NANOSTRUCTURES

Dipole-dipole interaction in a quantum dot and metallic nanorod hybrid syste:

We have studied quantum coherence and interference phenomena in a quantum dot (QD)-metallic nanorod (MNR) hybrid system. Probe and control laser fields are applied to the hybrid system. Induced dipole moments are created in the QD and the MNR, and they interact with each other via the dipole-dipole interaction. Using the density matrix method, it was found that the power spectrum of MNR has two transparent, states and they can be switched to one transparent state by the control field. Ultrafast switching and sensing nanodevices could be produced using this model.

Nonequilibrium Transport:

It has been a long-standing problem in SNs to explain the large suppression of the hot electron energy loss at low electron temperature. There has not been any theory to explain it. Recently we developed a theory for the first time where we showed that due to anharmonic phonon scattering, the hot electrons lose their energy by creating pairs of acoustic phonons via LO phonons. The large suppression of cthe electron energy loss rate can be predicted by our theory. This work provides the important information about many fundamental scattering processes that determine the high-field transport. The experimental results now have a firm theoretical foundation.

We have also predicted that when charge distribution is highly nonuniform in a sample, it displays quite abnormal behavior such as current flow against the applied voltage. The appearance of this negative electric current is a transient phenomenon occurring at the initial stage of the process. After this anomalous negative fluctuation, the electric current becomes normal as soon as the charge density becomes more uniform.

A theory of dispersive transport of carriers in amorphous nanostructures has also been developed in electric and magnetic fields. Our theory predicts that mobility has power laws in time.

Hot Electrons:

The reduction in size of electron devices made in order to attain high speed performance has greatly emphasized the role of hot electrons and phonons . Hot electrons and lattice are in Nonequilibrium states in these devices. Thus, any theoretical treatment of modern devices will deal with complex nonlinear systems consisting of coupled hot electron and phonon gases. Such a treatment is the aim of the present project. Our theory will be modified by including the above effects. This theory can also be extended to optical devices, quantum well lasers, organic semiconductors and polymers like polyacetylene, where hot electrons play an important role. Monte Carlo simulation methods will also be used.

Recombination and Resonant Tunneling:

We shall extend our theory of the recombination rate of section A1 for Resonant Tunneling Diodes (RTDs) and study phonon- and plasmon-assisted recombination rates. There are some interesting features of RTDs such as satellite peaks and a Fermi-edge singularity in the I-V curves in RTDs which can not be explained by a single band model . Most theories so far developed assume the single band model, that the transport is coherent with no inelastic scattering, and that RTS are flawless with no imperfections. Our theory will include an eight band model, many body effects and imperfections.

Electron-hole system:

We have discovered a new kind of electron-hole recombination phenomenon (activationless recombination process) in SNs. In semimetallic SNs (InAs/GaSb) the conduction band of InAs lies beneath the valence band of GaSb, and due to this overlapping of conduction and valence bands there is an activationless recombination process which does not require an extra excitation particle (phonon, photon). On the other hand, in the direct and indirect recombination processes when the electron and hole recombine a third particle is emitted. This discovery is going to have a major impact on making hot electron tunnelling transistors and related devices, and on the physics of current transport in SNs.

A theory of tunnelling theory based on an 8x8 Hamiltonian has been developed for resonant tunnelling diodes.

Excitons:

We have developed a theory for excitons in the presence of disorder since excitons play an important role in light-emitting devices, and to investigate the possibility of Bose-Einstein condensation of excitons. We considered that electrons and holes are spatially separated in SNs. We predicted several crossover regimes between the phases of bound electron-hole pairs and unbound electrons and holes. It has been shown that a sufficiently strong disorder promotes dissociation of bound electron-hole pairs and may decrease considerably the range of existence of an exciton gas. This theory is a major step toward understanding exciton problems in SNs.

There is considerable research interest in systems of excitons in SNs due to the important role excitons play in light-emitting and a possibility of Bose-Einstein condensation of excitons [4]. Recently, special attention has been attracted to spatially indirect excitons formed by spatially separated electrons and holes due to their strongly enhanced annihilation time. One of the problems in SNs is the presence of a disorder which hinders the manifestation of collective coherent effects. Interesting phenomena have been discovered such as non-usual behavior of the exciton diffusion coefficient and the luminescence intensity which are not explained yet. The kinetic processes such as exciton diffusion, exciton annihilation and transient luminescencr decay have not yet been studied theoretically in the presence of a disorder, particle-particle, and particle phonon interaction. Using our theory of section A1, we will study the above properties by including the functional integral representation of the statistical sum and the Keldysh diagrammatic technique.

Quantum Hall Effect (QHE) and Cyclotron Resonance (CR):

For the first time in the field, we have developed a theory for electron and hole CR in semiconductor superlattices by including electron-phonon and electron disorder interactions. Electron-disorder and electron-acoustic phonon interaction have been calculated self consistently. We predicted important new results. Among the predictions of our theory verified by experiments are that (i) cyclotron resonance line width is proportional to the square root of magnetic field; (ii) the QHE disappears at certain temperatures; (iii) the electron (hole) effective mass varies with temperature and magnetic field; (iv) and a new selection rule Dn= ±2 exists besides Dn= ±1.

Experiments to observe these resonances are being performed at different labs. We also predicted a new kind of CR such as LO phonon or plasmons assisted CR.

A semiconductor to semimetals transition due to band anisotropy and strong frequency dispersion in capacitance in type II heterostructures is also predicted

For the first time, we also developed a theory for photoluminescence in p-i-n-i-p narrow gap semiconductor (InSb) quantum wells and superlattices. We have predicted new photoluminescence lines in infrared and far-infrared regions. Experiments to verify these predictions are being done at Ioffe Institute and Imperial College.

We have studied the roles of plasmons and phonons on the quasi-periodic superlattices such as Fibonacci. We found new resonance states due to phonons and plasmons in the optical spectra. Our theory is able to explain the reflectance experiments on Fibonacci superlattice which until now could not be understood. (6) We also predicted a new effect in delta doped SL where the conductivity exhibits an oscillatory behavior due to localized states.

Recently some groups has performed fractional and normal QHE and CR in type II heterojunctions made from InAs and GaSb. They have observed a minigap in QHE and CR experiments as well as a giant magnetoresistance. Both electrons and hole carriers are present in these SNs due to an overlap of the conduction band of InAs and the valence band of GaSb. By varying the concentration of both carriers, they have also measured the QHE and CR. Most theories for QHE and CR include only one type of carrier in their calculations. We plan to develop a theory for QHE and CR by using an 8x8 matrix Hamiltonian which includes both types of carriers. The density of states (DOS) in the presence of impurities and electron-electron interactions will be calculated by using this Hamiltonian. These DOS will be used to calculate the QHE, CR, and giant negative magnetoresistance. We also propose to study the composite bosons, fermions and Skyrmions theories of QHE.

Group III Nitride Semiconductor Heterostructure:

During the past few years wide bandgap III-V nitride SNs (i.e. GaN) extended the field of semiconductor application to the limits where semiconductors such as Si and GaAs fail . They can emit light at shorter wavelength (blue and ultraviolet) and can operate at higher temperatures due to a large bandgap. Nitrides are grown as zinceblende(ZB) crystals and as well as wurtzite (WZ) crystals. However, there are many fundamental and device characteristics of the nitrides that are poorly understood. Some of them are as follows

• What is the difference between WZ and ZB nitrides?
• What are strain effects on these compounds?
• What are the characteristics of optical gains? In order to clarify these problems, we will study the k.p theory to calculate the band structure of ZB and WZ crystals. After this, we will use linear response theory and the Green’s function method to calculate the electronic and optical properties such as optical gain and conductivity in the presence of different scattering processes.

Macroscopic Quantum Coherence in Antiferromagnetic and SNs:

The study of macroscopic quantum coherence phenomena represents a subject of wide interest, ranging from the conceptual foundations of quantum mechanics to the physics of microelectronic devices [6]. The quantum coherence properties of the interacting two level systems are particularly important for the practical realization of quantum logic circuits and quantum computers. The systems of nuclear spins or quantum dots are particularly well suited for such applications. We plan to extend our theory of section A2 to investigate the feasibility of quantum computations using chains of nuclear spins or quantum dots.

HTS MATERIALS: Transport and Magnetic Properties.

Hopping Conduction and proximity effect in HTS Josephson Junctions:

We have developed a theory of electron and small polaron conductivity and mobility in Josephson S/N/S junctions (made from high temperature superconductors) and semiconductors SNs. Our theory predicts that the transport in thin films and junctions is due to the two-dimensional electron and small polaron variable range hopping mechanism. We have found new temperature, electric and magnetic electric field dependent power laws which are verified by experiments. For the first time, we have also predicted a phase transition in the conductivity due to electron-electron interaction which has been verified by experiments. This work provides an important mechanism for tunneling phenomena in Josephson Junctions and such knowledge is invaluable in making detectors and Squids.

We developed a theory for thermal conductivity (K) by postulating that defects such as vacancies and mass defects are randomly distributed, and electrons and phonons interact with these defects as well as experiencing electron-phonon interactions. Among the predictions of our theory verified by experiments are (i) K has T2 behavior at low temperatures, (ii) K has a hump at about Tc/2, (iii) vertex corrections are important in HTS and (iv) electron resistivity has a linear behavior in temperature.

Part of the work will be done with Dr. Tarutani group, Central Research Laboratory, HITACHI, Ltd., Tokyo. Recently, S/N/S junctions have been fabricated from HTSs where S is HTS and N is PBa2CuO{7-y} (PBCO) [10]. We propose to investigate some of the following properties of these junctions by extending our theory [11] and the Monte Carlo method. (1) Temperature, electric and magnetic dependent variable range hopping resistivity . (2) Size Effect: When the thickness of the N layer is smaller or equal to 0.2mm, the conductivity is independent of temperature for T< 4K. For T>4K, it follows hopping conduction. (3) Metal Insulator Transition: The Mott criterion for the Metal-insulator transition is not satisfied. (4) Proximity Effect: The proximity effect refers to the tunneling of Cooper pairs from the S layer to the N layer. In BCS superconductor junctions, the proximity effect is observed when the thickness of the normal metal is less than that of coherence length of the Cooper pairs. But in HTS based Junctions, the proximity effect is also observed even when the thickness of the N layer is larger than the coherence length of Cooper pairs. It is called the long range proximity effect. To study the proximity, each superconductor will be represented by a complex order parameter in the Ginzburg and Landau (GL) equations. The coupled GL equations will be solved numerically in the presence of the variable range hopping [11]. An alternate approach such as McMillan tunneling method will be also be used.

Magnetic Properties:

A theory for antiferromagnetic (AF) properties has been developed for HTS based on the quasi-two dimensional anisotropy Heisenberg model. We predicted weak interlayer AF coupling. This work examines the intimate connection between magnetism and superconductivity. Among the predictions of our theory verified by experiments are (i) the AF interlayer coupling between CuO planes plays an important role in understanding the magnetic properties of HTS and (ii) the theory is able to explain the temperature and doping dependent magnetization, the doping dependent Neel temperature, susceptibility and magnetic correlation length. (iii) Also it is predicted that the Neel temperature in the insulating state shows logarithmic behavior with doping concentration, (iv) the sublattice magnetization shows a square root of temperature behavior, and (v) the magnetic correlation length has exponential temperature dependence.

We also studied nonlinear spin motion in ferromagnets. The nonlinearity may be due to interacting electron and nuclear spins coupled with each other via hyperfine forces. Due to this nonlinearity, coherent motion of spins can develop resulting in their ultrafast relaxation. This type of ultrafast coherent relaxation can be used for studying the intrinsic properties of magnetic materials.

We also discovered the macroscopic quantum coherence phenomenon in one-dimensional AF materials.

One of the most captivating ongoing debates in condensed matter physics is the question of the pairing state and the mechanism of HTS. There are growing lists of theoretical calculations and experiments which have suggested that these materials may exhibit an unconventional pairing state different than the BCS pairing. One of the most striking universal properties of HTS is the close proximity between superconductivity and antiferromagnetism. They also exhibit strong magnetic interaction in theform of AF spin correlation that are usually mutually exclusive with superconductivity. There are experimental indications that spin fluctuations may also be responsible for the superconductivity. We developed a theory of superconductivity based on the spin fluctuations coupling [7]. The AF exchange coupling is responsible for the AF phase at half filling. The same coupling could lead to the formation of spin singlets, a prerequisite for superconductivity. Recently, a theory based on so(5) symmetry has been proposed for HTS unifying AF and d-wave SC phases and treating them on equal footing [8]. The so(5) symmetry provides a natural framework for the treatment of the pairing correlations in systems consisting of two components. We plan to study the excitation spectrum of a phenomenological Hamiltonian constructed using the so(5) generators, containing both pairing and antiferromagnetic interaction terms. Work is already in progress in this direction. Using a quasi-two dimensional Heisenberg model and model-based so(5) symmetry, we will also study the following magnetic properties. The effect of AF anisotropy which has been measured in doped and undoped CuO plane in HTS and has been ignored by most theories [9]. We will obtain the analytical expressions to explain the doping dependent magnetic moment, Neel temperatures, correlation length and susceptibility. Our theory is going to contain the coupled nonlinear Greens function equations between different sites, different layers and different spin orientations. We plan to solve these equations numerically by using numerical simulation methods.

PBG MATERIALS AND DISPERSIVE MEDIA

It is well known that a photonic gap exist in dispersive media (dielectric and III-V semiconductors) besides PBG materials. The existence of the photonic band gap in PBG is due to multiple photon scattering by spatially correlated scatterers. On the other hand, the photonic gap (polariton gap) in these media is caused by photon coupling to excitons and optical phonons. Recently, we discovered the following phenomena in dispersive media and SNs doped with quantum dots or quantum wells:

• The bound photon-atom state,
• the suppression of stimulated emission,
• superradiance and superradiance effects and
• photonic impurity bands and polariton effective mass.

It is also found that solitons containing an even number of polaritons (even solitons) propagate within the gap, while an odd soliton is pinned to the atom and forms a many-polariton-atom bound state. This discovery has opened a new research area in semiconductor physics. New experiments are going be performed to verify our predictions and new semiconductor devices such as lasers and photonic transistors can be made. PBG materials are difficult to prepare whereas III-V semiconductors are freely available in nature. Our theory is also applicable to PBS materials. Recent experiments in semiconductor macrocavities doped withquantum wells and dots are able to verify some of our predictions.

Recently great attention has been devoted to the study of the modification of photon-matter interaction due to quantified electromagnetic modes in PBS materials, dispersive media (DM) and quantum microcavities (QMCs). One of the aims is to control the spontaneous emission in its intensity and emission pattern. The dispersive media and microcavities like PBG materials have an energy gap in their polariton energy spectrum. This energy gap is caused by photon coupling to an elementary excitation such as excitons or the optical phonons of the media. The research in these materials is relatively new with most important developments having occurred in the last 5 years [12]. Potential applications of these materials exist in optoelectronic and photon devices. Much attention has been devoted experimentally to study the weak and strong exciton-photon coupling regimes in these materials when they are doped with one or more quantum wells or dots. They include the study of (i) the dispersion of cavity polaron , (ii) spontaneous emission, (iii) Rabi’s splitting and oscillations, (iv) the Rabi doublet changes into a triplet structure (dynamic Stark effect) in the high optical field and (v) solitons. The aim of this project is to modify our theory of section A3 by including both strong and weak exciton-photon coupling regimes. This theory will allow us to explain the above experiments and experiments with PBG materials. Some work is already in progress in this area. At the same time we are in contact with experimentalists in this area who are going to do experiments to observe our predicted effects of section A3.

POSITRON DIFFUSION & THIN FILM GROWTH IN SEMICONDUCTORS

Since the discovery of slow positrons, there is considerable interest in the study of positron diffusions in solids. At Western, positron techniques are used very successfully to find defects in semiconductors. Our theory [13] of positrons does not include the interaction of positrons with defects such as vacancy and impurities. We will extend our theory to include the above effect and compare our results with experiments of the Western group. Dr. Zinke-Allmang and his group study the fundamental processes during the initial stages of heterepitaxial growth of semiconductors and metals on semiconductors. We plan to study the mechanism of clustering processes during the growth by numerical simulations.