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At least 1,171 records · Page 65

Error analysis in the measurement of average power with application to switching controllers

Power measurement errors due to the bandwidth of a power meter and the sampling of the input voltage and current of a power meter were investigated assuming sinusoidal excitation and periodic signals generated by a model of a simple chopper system. Errors incurred in measuring power using a microcomputer with limited data storage were also considered. The behavior of the power measurement error due to the frequency responses of first order transfer functions between the input sinusoidal voltage, input sinusoidal current, and the signal multiplier was studied. Results indicate that this power measurement error can be minimized if the frequency responses of the first order transfer functions are identical. The power error analysis was extended to include the power measurement error for a model of a simple chopper system with a power source and an ideal shunt motor acting as an electrical load for the chopper. The behavior of the power measurement error was determined as a function of the chopper's duty cycle and back EMF of the shunt motor. Results indicate that the error is large when the duty cycle or back EMF is small. Theoretical and experimental results indicate that the power measurement error due to sampling of sinusoidal voltages and currents becomes excessively large when the number of observation periods approaches one-half the size of the microcomputer data memory allocated to the storage of either the input sinusoidal voltage or current.

Maisel, J. E.↗

Carbon and energy cost impacts of electrification of space heating with heat pumps in the US

In order to meet climate goals, it will be necessary to significantly reduce the greenhouse gases emitted by homes. A key factor in the US is to reduce the on-site combustion of fossil fuels for heating end-uses and to replace this with use of electric heat pump technologies connected to a low-carbon grid. The replacement of natural gas furnaces with electric heat pumps is a key home decarbonization strategy. However, the potential for space heating electrification to reduce greenhouse gas emissions depends on the carbon dioxide equivalent (CO 2 e) content of the electricity used by the heat pump. This varies considerably depending on the source of electricity, with large state to state variability. Furthermore, household energy costs are likely to be impacted by the electrification of space heating, because retail energy prices for both natural gas and electricity in each state vary by factors of seven and four, respectively. Contractors, energy programs, government and building code officials, as well as consumers need clear indications of the likely CO 2 e and energy cost impacts of proposed electrification projects, because these will affect decarbonization choices and rationales around scaled heating electrification. Government and utility programs also need to be aware of the likely outcomes of any supported/incentivized measures. Here, in this paper, we investigate these effects by looking at new metrics to analyze the change in CO 2 e emitted and the cost to meet home heating loads when switching from a natural gas furnace to a heat pump for the contiguous 48 states of the mainland US.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

High-performance photonic transformers for DC voltage conversion

Abstract Direct current (DC) converters play an essential role in electronic circuits. Conventional high-efficiency DC voltage converters, especially step-up type, rely on switching operation, where energy is periodically stored within and released from inductors and/or capacitors connected in a variety of circuit topologies. Since these energy storage components, especially inductors, are fundamentally difficult to scale down, miniaturization of switching converters proves challenging. Furthermore, the resulting switching currents produce significant electromagnetic noise. To overcome the limitations of switching converters, photonic transformers, where voltage conversion is achieved through light emission and detection processes, have been demonstrated. However, the demonstrated efficiency is significantly below that of the switching converter. Here we perform a detailed balance analysis and show that with a monolithically integrated design that enables efficient photon transport, the photonic transformer can operate with a near-unity conversion efficiency and high voltage conversion ratio. We validate the theory with a transformer constructed with off-the-shelf discrete components. Our experiment showcases near noiseless operation and a voltage conversion ratio that is significantly higher than obtained in previous photonic transformers. Our findings point to the possibility of a high-performance optical solution to miniaturizing DC power converters and improving the electromagnetic compatibility and quality of electrical power.

42 ENGINEERING↗

Detector Assembly and the Ultralow-Temperature Refrigerator for XRS

The X-ray spectrometer (XRS) on the Japanese Astro-E Spacecraft is the first ultra low temperature space borne instrument. The system utilizes a 900g Ferric Ammonium Alum (FAA) Adiabatic Demagnetization Refrigerator (ADR) with a helium-3 gas gap heat switch to cool the detector assembly to 0.060K. The system operates in a "single shot" configuration allowing the system to remain at its operating temperature for about 40 hours in the lab. The on-orbit performance is expected to be about 35 hours with a 97% duty cycle. The detector assembly for XRS consists of a 32 channel microcalorimeter array bias electronics, thermometry, and an anti-coincidence detector that are attached to the cold stage of the ADR. To thermally Isolate the detector system from the superfluid helium reservoir, the detector system is suspended by Kevlar cords and electrical connection in made by L30, 17-micron diameter, tensioned NbTi leads. The detectors are read out in a source-follower arrangement using FET amplifiers operating at 130K mounted in multiply-thermally-isolated assemblies that also use Kevlar and stainless steel wiring. The design and thermal performance of this system will be discussed and compared to the theoretical limits.

Porter, F. S.↗

NASA Tech Briefs, September 2012

Topics covered include: Beat-to-Beat Blood Pressure Monitor; Measurement Techniques for Clock Jitter; Lightweight, Miniature Inertial Measurement System; Optical Density Analysis of X-Rays Utilizing Calibration Tooling to Estimate Thickness of Parts; Fuel Cell/Electrochemical Cell Voltage Monitor; Anomaly Detection Techniques with Real Test Data from a Spinning Turbine Engine-Like Rotor; Measuring Air Leaks into the Vacuum Space of Large Liquid Hydrogen Tanks; Antenna Calibration and Measurement Equipment; Glass Solder Approach for Robust, Low-Loss, Fiber-to-Waveguide Coupling; Lightweight Metal Matrix Composite Segmented for Manufacturing High-Precision Mirrors; Plasma Treatment to Remove Carbon from Indium UV Filters; Telerobotics Workstation (TRWS) for Deep Space Habitats; Single-Pole Double-Throw MMIC Switches for a Microwave Radiometer; On Shaft Data Acquisition System (OSDAS); ASIC Readout Circuit Architecture for Large Geiger Photodiode Arrays; Flexible Architecture for FPGAs in Embedded Systems; Polyurea-Based Aerogel Monoliths and Composites; Resin-Impregnated Carbon Ablator: A New Ablative Material for Hyperbolic Entry Speeds; Self-Cleaning Particulate Prefilter Media; Modular, Rapid Propellant Loading System/Cryogenic Testbed; Compact, Low-Force, Low-Noise Linear Actuator; Loop Heat Pipe with Thermal Control Valve as a Variable Thermal Link; Process for Measuring Over-Center Distances; Hands-Free Transcranial Color Doppler Probe; Improving Balance Function Using Low Levels of Electrical Stimulation of the Balance Organs; Developing Physiologic Models for Emergency Medical Procedures Under Microgravity; PMA-Linked Fluorescence for Rapid Detection of Viable Bacterial Endospores; Portable Intravenous Fluid Production Device for Ground Use; Adaptation of a Filter Assembly to Assess Microbial Bioburden of Pressurant Within a Propulsion System; Multiplexed Force and Deflection Sensing Shell Membranes for Robotic Manipulators; Whispering Gallery Mode Optomechanical Resonator; Vision-Aided Autonomous Landing and Ingress of Micro Aerial Vehicles; Self-Sealing Wet Chemistry Cell for Field Analysis; General MACOS Interface for Modeling and Analysis for Controlled Optical Systems; Mars Technology Rover with Arm-Mounted Percussive Coring Tool, Microimager, and Sample-Handling Encapsulation Containerization Subsystem; Fault-Tolerant, Real-Time, Multi-Core Computer System; Water Detection Based on Object Reflections; SATPLOT for Analysis of SECCHI Heliospheric Imager Data; Plug-in Plan Tool v3.0.3.1; Frequency Correction for MIRO Chirp Transformation Spectroscopy Spectrum; Nonlinear Estimation Approach to Real-Time Georegistration from Aerial Images; Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications; Low-Cost Telemetry System for Small/Micro Satellites; Operator Interface and Control Software for the Reconfigurable Surface System Tri-ATHLETE; and Algorithms for Determining Physical Responses of Structures Under Load.

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The impacts of building characteristics, social psychological and cultural factors on indoor environment quality productivity belief

Indoor environmental quality (IEQ) plays a key role in determining occupants' productivity at work; however, analyses of the interconnected factors among building physical, attitudinal, social and demographic components in one study are lacking. To fill this research gap, this study investigates these interconnected factors' influence on occupants’ IEQ-productivity belief, defined as a personal, subjective evaluation of the linkage between the impacts of five IEQ aspects (the quality of indoor temperature, air, natural and electric lighting, and acoustics) and productivity. A cross-sectional survey data was collected in university offices from six countries (Brazil, Italy, Poland, Switzerland, Taiwan and the U.S.). Results of multiple linear regression models indicate that IEQ satisfaction is the strongest positive predictor of the IEQ-productivity belief and this relationship is stronger in private offices. Country of residence is the second primary predictor. Several attitudinal-behavioral factors, including thermal comfort, perceived ease of controlling indoor environmental features, and attitudes toward sharing controls are all positively associated with IEQ-productivity belief. Interestingly, the level of control accessibility to light switches has the strongest impact as opposed to other controls. On the other hand, group norms and conformity intention are not significant predictors. Regarding demographics, men are more likely than women to perceive the IEQs to have positive impacts on their productivity, without considering other variables in the regression model; however, women are more likely than men to consider all IEQs as having positive impacts on productivity, after considering other variables. Furthermore, our findings provide suggestions for prioritizing wellness in the workplace since the early design stage.

99 GENERAL AND MISCELLANEOUS↗

Two-component exciton condensates in an electron–hole bilayer

Macroscopic quantum coherence emerges when bosons condense into a Bose–Einstein condensate (BEC). Excitons are a long-sought solid-state route to high-temperature BECs with strong interactions, electrical tunability and potentially multicomponent spinor order, but conclusive evidence for equilibrium condensation has remained elusive. Here we report evidence for two-component exciton BECs in MoSe 2 /hBN/WSe 2 electron–hole bilayers by probing the spin–valley susceptibility of constituent electrons and holes. This heterostructure hosts equilibrium exciton fluids with four spin–valley flavours. Magneto-optical spectroscopy in a dilution refrigerator reveals three exciton condensate phases with distinct flavour polarizations. At zero magnetic field, the many-body ground state is a coherent superposition of two condensed intravalley exciton flavours. Under a magnetic field, the intravalley exciton condensate first switches to a two-component intervalley condensate through a first-order quantum phase transition at a weak critical field and then turns into a fully polarized single-component condensate at high fields. The condensate signatures form a dome in density–temperature space, persisting up to approximately 1.8 K. Our results establish van der Waals electron–hole bilayers as a versatile platform for strongly interacting, multicomponent exciton BECs.

Qi, Ruishi [University of California, Berkeley, CA↗

Quantifying the Protectability of Power Systems for Restoration Applications

With the increasing availability of distributed energy resources, controllable switches, and advanced metering infrastructure, distribution systems are exploring opportunities for improving system reliability through fault location, isolation, and service restoration. During permanent outages, this requires islanding microgrids and/or reconfiguration of the feeders; however, it is critical to assess the protection of the islanded/reconfigured networks before transition because the rated load and fault current conditions change. This paper presents a novel “protectability” metric that quantifies the protection performance and allows the operators to compare the effectiveness of the protection between two or more possible reconfiguration and islanding approaches. We present the mathematical formulation and assumptions for the metric. Multiple configurations of the Electric Power Research Institute J1 feeder, both in grid-connected and weak-sourced islanded operation, are used to demonstrate the performance of the metric with reference to overcurrent protection. Takeaways for future studies on system planning integration are provided.

distributed energy resources↗

Surge-Energy and Overvoltage Ruggedness of P-Gate GaN HEMTs

An essential ruggedness of power devices is the capability of safely withstanding the surge energy. The surge ruggedness of the GaN high-electron-mobility transistor (HEMT), a power transistor with no or minimal avalanche capability, has not been fully understood. This article unveils the comprehensive physics associated with the surge-energy withstand process and the failure mechanisms of p-gate GaN HEMTs. Two commercial p-gate GaN HEMTs with Ohmic- and Schottky-type gate contacts are studied. Two circuits are developed to study the device surge ruggedness: an unclamped inductive switching circuit is first used to identify the withstand dynamics and failure mechanisms, and a clamped inductive switching circuit with a controllable parasitic inductance is then designed to mimic the surge energy in converter-like switching events. The p-gate GaN HEMT is found to withstand the surge energy through a resonant energy transfer between the device capacitance and the load/parasitic inductance rather than a resistive energy dissipation as occurred in the avalanche. If the device resonant voltage goes below zero, the device reversely turns on and the inductor is discharged. The device failure occurs at the transient of peak resonant voltage and is limited by the device overvoltage capability rather than the surge energy, dV/dt , or overvoltage duration. Almost no energy is dissipated in the resonant withstand process and the device failure is dominated by an electric field rather than a thermal runaway. Furthermore, these results provide critical understandings on the ruggedness of GaN HEMTs and important references for their qualifications and applications.

42 ENGINEERING↗

Magnetic Launch Assist

With the ever-increasing cost of getting to space and the need for safe, reliable, and inexpensive ways to access space, NASA is taking a look at technologies that will get us there. One of these technologies is Magnetic Launch Assist (MagLev). This is the concept of using both magnetic levitation and magnetic propulsion to provide an initial velocity by using electrical power from ground sources. The use of ground based power can significantly reduce operational costs over the consumables necessary to attain the same velocity. The technologies to accomplish this are both old and new. The concept of MagLev has been around for a long time and several MagLev Trains have already been made. Where NASA's MagLev diverges from the traditional train is in the immense power required to propel this vehicle to 600 feet per second in less than 10 seconds. New technologies or the upgrade of existing technologies will need to be investigated in areas of energy storage and power switching. Plus the separation of a very large mass (the space vehicle) and the aerodynamics of that vehicle while on the carrier are also of great concern and require considerable study and testing. NASA's plan is to mature these technologies in the next 10 years to achieve our goal of launching a full sized space vehicle off a MagLev rail.

Jacobs, W. A.↗

Development of mid-infrared solid state lasers for spaceborne lidar

The laser performance of a Ho(3+):Tm(3+):Cr(3+):YAG crystal was measured under flashlamp pumping at various operating temperatures. The normal mode laser thresholds of a Ho(3+)(0.45 at. percent):Tm(3+)(2.5 at. percent):Cr(3+)(1.5 at. percent ):YAG crystal were found to range from 26 to 50 J between 120 and 200 K with slope efficiencies up to 0.36 percent with a 60 percent reflective output mirror. From the Q-switched operations a slope efficiency corresponding to 90 percent of the normal mode operation was observed. Laser wavelengths were measured for various operating conditions and fluorescence spectra were obtained at various temperatures in order to help understand the dynamic energy processes among the Ho(3+), Tm(3+), and Cr(3+) ions. A pulse forming network for a flashlamp pumped Cr:GSAG laser, which is to be used as a high power laser diode simulator in rare earth laser pumping, was completed and tested. The network provided critically damped, 1 ms FWHM, square pulses with a rise time of about 160 micrometers at an input electrical energy of 300 J.

Whitney, Donald A.↗

Radiation Protection of New Lightweight Electromagnetic Interference Shielding Materials Determined

Weight savings as high as 80 percent could be achieved by simply switching from aluminum electromagnetic interference (EMI) shielding covers for spacecraft power systems to EMI covers made from intercalated graphite fiber composites. Because EMI covers typically make up about one-fifth of the power system mass, this change would decrease the mass of a spacecraft power system by more than 15 percent. Intercalated graphite fibers are made by diffusing guest atoms or molecules, such as bromine, between the carbon planes of the graphite fibers. The resulting bromine-intercalated fibers have mechanical and thermal properties nearly identical to pristine graphite fibers, but their resistivity is lower by a factor of 5, giving them better electrical conductivity than stainless steel and making these composites suitable for EMI shielding.

Source record↗

Enhanced Switching Reliability of Hf 0.5 Zr 0.5 O 2 Ferroelectric Films Induced by Interface Engineering

Ferroelectric materials have been widely researched for applications in memory and energy storage. Among these materials and benefiting from their excellent chemical compatibility with complementary metal–oxide–semiconductor (CMOS) devices, hafnia-based ferroelectric thin films hold great promise for highly scaled semiconductor memories, including nonvolatile ferroelectric capacitors and transistors. However, variation in the switched polarization of this material during field cycling and a limited understanding of the responsible mechanisms have impeded their implementation in technology. Here, we show that ferroelectric Hf 0.5 Zr 0.5 O 2 (HZO) capacitors that are nearly free of polarization “wake-up”─a gradual increase in switched polarization as a function of the number of switching cycles─can be achieved by introducing ultrathin HfO 2 buffer layers at the HZO/electrodes interface. High-resolution transmission electron microscopy (HRTEM) reveals crystallite sizes substantially greater than the film thickness for the buffer layer capacitors, indicating that the presence of the buffer layers influences the crystallization of the film (e.g., a lower ratio of nucleation rate to growth rate) during postdeposition annealing. This evidently promotes the formation of a polar orthorhombic (O) phase in the as-fabricated buffer layer samples. Synchrotron X-ray diffraction (XRD) reveals the conversion of the nonpolar tetragonal (T) phase to the polar orthorhombic (O) phase during electric field cycling in the control (no buffer) devices, consistent with the polarization wake-up observed for these capacitors. The extent of T–O transformation in the nonbuffer samples is directly dependent on the duration over which the field is applied. Here these results provide insight into the role of the HZO/electrodes interface in the performance of hafnia-based ferroelectrics and the mechanisms driving the polarization wake-up effect.

36 MATERIALS SCIENCE↗

ARC-SAFE: Accelerated Response semiconducting Contactors and Surge Attenuation For DC Electrical systems (Final Scientific/Technical Report)

The landscape of power transmission and distribution is quickly evolving as more power conversion is done through power electronics and transmitted or distributed at medium voltage direct current (MVDC). As power electronics tend to store less energy and be less resilient to faults than conventional power transformers, a reliable and fast protection against faults is critical to protect power electronics (PE) based infrastructure, especially for medium- and high-voltage applications. This motivates the development of PE based protection circuits to replace slower contemporary electromechanical breakers. In this project a novel PE based MVDC circuit breaker is developed; the new design is comprised of 1) a normally-on leg made of commercially-available, cascaded SiC junction field effect transistors (JFETs) with a passive balancing network, and 2) a normally-off leg based on an optically-triggered gallium nitride (GaN) photoconductive semiconductor switch (PCSS). The normally-off leg was designed to be quickly turned on, to divert current to an auxiliary dissipative circuit, as the normally-on leg is turned off. This approach, using solid-state devices, was selected for a high-performance, fast-switching operation for the DC circuit breaker as compared to approaches that use slower mechanical switches. To be practical, the circuit breaker must have low conduction loss (low Ron) in the normally-on leg and fast coordinated triggering of the normally-off leg to avoid damage from inductive flyback, which could be considerable for long lengths of cable.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Radiant Temperature Nulling Radiometer

A self-calibrating nulling radiometer for non-contact temperature measurement of an object, such as a body of water, employs a black body source as a temperature reference, an optomechanical mechanism, e.g., a chopper, to switch back and forth between measuring the temperature of the black body source and that of a test source, and an infrared detection technique. The radiometer functions by measuring radiance of both the test and the reference black body sources; adjusting the temperature of the reference black body so that its radiance is equivalent to the test source; and, measuring the temperature of the reference black body at this point using a precision contact-type temperature sensor, to determine the radiative temperature of the test source. The radiation from both sources is detected by an infrared detector that converts the detected radiation to an electrical signal that is fed with a chopper reference signal to an error signal generator, such as a synchronous detector, that creates a precision rectified signal that is approximately proportional to the difference between the temperature of the reference black body and that of the test infrared source. This error signal is then used in a feedback loop to adjust the reference black body temperature until it equals that of the test source, at which point the error signal is nulled to zero. The chopper mechanism operates at one or more Hertz allowing minimization of l/f noise. It also provides pure chopping between the black body and the test source and allows continuous measurements.

Robert Ryan↗

Historic Context, Character-Defining Elements, And Photographic Record For A 26.45-Mile Segment Of The 138-Kilovolt Power Transmission System, Areas 3, 5, 6, And 23, Nevada National Security Site, Nye County, Nevada

The subject of this report is the 138-kilovolt (kV) power transmission line on the Nevada National Security Site (NNSS) (see Figure 1). The NNSS, formerly the Nevada Test Site (NTS), was the main continental nuclear test site for the United States between 1951 and 1992. Known as the battleground of the Cold War, the NNSS hosted a total of 928 nuclear tests during that period. It also served as the location of numerous scientific advancements in the fields of rocketry, big-hole drilling, nuclear waste management, and defense. From its construction in the 1960s through the present day, the 138 kV line has provided electrical power to the numerous buildings, facilities, experiments, and tests on the NNSS. The Department of Energy (DOE), in consultation with the Nevada State Historic Preservation Officer (SHPO), has determined that it may contribute to the character and significance of the Mercury Historic District (MHD) on the NNSS, as well as other historic districts that have not been recorded or evaluated yet. The purpose of this report is to fulfill two of the stipulations in the Memorandum of Agreement DEGM58-22NA25553 between the U.S. Department of Energy and the Nevada State Historic Preservation Officer Regarding Installation of a 138-kilovolt Transmission Line from the Mercury Switching Station to the U1a Facility and the Removal of the Historic 138-kilovolt Transmission Line from the Mercury Switching Station to the U1a Facility in Areas 1, 3, 5, 6, and 23 of the Nevada National Security Site (MOA). The MOA was executed as part of the DOE’s obligations under Section 106 of the National Historic Preservation Act (NHPA) to mitigate the adverse effects of two undertakings on historic properties. In particular, this report fulfills MOA Stipulations III.C.1-3, which state that the Department of Energy (DOE) will prepare the following: A historic context for the 138 kV transmission line and identification of the line’s characterdefining elements; High-quality digital images of the 26.45-mile segment of the 138 kV transmission line that is subject to the two undertakings for which the MOA was executed; and Photograph catalogs and map keys showing photograph viewpoints and directions.

54 ENVIRONMENTAL SCIENCES↗

Electrocatalytic Reduction of CO 2 to CO over Ag(110) and Cu(211) Modeled by Grand-Canonical Density Functional Theory

We report the results of modeling CO 2 reduction (CO 2 R) to CO over Ag(110) and Cu(211) surfaces at different applied potentials using grand-canonical density functional theory (GC-DFT), a method specifically designed to accurately model electrochemical systems. In addition to demonstrating GC-DFT’s ability to accurately model electrochemical processes, we also compare it with the computational hydrogen electrode (CHE) approach. GC-DFT predicts that the geometries of these reacting systems strongly depend on the applied potential and the Helmholtz free energies vary nonlinearly with the applied potential, which contradicts a central assumption of the CHE approach. The CHE approach neglects the change in the number of electrons on the electrode surface at different applied potentials, which reduces its accuracy as the potential changes from the potential of zero charge. Our results further demonstrate that the grand free energies of the reaction intermediates not only depend on the value of the applied potential but also on the metal surface type, adsorption site, and adsorbate. GC-DFT’s ability to predict the effect of the applied potential on adsorbate geometry enables it to evaluate different possible reaction mechanisms at different applied potentials. For instance, GC-DFT predicts that the first step of CO2R likely switches from proton-coupled electron transfer to sequential electron transfer and then proton transfer at more reducing potentials, a result that cannot be determined by the CHE because it assumes that all electron transfers are coupled to proton transfers and neglects the effect of the applied potential on the adsorbate geometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A light-induced phononic symmetry switch and giant dissipationless topological photocurrent in ZrTe 5

Dissipationless currents from topologically protected states are promising for disorder-tolerant electronics and quantum computation. In this work, we photogenerate giant anisotropic terahertz nonlinear currents with vanishing scattering, driven by laser-induced coherent phonons of broken inversion symmetry in a centrosymmetric Dirac material ZrTe 5 . Our work suggests that this phononic terahertz symmetry switching leads to formation of Weyl points, whose chirality manifests in a transverse, helicity-dependent current, orthogonal to the dynamical inversion symmetry breaking axis, via circular photogalvanic effect. The temperature-dependent topological photocurrent exhibits several distinct features: Berry curvature dominance, particle–hole reversal near conical points and chirality protection that is responsible for an exceptional ballistic transport length of ~10 μm. These results, together with first-principles modelling, indicate two pairs of Weyl points dynamically created by B 1u phonons of broken inversion symmetry. Such phononic terahertz control breaks ground for coherent manipulation of Weyl nodes and robust quantum transport without application of static electric or magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗