometer, the electron effective mass increase was observed at the strong magnetic fields which arises from the resonant polaron effect. Transmission spectra recorded using the THz laser show a deep symmetric CR minimum for the reference sample (that without a metal grid). For the samples with the metal grid, on the low-$B$ shoulder of CR dip, additional features were present. They were observed for two different laser frequencies and for two metal grids of a different periodicity. According to the theoretical calculations, these features are the first four harmonics of magnetoplasmons, with wavevectors defined by the period of the grating. These plasmons were shown to be a mixture of screened plasmons existing under metal fingers and unscreened plasmons existing in the openings of the grid. The proportion of plasmons of each type in the mixture were found to be approximately equal to the geometrical aspect ratio of the grating. Also, comparing experimental results with the theory it was found that the 2D plasmon frequency in n-doped CdTe/CdMgTe QWs of high electron mobility is strongly influenced by the plasmon-phonon interaction. To sum up, resonant (cyclotron transition and 2D plasmons) and non-resonant (SdH oscillations) THz detection was demonstrated in the high electron mobility CdTe/CdMgTe QWs. Also, effects arising from polar nature of CdTe lattice were such as resonant polaron effect and plasmon-phonon interaction were shown to be important. To the best knowledge of the author 2D plasmons excited by THz radiation were demonstrated in CdTe/CdMgTe QWs for the first time

Polynomials of Meixner's type in infinite dimensions-Jacobi fields and orthogonality measures

The classical polynomials of Meixner's type--Hermite, Charlier, Laguerre, Meixner, and Meixner--Pollaczek polynomials--are distinguished through a special form of their generating function, which involves the Laplace transform of their orthogonality measure. In this paper, we study analogs of the latter three classes of polynomials in infinite dimensions. We fix as an underlying space a (non-compact) Riemannian manifold $X$ and an intensity measure $\sigma$ on it. We consider a Jacobi field in the extended Fock space over $L^2(X;\sigma)$, whose field operator at a point $x\in X$ is of the form \di_x^\dag+\lambda\di_x^\dag \di_x+\di_x+\di^\dag_x\di_x\di_x, where $\lambda$ is a real parameter. Here, \di_x and \di_x^\dag are, respectively, the annihilation and creation operators at the point $x$. We then realize the field operators as multiplication operators in $L^2({\cal D}';\mu_\lambda)$, where ${\cal D}'$ is the dual of ${\cal D}{:=}C_0^\infty(X)$, and $\mu_\lambda$ is the spectral measure of the Jacobi field. We show that $\mu_\lambda$ is a gamma measure for $|\lambda|=2$, a Pascal measure for $|\lambda|>2$, and a Meixner measure for $|\lambda|<2$. In all the cases, $\mu_\lambda$ is a L\'evy noise measure. The isomorphism between the extended Fock space and $L^2({\cal D}';\mu_\lambda)$ is carried out by infinite-dimensional polynomials of Meixner's type. We find the generating function of these polynomials and using it, we study the action of the operators \di_x and \di_x^\dag in the functional realization

Stochastic Calculus for Assets with Non-Gaussian Price Fluctuations

From the path integral formalism for price fluctuations with non-Gaussian distributions I derive the appropriate stochastic calculus replacing Ito's calculus for stochastic fluctuations.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper (including all PS fonts) at http://www.physik.fu-berlin.de/~kleinert/32

Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also L\'evy processes, of which Brownian Motion is a special case, have become increasingly popular. L\'evy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include L\'evy processes and in particular Brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the generation of sample paths of Feller processe

Exponential ergodicity of the jump-diffusion CIR process

In this paper we study the jump-diffusion CIR process (shorted as JCIR), which is an extension of the classical CIR model. The jumps of the JCIR are introduced with the help of a pure-jump L\'evy process $(J_t, t \ge 0)$. Under some suitable conditions on the L\'evy measure of $(J_t, t \ge 0)$, we derive a lower bound for the transition densities of the JCIR process. We also find some sufficient condition guaranteeing the existence of a Forster-Lyapunov function for the JCIR process, which allows us to prove its exponential ergodicity.Comment: 14 page

Signal processing with Levy information

Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a "message", then under the transformed measure the original Levy process takes on the character of an "information process". In this paper we develop a theory of such Levy information processes. The underlying Levy process, which we call the fiducial process, represents the "noise type". Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian, and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, $\sigma=\pm1/2$, alternated with spins that can take the four values, $S=\pm3/2, \pm1/2$. We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude $(h)$ and reduced temperature $(T)$ plane, and in the reduced temperature and interaction parameter planes, namely in the $(h, T)$ and $(d, T)$ planes, $d$ is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in $(h, T)$ plane, but do not exhibit in the $(d, T)$ plane for low values of $h$. The dynamic multicritical point or dynamic critical end point exist in the $(d, T)$ plane for low values of $h$. Moreover, phase diagrams contain paramagnetic $(p)$, ferromagnetic $(f)$, ferrimagnetic $(i)$ phases, two coexistence or mixed phase regions, $(f+p)$ and $(i+p)$, that strongly depend on interaction parameters.Comment: 13 pages, 6 figures, submitted to Journal of Magnetism and Magnetic Material

Superimposed Renewal Processes in Reliability

This paper reviews the existing literature on the superimposed renewal process, with its foci on probabilistic and statistical properties, statistical inference, and applications in reliability analysis and maintenance policy optimisation. It then proposes future research topics