There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

https://www.surfacesciencewestern.com/wp-content/uploads/2012/01/ass11_biesinger.pdf

Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn

Preface to the Second Edition. Preface to the First Edition. 1 Introduction. 2 Network Analysis. 2.1 Network Variables. 2.2 Scattering Parameters. 2.3 Short-Circuit Admittance Parameters. 2.4 Open-Circuit Impedance Parameters. 2.5 ABCD Parameters. 2.6 Transmission-Line Networks. 2.7 Network Connections. 2.8 Network Parameter Conversions. 2.9 Symmetrical Network Analysis. 2.10 Multiport Networks. 2.11 Equivalent and Dual Network. 2.12 Multimode Networks. 3 Basic Concepts and Theories of Filters. 3.1 Transfer Functions. 3.2 Lowpass Prototype Filters and Elements. 3.3 Frequency and Element Transformations. 3.4 Immittance Inverters. 3.5 Richards' Transformation and Kuroda Identities. 3.6 Dissipation and Unloaded Quality Factor. 4 Transmission Lines and Components. 4.1 Microstrip Lines. 4.2 Coupled Lines. 4.3 Discontinuities and Components. 4.4 Other Types of Microstrip Lines. 4.5 Coplanar Waveguide (CPW). 4.6 Slotlines. 5 Lowpass and Bandpass Filters. 5.1 Lowpass Filters. 5.2 Bandpass Filters. 6 Highpass and Bandstop Filters. 6.1 Highpass Filters. 6.2 Bandstop Filters. 7 Coupled-Resonator Circuits. 7.1 General Coupling Matrix for Coupled-Resonator Filters. 7.2 General Theory of Couplings. 7.3 General Formulation for Extracting Coupling Coefficient k. 7.4 Formulation for Extracting External Quality Factor Qe. 7.5 Numerical Examples. 7.6 General Coupling Matrix Including Source and Load. 8 CAD for Low-Cost and High-Volume Production. 8.1 Computer-Aided Design (CAD) Tools. 8.2 Computer-Aided Analysis (CAA). 8.3 Filter Synthesis by Optimization. 8.4 CAD Examples. 9 Advanced RF/Microwave Filters. 9.1 Selective Filters with a Single Pair of Transmission Zeros. 9.2 Cascaded Quadruplet (CQ) Filters. 9.3 Trisection and Cascaded Trisection (CT) Filters. 9.4 Advanced Filters with Transmission-Line Inserted Inverters. 9.5 Linear-Phase Filters. 9.6 Extracted Pole Filters. 9.7 Canonical Filters. 9.8 Multiband Filters. 10 Compact Filters and Filter Miniaturization. 10.1 Miniature Open-Loop and Hairpin Resonator Filters. 10.2 Slow-Wave Resonator Filters. 10.3 Miniature Dual-Mode Resonator Filters. 10.4 Lumped-Element Filters. 10.5 Miniature Filters Using High Dielectric-Constant Substrates. 10.6 Multilayer Filters. 11 Superconducting Filters. 11.1 High-Temperature Superconducting (HTS) Materials. 11.2 HTS Filters for Mobile Communications. 11.3 HTS Filters for Satellite Communications. 11.4 HTS Filters for Radio Astronomy and Radar. 11.5 High-Power HTS Filters. 11.6 Cryogenic Package. 12 Ultra-Wideband (UWB) Filters. 12.1 UWB Filters with Short-Circuited Stubs. 12.2 UWB-Coupled Resonator Filters. 12.3 Quasilumped Element UWB Filters. 12.4 UWB Filters Using Cascaded Miniature High- And Lowpass Filters. 12.5 UWB Filters with Notch Band(s). 13 Tunable and Reconfigurable Filters. 13.1 Tunable Combline Filters. 13.2 Tunable Open-Loop Filters without Via-Hole Grounding. 13.3 Reconfigurable Dual-Mode Bandpass Filters. 13.4 Wideband Filters with Reconfigurable Bandwidth. 13.5 Reconfigurable UWB Filters. 13.6 RF MEMS Reconfigurable Filters. 13.7 Piezoelectric Transducer Tunable Filters. 13.8 Ferroelectric Tunable Filters. Appendix: Useful Constants and Data. A.1 Physical Constants. A.2 Conductivity of Metals at 25 C (298K). A.3 Electical Resistivity rho in 10-8 m of Metals. A.4 Properties of Dielectric Substrates. Index.

Microstrip filters for RF/microwave applications

Electrons in correlated insulators are prevented from conducting by Coulomb repulsion between them. When an insulator-to-metal transition is induced in a correlated insulator by doping or heating, the resulting conducting state can be radically different from that characterized by free electrons in conventional metals. We report on the electronic properties of a prototypical correlated insulator vanadium dioxide in which the metallic state can be induced by increasing temperature. Scanning near-field infrared microscopy allows us to directly image nanoscale metallic puddles that appear at the onset of the insulator-to-metal transition. In combination with far-field infrared spectroscopy, the data reveal the Mott transition with divergent quasi-particle mass in the metallic puddles. The experimental approach used sets the stage for investigations of charge dynamics on the nanoscale in other inhomogeneous correlated electron systems.

Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging

An innovative technique uses ultrafast below-bandgap electric-field pulses to induce and probe an insulator–metal transition in an oxide thin film on which a metamaterial structure has been deposited. The transition from insulating to metallic behaviour and the microscopic interactions that accompany the transition are important phenomena in electronic materials. Until now it has not been possible to observe the transition directly in a time-resolved manner. Here, Richard Averitt and colleagues use ultrafast terahertz pulses to induce a phase transition in a prototypical insulator–metal transition material (vanadium dioxide) on which a metamaterial structure has been deposited. The metamaterial serves to amplify the local terahertz field, as well as to detect macroscopic changes in vanadium dioxide. Through direct, time-resolved observations, the authors establish a detailed microscopic picture of the structural and electronic changes underlying the insulator–metal transition. They conclude that their technique is versatile and could even be used to study phase transitions in superconductors. Electron–electron interactions can render an otherwise conducting material insulating1, with the insulator–metal phase transition in correlated-electron materials being the canonical macroscopic manifestation of the competition between charge-carrier itinerancy and localization. The transition can arise from underlying microscopic interactions among the charge, lattice, orbital and spin degrees of freedom, the complexity of which leads to multiple phase-transition pathways. For example, in many transition metal oxides, the insulator–metal transition has been achieved with external stimuli, including temperature, light, electric field, mechanical strain or magnetic field2,3,4,5,6,7. Vanadium dioxide is particularly intriguing because both the lattice and on-site Coulomb repulsion contribute to the insulator-to-metal transition at 340 K (ref. 8). Thus, although the precise microscopic origin of the phase transition remains elusive, vanadium dioxide serves as a testbed for correlated-electron phase-transition dynamics. Here we report the observation of an insulator–metal transition in vanadium dioxide induced by a terahertz electric field. This is achieved using metamaterial-enhanced picosecond, high-field terahertz pulses to reduce the Coulomb-induced potential barrier for carrier transport9. A nonlinear metamaterial response is observed through the phase transition, demonstrating that high-field terahertz pulses provide alternative pathways to induce collective electronic and structural rearrangements. The metamaterial resonators play a dual role, providing sub-wavelength field enhancement that locally drives the nonlinear response, and global sensitivity to the local changes, thereby enabling macroscopic observation of the dynamics10,11. This methodology provides a powerful platform to investigate low-energy dynamics in condensed matter and, further, demonstrates that integration of metamaterials with complex matter is a viable pathway to realize functional nonlinear electromagnetic composites.

Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial

An abrupt Mott metal-insulator transition (MIT) rather than the continuous Hubbard MIT near a critical on-site Coulomb energy U/U_c=1 is observed for the first time in VO_2, a strongly correlated material, by inducing holes of about 0.018% into the conduction band. As a result, a discontinuous jump of the density of states on the Fermi surface is observed and inhomogeneity inevitably occurs. The gate effect in fabricated transistors is clear evidence that the abrupt MIT is induced by the excitation of holes.

http://arxiv.org/pdf/cond-mat/0308042.pdf

Observation of Mott Transition in VO_2 Based Transistors

An abrupt first-order metal-insulator transition (MIT) as a current jump has been observed by applying a dc electric field to Mott insulator VO2-based two-terminal devices. The size of the jumps was measured to be asymmetrical depending on the direction of the applied voltage due to heating effects. The structure of VO2 is investigated by micro-Raman scattering experiments. An analysis of the Raman-active Ag modes at 195 and 222cm−1, explained by pairing and tilting of V cations, and 622cm−1, shows that the modes below a low compliance (restricted) current do not change when the MIT occurs, whereas a structural phase transition above the low compliance current is found to occur secondarily, due to heating effects in the device induced by the MIT. The MIT has applications in the development of high-speed and high-gain switching devices.

Raman study of electric-field-induced first-order metal-insulator transition in VO2-based devices

An abrupt first-order metal-insulator transition (MIT) without structural phase transition is first observed by current-voltage measurements and micro-Raman scattering experiments, when a DC electric field is applied to a Mott insulator VO_2 based two-terminal device. An abrupt current jump is measured at a critical electric field. The Raman-shift frequency and the bandwidth of the most predominant Raman-active A_g mode, excited by the electric field, do not change through the abrupt MIT, while, they, excited by temperature, pronouncedly soften and damp (structural MIT), respectively. This structural MIT is found to occur secondarily.

https://arxiv.org/pdf/cond-mat/0402485.pdf

Observation of First-Order Metal-Insulator Transition without Structural Phase Transition in VO_2

Ferroelectric BaTiO3 thin films with perovskite structure were grown by sol-gel spin-on processing onto (111)Pt/Ti/SiO2/Si substrates. In order to investigate the effects of space charge in BaTiO3 thin films, we measured the relative dielectric constant and the ac conductivity of the films as a function of frequency, ac oscillation amplitude, and temperature. Dielectric constant and dielectric loss were 147 and 0.03 at 100 kHz, respectively. Also, BaTiO3 thin films exhibited marked dielectric relaxation above the Curie temperature and in the low-frequency region below 100 Hz. This low-frequency dielectric relaxation is attributed to the ionized space-charge carriers such as oxygen vacancies and defects in BaTiO3 film and the interfacial polarization. The thermal activation energy for the relaxation process of the ionized space-charge carriers was 0.72 eV.

Low-frequency dielectric relaxation of BaTiO3 thin-film capacitors

The effects of anisotropic dielectric properties of ferroelectric Ba1−xSrxTiO3 (BST) films on the characteristics of the interdigital (IDT) capacitors have been studied in microwave regions at room temperature. Ferroelectric BST films with (001), (011), and (111) orientation were epitaxially grown on (001), (011), and (111) MgO substrates, respectively, by the pulsed laser deposition method. The microwave properties of orientation engineered BST films were investigated using interdigital capacitors. The calculated dielectric constant tunability with 40 V dc bias variation and the calculated dielectric quality factor values for IDT capacitors based on (001), (011), and (111) oriented BST films at 9 GHz with no dc bias were about 47%, 55%, 43%, and 12, 14, 21, respectively.

Kwang-Yong Kang

Papers

Observation of Mott Transition in VO_2 Based Transistors

Raman study of electric-field-induced first-order metal-insulator transition in VO2-based devices

Observation of First-Order Metal-Insulator Transition without Structural Phase Transition in VO_2

Low-frequency dielectric relaxation of BaTiO3 thin-film capacitors

Orientation dependent microwave dielectric properties of ferroelectric Ba1−xSrxTiO3 thin films