Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Single layer lead iodide : computational exploration of structural, electronic and optical properties, strain induced band modulation and the role of spin-orbital-coupling

Graphitic like layered materials exhibit intriguing electronic structures and thus the search for new types of two-dimensional (2D) monolayer materials is of great interest for developing novel nano-devices. By using density functional theory (DFT) method, here we for the first time investigate the structure, stability, electronic and optical properties of monolayer lead iodide (PbI2). The stability of PbI2 monolayer is first confirmed by phonon dispersion calculation. Compared to the calculation using generalized gradient approximation, screened hybrid functional and spin-orbit coupling effects can not only predicts an accurate bandgap (2.63 eV), but also the correct position of valence and conduction band edges. The biaxial strain can tune its bandgap size in a wide range from 1 eV to 3 eV, which can be understood by the strain induced uniformly change of electric field between Pb and I atomic layer. The calculated imaginary part of the dielectric function of 2D graphene/PbI2 van der Waals type hetero-structure shows significant red shift of absorption edge compared to that of a pure monolayer PbI2. Our findings highlight a new interesting 2D material with potential applications in nanoelectronics and optoelectronics.

Kinetics of electron recombination of dye-senitized solar cells based on TiO2 nanorod arrays sensitized with different dyes

The performance and electron recombination kinetics of dye-sensitized solar cells based on TiO2 films consisting of one-dimensional nanorod arrays (NR-DSSCs) which are sensitized with dye N719, C218 and D205 respectively have been studied. It has been found that the best efficiency is obtained with the dye C218 based NR-DSSCs, benefiting from a 40% higher short-circuit photocurrent density. However, the open circuit photovoltage of the N719 based cell is 40 mV higher than that of the organic dye C218 and D205 based devices. Investigation of the electron recombination kinetics of the NR-DSSCs has revealed that the effective electron lifetime, τn, of the N719 based NR-DSSC is the lowest whereas the τn of the C218 based NR-DSSC is the highest among the three dyes. The higher Voc with the N719 based NR-DSSC is originated from the more negative energy level of the conduction band of the TiO2 film. In addition, in comparison to the DSSCs with conventional nanocrystalline particles based TiO2 films, the NR-DSSCs have shown over two orders of magnitude higher τn when employing N719 as the sensitizer. Nevertheless, the τn of the DSSCs with the C218 based nanorod arrays is only ten-fold higher than the that of the nanoparticles based devices. The remarkable characteristic of the dye C218 in suppressing the electron recombination of DSSCs is discussed.

Reduced electron recombination of dye-sensitized solar cells based on TiO 2 spheres consisting of ultrathin nanosheets with [001] facet exposed

An anatase TiO 2 material with hierarchically structured spheres consisting of ultrathin nanosheets with 100% of the [001] facet exposed was employed to fabricate dye-sensitized solar cells (DSC s). Investigation of the electron transport and back reaction of the DSCs by electrochemical impedance spectroscopy showed that the spheres had a threefold lower electron recombination rate compared to the conventional TiO 2 nanoparticles. In contrast, the effective electron diffusion coefficient, D n, was not sensitive to the variation of the TiO 2 morphology. The TiO 2 spheres showed the same Dn as that of the nanoparticles. The influence of TiCl 4 post-treatment on the conduction band of the TiO 2 spheres and on the kinetics of electron transport and back reactions was also investigated. It was found that the TiCl 4 post-treatment caused a downward shift of the TiO 2 conduction band edge by 30 meV. Meanwhile, a fourfold increase of the effective electron lifetime of the DSC was also observed after TiCl4 treatment. The synergistic effect of the variation of the TiO 2 conduction band and the electron recombination determined the open-circuit voltage of the DSC. © 2012 Wang et al.

Influence of electrolyte cations on electron transport and electron transfer in dye-sensitized solar cells

The influence of different electrolyte cations ((Li+, Na+, Mg2+, tetrabutyl ammonium (TBA+)) on the TiO2 conduction band energy (Ec) the effective electron lifetime (τn), and the effective electron diffusion coefficient (Dn) in dye-sensitized solar cells (DSCs) was studied quantitatively. The separation between Ec and the redox Fermi level, EF,redox, was found to decrease as the charge/radius ratio of the cations increased. Ec in the Mg2+ electrolyte was found to be 170 meV lower than that in the Na+ electrolyte and 400 meV lower than that in the TBA+ electrolyte. Comparison of Dn and τn in the different electrolytes was carried out by using the trapped electron concentration as a measure of the energy difference between Ec and the quasi-Fermi level, nEF, under different illumination levels. Plots of Dn as a function of the trapped electron density, nt, were found to be relatively insensitive to the electrolyte cation, indicating that the density and energetic distribution of electron traps in TiO2 are similar in all of the electrolytes studied. By contrast, plots of τn versus nt for the different cations showed that the rate of electron back reaction is more than an order of magnitude faster in the TBA+ electrolyte compared with the Na+ and Li+ electrolytes. The electron diffusion lengths in the different electrolytes followed the sequence of Na+ > Li+ > Mg2+ > TBA+. The trends observed in the AM 1.5 current–voltage characteristics of the DSCs are rationalized on the basis of the conduction band shifts and changes in electron lifetime.

Nano-scale morphology and electron spectrum of defect states in low-k SiOCH films

Results of experimental investigations on the relationship between nanoscale morphology of carbon doped hydrogenated silicon-oxide (SiOCH) low-k films and their electron spectrum of defect states are presented. The SiOCH films have been deposited using trimethylsilane (3MS) - oxygen mixture in a 13.56 MHz plasma enhanced chemical vapor deposition (PECVD) system at variable RF power densities (from 1.3 to 2.6 W/cm2) and gas pressures of 3, 4, and 5 Torr. The atomic structure of the SiOCH films is a mixture of amorphous-nanocrystalline SiO2-like and SiC-like phases. Results of the FTIR spectroscopy and atomic force microscopy suggest that the volume fraction of the SiC-like phase increases from ∼0.2 to 0.4 with RF power. The average size of the nanoscale surface morphology elements of the SiO2-like matrix can be controlled by the RF power density and source gas flow rates. Electron density of the defect states N(E) of the SiOCH films has been investigated with the DLTS technique in the energy range up to 0.6 eV from the bottom of the conduction band. Distinct N(E) peaks at 0.25 - 0.35 eV and 0.42 - 0.52 eV below the conduction band bottom have been observed. The first N(E) peak is identified as originated from E1-like centers in the SiC-like phase. The volume density of the defects can vary from 1011 - 1017 cm-3 depending on specific conditions of the PECVD process.

Electronic structure studies and photocatalytic properties of cubic Bi1.5ZnNb1.5O7

The photocatalytic ability of cubic Bi1.5ZnNb1.5O7 (BZN) pyrochlore for the decolorization of an acid orange 7 (AO7) azo dye in aqueous solution under ultraviolet (UV) irradiation has been investigated for the first time. BZN catalyst powders prepared using low temperature sol-gel and higher temperature solid-state methods have been evaluated and their reaction rates have been compared.The experimental band gap energy has been estimated from the optical absorption edge and has been used as reference for theoretical calculations. The electronic band structure of BZN has been investigated using first-principles density functional theory (DFT) calculations for random, completely and partially ordered solid solutions of Zn cations in both the A and B sites of the pyrochlore structure.The nature of the orbitals in the valence band (VB) and the conduction band (CB) has been identified and the theoretical band gap energy has been discussed in terms of the DFT model approximations.

Theory For The Anomalous Hall Constant Of Mixed-Valence Systems

We show that the large anomalous Hall constants of mixed-valence and Kondo-lattice systems can be understood in terms of a simple resonant-level Fermi-liquid model. Splitting of a narrow, orbitally unquenched, spin-orbit split, f resonance in a magnetic field leads to strong skew scattering of band electrons. We interpret both the anomalous signs and the strong temperature dependence of Hall mobilities in CeCu2Si2, SmB6, and CePd3 in terms of this theory.

Can Nano Silicon Be Made Optically Active?

There has been a lot of effort to make Silicon optically active. In this work we examine two methods of generating nanocrystals of Silicon from bulk fragments. This approach of ours allows us to play with the shape of the nanocrystals and therefore the degeneracy of the conduction band minimum. We go on to examine whether similar sized particles with different shapes have the same physical properties, and finally whether Silicon may be rendered optically active by this route. While we do find that similar sized particles with different shapes may have different band gaps, this route of modifying the degeneracy of the conduction band minimum makes nano Si slightly optically active.

Properties of the gold related acceptor level in silicon

The apparent thermal activation energy of 0.56 eV and the electron thermal capture cross section of 2.0 × 10-16 cm2 are measured for the gold related acceptor level in p+ nn+ silicon diodes by isothermal current transient and DLTS techniques. Using the emission and capture rate data and a degeneracy ratio of 2, the energy separation of the trap level from the conduction band is calculated and found to have the same temperature dependence as the band gap indicating that the acceptor level is pinned with respect to the valence band a t Ev + 0.637 eV.

Continually adjustable oriented 1D TiO2 nanostructure arrays with controlled growth of morphology and their application in dye-sensitized solar cells

Oriented, single-crystalline, one-dimensional (1D) TiO2 nanostructures would be most desirable for providing fascinating properties and features, such as high electron mobility or quantum confinement effects, high specific surface area, and even high mechanical strength, but achieving these structures has been limited by the availability of synthetic techniques. In this study, a concept for precisely controlling the morphology of 1D TiO2 nanostructures by tuning the hydrolysis rate of titanium precursors is proposed. Based on this innovation, oriented 1D rutile TiO2 nanostructure arrays with continually adjustable morphologies, from nanorods (NRODs) to nanoribbons (NRIBs), and then nanowires (NWs), as well as the transient state morphologies, were successfully synthesized. The proposed method is a significant finding in terms of controlling the morphology of the 1D TiO2 nano-architectures, which leads to significant changes in their band structures. It is worth noting that the synthesized rutile NRIBs and NWs have a comparable bandgap and conduction band edge height to those of the anatase phase, which in turn enhances their photochemical activity. In photovoltaic performance tests, the photoanode constructed from the oriented NRIB arrays possesses not only a high surface area for sufficient dye loading and better light scattering in the visible light range than for the other morphologies, but also a wider bandgap and higher conduction band edge, with more than 200% improvement in power conversion efficiency in dye-sensitized solar cells (DSCs) compared with NROD morphology.

Intrinsic Electron localization in manganites

We mention here an unusual disorder effect in manganites, namely the ubiquitous hopping behavior for electron transport observed in them over a wide range of doping. We argue that the implied Anderson localization is intrinsic to manganites, because of the existence of polarons in them which are spatially localized, generally at random sites (unless there is polaron ordering). We have developed a microscopic two fluid lb model for manganites, where l denotes lattice site localized l polarons, and b denotes band electrons. Using this, and the self-consistent theory of localization, we show that the occupied b states are Anderson localized in a large range of doping due to the scattering of b electrons from l polarons. Numerical simulations which further include the effect of long range Coulomb interactions support this, as well the existence of a novel polaronic Coulomb glass. A consequence is the inevitable hopping behaviour for electron transport observed in doped insulating manganites.

Structure and electron transport anomalies in InSe-In6Se 7 composite

Rapid solidification of an equiatomic In-Se alloy resulted in the formation of an equilibrium InSe-In6Se7 phase mixture. The InSe phase was found to be polytypic and exhibited the structural variants 2H, 3H, and 4H. The 4H polytype was found to be in considerably higher proportion compared to 2H and 3H types. The In6Se7 phase was found to be hexagonal with a=0.8919 nm and c=1.4273 nm. Both In6Se 7 and the polytypes of InSe could be identified with the space group P61. The conductivity σ variation with temperature was found to be similar to that observed in disordered semiconducting materials. For temperatures >200 K, ln σ decreased linearly with T-1, phonon-assisted carrier excitation. For temperatures <200 K, ln σ decrease followed T-1/3 behavior, representative of variable-range hopping conduction of electrons.

Optical absorption and photoluminescence studies on heavily doped (Ga,Mn)Sb crystals

Ga1-xMnxSb crystals are grown with different Mn doping concentrations by the horizontal Bridgman method (x = 0 - 0.04). Optical absorption and photoluminescence studies are carried out in the temperature range 3-300 K. Optical absorption studies reveal that the inter-valence band transition from the spin-orbit split-off band to the light/heavy hole bands is dominant over the fundamental valence band to conduction band absorption. In higher doped crystals, the fundamental absorption peak is merged with the inter-valence band transition and could not be resolved. Photoluminescence measurements in heavily doped crystals reveal the band gap narrowing and band filling effects due to the Fermi level shifting into the valence band.

Analysis of the Gd 4d-XY Auger spectrum using synchrotron radiation

We report the 4d-XY (X, Y = 5p, 4f, and the conduction band) Auger spectra of clean Gd using a monochromatic photon source with energies above and below the 3d threshold. The spectra with higher hv show the existence of intense spectator-hole Auger transitions. Comparison of these spectra with those obtained with a primary electron source allows detailed interpretation of the various features and explains the unusual spin polarization of the electron-induced spectrum reported earlier.