Shining Light on The Phase Transitions of Vanadium Dioxide

The salient feature of the familiar structural transition accompanying the thermally-driven metal-insulator transition in bulk vanadium dioxide (VO2) is a pairing of all the vanadium ions in the monoclinic M¬1 insulating phase. Whether this pairing (unit cell doubling) alone is sufficient to open the energy gap has been the central question of a classic debate which has continued for almost sixty years. Interestingly, there are two less familiar insulating states, monoclinic M2 and triclinic, which are accessible via strain or chemical doping. These phases are noteworthy in that they exhibit distinctly different V-V pairing. With infrared and optical photon spectroscopy, we investigate how the changes in crystal structure affect the electronic structure. We find that the energy gap and optical inter-band transitions are insensitive to changes in the vanadium-vanadium pairing. This result is confirmed by DFT+U and HSE calculations. Hence, our work conclusively establishes that intra-atomic Coulomb repulsion between electrons provides the dominant contribution to the energy gap in all insulating phases of VO2. VO2 is a candidate material for novel technologies, including ultrafast data storage, memristors, photonic switches, smart windows, and transistors which move beyond the limitations of silicon. The attractiveness of correlated materials for technological application is due to their novel properties that can be tuned by external factors such as strain, chemical doping, and applied fields. For advances in fundamental physics and applications, it is imperative that these properties be measured over a wide range of regimes. Towards this end, we study a single domain VO2 crystal with polarized light to characterize the anisotropy of the optical properties. In addition, we study the effects of compressive strain in a VO2 thin film in which we observe remarkable changes in electronic structure and transition temperature. Furthermore, we find evidence that electronic correlations are active in the metallic rutile phase as well. VO2 films exhibit phase coexistence in the vicinity of the metal-insulator transition. Using scanning near-field infrared microscopy, we have studied the patterns of phase coexistence in the same area on repeated heating and cooling cycles. We find that the pattern formation is reproducible each time. This is an unexpected result from the viewpoint of classical nucleation theory that anticipates some degree of randomness. The completely deterministic nature of nucleation and growth of domains in a VO2 film with imperfections is a fundamental finding. This result also holds promise for producing reliable nanoscale VO2 devices

Experimental and Computational Exploration of the Dilute Magnetic Delafossite CuAl1-xFexO2 Alloys

CuAlO2 is among several ternary delafossites, which is a rare p-type semiconductor with potential applications as a transparent conductive oxide, photocatalyst, and spintronics when doped with transition metal ions. Reported in this thesis are results from our investigations of CuAl1-xFexO2 (x = 0 to1) with a focus on the x-dependence of structural, magnetic, vibrational, optical properties, and the role of defects and impurities. Samples are prepared by solid-state reactions. We performed a complete study of magnetic properties to investigate the possibility of room temperature ferromagnetic alloys, which are used in transparent ferromagnet applications, suggested by a computational study. Analysis of magnetization (M) vs. temperature (T, from 2 to 300 K) data by Curie-Weiss law confirms Fe3+ as the electronic state of Fe; this analysis also yields a negative θ characteristic of an antiferromagnetic Fe3+-Fe3+ exchange coupling and magnitudes of x in good agreement with the nominal values. The isothermal M vs. H (up to H= 90 kOe) data analyzed by the modified Brillouin function support the results obtained from the M vs. T analysis. High-resolution M-H loop measurements at 300 K and 10 K show negligible coercivity (HC)at 10 K but HC ~ 100 Oe at 300K. The results suggest that the room temperature ferromagnetism can originate from hematite impurity, but not for CuAl1-xFexO2 alloys. The understanding of the phonon dynamics of alloys is crucial because they have a fundamental indirect bandgap. I introduce a new approach, which is applicable to anisotropic, dilute alloys with allowance for a large variety of alloying elements. This approach has significant advantages over previously reported methods, especially for the lattice dynamics of such complex alloys. We use this approach to model the effects of Fe-doping on the vibrational modes in dilute alloys of CuAl1-xFexO2 (x = 0-0.10) delafossite powders. Raman and FTIR spectroscopies are performed to measure optical phonon frequencies. For the phonon calculations, an approach using a disordered supercell is not feasible because it is computationally expensive. Instead, we developed our weighted dynamical matrix (WDM) approach that uses a straightforward ordered supercell for force-constant calculations of the CuAlO2 and CuFeO2 parent endpoints and combines them using a WDM approach. Computationally, when Fe is substituted for Al (increasing x), an increase in the bond length is observed, leading to a redshift in the peak positions in all the phonon modes vs. x, in agreement with the experimentally observed trend. CuAlO2, with an indirect bandgap ~3 eV, is a good candidate for photocatalysis applications because of its chemical stability and absorption in the solar region. However, efforts to improve its optical absorption continue. Here, I report the effect of alloying on the optical absorption of CuAl1-xFexO2(x = 0.0-1.0) by measuring the optical absorption of alloys from 1 to 6 eV and comparing these results to electronic band structures calculated using density functional theory (DFT) calculations. The calculations use DFT+U supercell methods, including spin. Experimentally, we observe a new absorption feature associated with Fe at about 1.8 eV for x = 0.01 shifting to 1.4 eV for x = 0.10. The energy of this feature and its redshift with x agrees with calculated spin-down Fe-3d states. This added feature will lead to more optical absorption. The major conclusions from this research are that by alloying CuAlO2 with Fe, the optical absorption will improve. Also, we proposed a straightforward, computationally efficient WDM approach, which confirms the redshift associated with the optical phonon modes. With our magnetic measurements, we confirmed that the dilute alloys are not ferromagnetic at room temperature

Reactive Flow and Transport Through Complex Systems

The meeting focused on mathematical aspects of reactive flow, diffusion and transport through complex systems. The research interest of the participants varied from physical modeling using PDEs, mathematical modeling using upscaling and homogenization, numerical analysis of PDEs describing reactive transport, PDEs from fluid mechanics, computational methods for random media and computational multiscale methods

Dynamics of Patterns

Patterns and nonlinear waves arise in many applications. Mathematical descriptions and analyses draw from a variety of fields such as partial differential equations of various types, differential and difference equations on networks and lattices, multi-particle systems, time-delayed systems, and numerical analysis. This workshop brought together researchers from these diverse areas to bridge existing gaps and to facilitate interaction

Delay-dependent Stability of Genetic Regulatory Networks

Genetic regulatory networks are biochemical reaction systems, consisting of a network of interacting genes and associated proteins. The dynamics of genetic regulatory networks contain many complex facets that require careful consideration during the modeling process. The classical modeling approach involves studying systems of ordinary differential equations (ODEs) that model biochemical reactions in a deterministic, continuous, and instantaneous fashion. In reality, the dynamics of these systems are stochastic, discrete, and widely delayed. The first two complications are often successfully addressed by modeling regulatory networks using the Gillespie stochastic simulation algorithm (SSA), while the delayed behavior of biochemical events such as transcription and translation are often ignored due to their mathematically difficult nature. We develop techniques based on delay-differential equations (DDEs) and the delayed Gillespie SSA to study the effects of delays, in both continuous deterministic and discrete stochastic settings. Our analysis applies techniques from Floquet theory and advanced numerical analysis within the context of delay-differential equations, and we are able to derive stability sensitivities for biochemical switches and oscillators across the constituent pathways, showing which pathways in the regulatory networks improve or worsen the stability of the system attractors. These delay sensitivities can be far from trivial, and we offer a computational framework validated across multiple levels of modeling fidelity. This work suggests that delays may play an important and previously overlooked role in providing robust dynamical behavior for certain genetic regulatory networks, and perhaps more importantly, may offer an accessible tuning parameter for robust bioengineering

Applications of Asymptotic Analysis

This workshop focused on asymptotic analysis and its fundamental role in the derivation and understanding of the nonlinear structure of mathematical models in various fields of applications, its impact on the development of new numerical methods and on other fields of applied mathematics such as shape optimization. This was complemented by a review as well as the presentation of some of the latest developments of singular perturbation methods