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DOE OSTI2023

Can we observe the ion-neutral drift velocity in prestellar cores?

Given the low-ionization fraction of molecular clouds, ambipolar diffusion is thought to be an integral process in star formation. However, chemical and radiative-transfer effects, observational challenges, and the fact that the ion-neutral drift velocity is inherently very small render a definite detection of ambipolar diffusion extremely non-trivial. Here, we study the ion-neutral drift velocity in a suite of chemodynamical, non-ideal magnetohydrodynamic (MHD), two-dimensional axisymmetric simulations of prestellar cores where we alter the temperature, cosmic-ray ionization rate, visual extinction, mass-to-flux ratio, and chemical evolution. Subsequently, we perform a number of non-local thermodynamic equilibrium (non-LTE) radiative-transfer calculations considering various idealized and non-idealized scenarios in order to assess which factor (chemistry, radiative transfer, and/or observational difficulties) is the most challenging to overcome in our efforts to detect the ion-neutral drift velocity. We find that temperature has a significant effect in the amplitude of the drift velocity with the coldest modelled cores (T = 6 K) exhibiting drift velocities comparable to the sound speed. Against expectations, we find that in idealized scenarios (where two species are perfectly chemically co-evolving) the drift velocity ‘survives’ radiative-transfer effects and can in principle be observed. However, we find that observational challenges and chemical effects can significantly hinder our view of the ion-neutral drift velocity. Finally, we propose that HCN and HCNH + ⁠, being chemically co-evolving, could be used in future observational studies aiming to measure the ion-neutral drift velocity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Hawai‘i Supernova Flows: a peculiar velocity survey using over a Thousand Supernovae in the near-infrared

ABSTRACT We introduce the Hawai‘i Supernova Flows project and present summary statistics of the first 1217 astronomical transients observed, 668 of which are spectroscopically classified Type Ia Supernovae (SNe Ia). Our project is designed to obtain systematics-limited distances to SNe Ia while consuming minimal dedicated observational resources. To date, we have performed almost 5000 near-infrared (NIR) observations of astronomical transients and have obtained spectra for over 200 host galaxies lacking published spectroscopic redshifts. In this survey paper, we describe the methodology used to select targets, collect/reduce data, calculate distances, and perform quality cuts. We compare our methods to those used in similar studies, finding general agreement or mild improvement. Our summary statistics include various parametrizations of dispersion in the Hubble diagrams produced using fits to several commonly used SN Ia models. We find the lowest dispersions using the SNooPy package’s EBV_model2, with a root mean square deviation of 0.165 mag and a normalized median absolute deviation of 0.123 mag. The full utility of the Hawai‘i Supernova Flows data set far exceeds the analyses presented in this paper. Our photometry will provide a valuable test bed for models of SN Ia incorporating NIR data. Differential cosmological studies comparing optical samples and combined optical and NIR samples will have increased leverage for constraining chromatic effects like dust extinction. We invite the community to explore our data by making the light curves, fits, and host galaxy redshifts publicly accessible.

Do, Aaron (ORCID:0000000334297845)↗

DOE OSTI2024

Measuring M31 globular cluster ages and metallicities using both photometry and spectroscopy

ABSTRACT The ages and metallicities of globular clusters play an important role not just in testing models for their formation and evolution but also in understanding the assembly history of their host galaxies. Here, we use a combination of imaging and spectroscopy to measure the ages and metallicities of globular clusters in M31, the closest massive galaxy to our own. We use the strength of the near-infrared calcium triplet spectral feature to provide a relatively age-insensitive prior on the metallicity when fitting stellar population models to the observed photometry. While the age–extinction degeneracy is an issue for globular clusters projected on to the disc of M31, we find generally old ages for globular clusters in the halo of M31 and in its satellite galaxy NGC 205 in line with previous studies. We measure ages for a number of outer halo globular clusters for the first time, finding that globular clusters associated with halo substructure extend to younger ages and higher metallicities than those associated with the smooth halo. This is in line with the expectation that the smooth halo was accreted earlier than the substructured halo.

Usher, Christopher (ORCID:0000000273837106)↗

DOE OSTI2024

Local primordial non-Gaussianity from the large-scale clustering of photometric DESI luminous red galaxies

ABSTRACT We use angular clustering of luminous red galaxies from the Dark Energy Spectroscopic Instrument (DESI) imaging surveys to constrain the local primordial non-Gaussianity parameter fNL. Our sample comprises over 12 million targets, covering 14 000 deg2 of the sky, with redshifts in the range 0.2 < z < 1.35. We identify Galactic extinction, survey depth, and astronomical seeing as the primary sources of systematic error, and employ linear regression and artificial neural networks to alleviate non-cosmological excess clustering on large scales. Our methods are tested against simulations with and without fNL and systematics, showing superior performance of the neural network treatment. The neural network with a set of nine imaging property maps passes our systematic null test criteria, and is chosen as the fiducial treatment. Assuming the universality relation, we find $f_{\rm NL} = 34^{+24(+50)}_{-44(-73)}$ at 68 per cent (95 per cent) confidence. We apply a series of robustness tests (e.g. cuts on imaging, declination, or scales used) that show consistency in the obtained constraints. We study how the regression method biases the measured angular power spectrum and degrades the fNL constraining power. The use of the nine maps more than doubles the uncertainty compared to using only the three primary maps in the regression. Our results thus motivate the development of more efficient methods that avoid overcorrection, protect large-scale clustering information, and preserve constraining power. Additionally, our results encourage further studies of fNL with DESI spectroscopic samples, where the inclusion of 3D clustering modes should help separate imaging systematics and lessen the degradation in the fNL uncertainty.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

The ambiguous AT2022rze: changing-look AGN mimicking a supernova in a merging galaxy system

AT2022rze is a luminous, ambiguous transient located south-east of the geometric centre of its host galaxy at redshift $z = 0.08$. The host appears to be formed by a merging galaxy system. The observed characteristics of AT2022rze are reminiscent of active galactic nuclei (AGNs), tidal disruption events, and superluminous supernovae. The transient reached a peak absolute magnitude of $-$20.2 $\pm$ 0.2 mag, showing a sharp rise (t$_{\mathrm{rise,1/e}} = 27.5 \pm 0.6$ d) followed by a slow decline (t$_{\mathrm{dec,1/e}} = 382.9 \pm 0.6$). Its bumpy light curve and narrow Balmer lines indicate the presence of gas (and dust). Its light curve shows rather red colours, indicating that the transient could be affected by significant host extinction. The spectra reveal coronal lines, indicative of high-energy (X-ray/UV) emission. Archival data reveal no prior activity at this location, disfavouring a steady-state AGN, although an optical spectrum obtained prior to the transient is consistent with an AGN classification of the host. Based on this, we conclude that the transient most likely represents a changing-look AGN at the centre of the smallest component of the merging system.

galaxies: active↗

DOE OSTI2025

DAmodel: hierarchical Bayesian modelling of DA white dwarfs for spectrophotometric calibration

We use hierarchical Bayesian modelling to calibrate a network of 32 all-sky faint DA white dwarf (DA WD) spectrophotometric standards (⁠16.5 < V , 19.5⁠) alongside three CALSPEC standards, from 912 Å to 32 μm. The framework is the first of its kind to jointly infer photometric zero points and WD parameters (surface gravity log g⁠, effective temperature T eff ⁠, extinction A V ⁠, dust relation parameter R V ) by simultaneously modelling both photometric and spectroscopic data. We model panchromatic Hubble Space Telescope Wide Field Camera 3 (HST/WFC3) UVIS and IR photometry, HST/STIS UV spectroscopy, and ground-based optical spectroscopy to sub-per cent precision. Photometric residuals for the sample are the lowest yet yielding < 0.004 mag RMS on average from the UV to the NIR, achieved by jointly inferring time-dependent changes in system sensitivity and WFC3/IR count-rate nonlinearity. Our GPU-accelerated implementation enables efficient sampling via Hamiltonian Monte Carlo, critical for exploring the high-dimensional posterior space. The hierarchical nature of the model enables population analysis of intrinsic WD and dust parameters. Inferred spectral energy distributions from this model will be essential for calibrating the James Webb Space Telescope as well as next-generation surveys, including Vera Rubin Observatory’s Legacy Survey of Space and Time and the Nancy Grace Roman Space Telescope.

methods: statistical↗

DOE OSTI2023

Kinematic and thermal signatures of the directly imaged protoplanet candidate around Elias 2−24

We report kinematic and thermal signatures associated with the directly imaged protoplanet candidate in the Elias 2–24 disc. Using the DSHARP (Disc Substructures at High Angular Resolution Project) ALMA (Atacama Large Millimetre/submillimetre Array) observations of the 12 CO J = 2 − 1 line, we show that the disc kinematics are perturbed, with a detached CO emission spot at the location of the planet candidate and traces of spiral wakes, and also that the observed CO emission intensities require local heating. While the foreground extinction hides the velocity channels associated with the planet, preventing a planet mass estimate, the level of gas heating implied by the CO emission indicates the presence of a warm, embedded giant planet. Comparison with models shows that this could either be a ≳5 M Jup or a lower mass (≳2 M Jup ) but accreting protoplanet.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

DNA Breaks-Mediated Fitness Cost Reveals RNase HI as a New Target for Selectively Eliminating Antibiotic-Resistant Bacteria

Abstract Antibiotic resistance often generates defects in bacterial growth called fitness cost. Understanding the causes of this cost is of paramount importance, as it is one of the main determinants of the prevalence of resistances upon reducing antibiotics use. Here we show that the fitness costs of antibiotic resistance mutations that affect transcription and translation in Escherichia coli strongly correlate with DNA breaks, which are generated via transcription–translation uncoupling, increased formation of RNA–DNA hybrids (R-loops), and elevated replication–transcription conflicts. We also demonstrated that the mechanisms generating DNA breaks are repeatedly targeted by compensatory evolution, and that DNA breaks and the cost of resistance can be increased by targeting the RNase HI, which specifically degrades R-loops. We further show that the DNA damage and thus the fitness cost caused by lack of RNase HI function drive resistant clones to extinction in populations with high initial frequency of resistance, both in laboratory conditions and in a mouse model of gut colonization. Thus, RNase HI provides a target specific against resistant bacteria, which we validate using a repurposed drug. In summary, we revealed key mechanisms underlying the fitness cost of antibiotic resistance mutations that can be exploited to specifically eliminate resistant bacteria.

Balbontín, Roberto↗

DOE OSTI2021

Cross-scale dynamics and the evolutionary emergence of infectious diseases

When emerging pathogens encounter new host species for which they are poorly adapted, they must evolve to escape extinction. Pathogens experience selection on traits at multiple scales, including replication rates within host individuals and transmissibility between hosts. We analyze a stochastic model linking pathogen growth and competition within individuals to transmission between individuals. Our analysis reveals a new factor, the cross-scale reproductive number of a mutant virion, that quantifies how quickly mutant strains increase in frequency when they initially appear in the infected host population. This cross-scale reproductive number combines with viral mutation rates, single-strain reproductive numbers, and transmission bottleneck width to determine the likelihood of evolutionary emergence, and whether evolution occurs swiftly or gradually within chains of transmission. We find that wider transmission bottlenecks facilitate emergence of pathogens with short-term infections, but hinder emergence of pathogens exhibiting cross-scale selective conflict and long-term infections. Furthermore, our results provide a framework to advance the integration of laboratory, clinical, and field data in the context of evolutionary theory, laying the foundation for a new generation of evidence-based risk assessment of emergence threats.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

A new Devonian euthycarcinoid reveals the use of different respiratory strategies during the marine-to-terrestrial transition in the myriapod lineage

Myriapods were, together with arachnids, the earliest animals to occupy terrestrial ecosystems, by at least the Silurian. The origin of myriapods and their land colonization have long remained puzzling until euthycarcinoids, an extinct group of aquatic arthropods considered amphibious, were shown to be stem-group myriapods, extending the lineage to the Cambrian and evidencing a marine-to-terrestrial transition. Although possible respiratory structures comparable to the air-breathing tracheal system of myriapods are visible in several euthycarcinoids, little is known about the mechanism by which they respired. Here, we describe a new euthycarcinoid from Upper Devonian alluvio-lagoonal deposits of Belgium. Synchrotron-based elemental X-ray analyses were used to extract all available information from the only known specimen. Sulfur X-ray fluorescence (XRF) mapping and spectroscopy unveil sulfate evaporation stains, spread over the entire slab, suggestive of a very shallow-water to the terrestrial environment prior to burial consistent with an amphibious lifestyle. Trace metal XRF mapping reveals a pair of ventral spherical cavities or chambers on the second post-abdominal segment that do not compare to any known feature in aquatic arthropods, but might well play a part in air-breathing. Our data provide additional support for amphibious lifestyle in euthycarcinoids and show that different respiratory strategies were used during the marine-to-terrestrial transition in the myriapod lineage.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Spatial and temporal variation in nest temperatures forecasts sex ratio skews in a crocodilian with environmental sex determination

Species displaying temperature-dependent sex determination (TSD) are especially vulnerable to the effects of a rapidly changing global climate due to their profound sensitivity to thermal cues during development. Predicting the consequences of climate change for these species, including skewed offspring sex ratios, depends on understanding how climatic factors interface with features of maternal nesting behaviour to shape the developmental environment. Here, we measure thermal profiles in 86 nests at two geographically distinct sites in the northern and southern regions of the American alligator's ( Alligator mississippiensis ) geographical range, and examine the influence of both climatic factors and maternally driven nest characteristics on nest temperature variation. Changes in daily maximum air temperatures drive annual trends in nest temperatures, while variation in individual nest temperatures is also related to local habitat factors and microclimate characteristics. Without any compensatory nesting behaviours, nest temperatures are projected to increase by 1.6–3.7°C by the year 2100, and these changes are predicted to have dramatic consequences for offspring sex ratios. Exact sex ratio outcomes vary widely depending on site and emission scenario as a function of the unique temperature-by-sex reaction norm exhibited by all crocodilians. By revealing the ecological drivers of nest temperature variation in the American alligator, this study provides important insights into the potential consequences of climate change for crocodilian species, many of which are already threatened by extinction.

Environmental Sciences & Ecology↗

DOE OSTI2023

Tuning structural, transport, and magnetic properties of epitaxial SrRu O 3 through Ba substitution

The perovskite ruthenates (A RuO 3 , A=Ca, Ba, or Sr) exhibit unique properties owing to a subtle interplay of crystal structure and electronic-spin degrees of freedom. Here, in this study, we demonstrate an intriguing continuous tuning of crystal symmetry from orthorhombic to tetragonal (no octahedral rotations) phases in epitaxial SrRuO 3 achieved via Ba substitution (Sr 1-x Ba x RuO 3 with 0 ≤ x ≤ 0.7 ). An initial Ba substitution to SrRuO 3 not only changes the ferromagnetic properties, but also tunes the perpendicular magnetic anisotropy via flattening the Ru–O–Ru bond angle (to 180°), resulting in the maximum Curie temperature and an extinction of RuO 6 rotational distortions at x≈0.20. For x ≤ 0.2, the reduction of RuO 6 octahedral rotational distortion dominantly enhances the ferromagnetism in the system, though competing with the effect of the RuO 6 tetragonal distortion. Further increasing Ba substitution (x > 0.2) gradually enhances the tetragonal-type distortion, resulting in the tuning of Ru-4d orbital occupancy and suppression of ferromagnetism. Our results demonstrate that isovalent substitution of the A-site cations significantly and controllably impacts both electronic and magnetic properties of perovskite oxides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Europium c -axis ferromagnetism in Eu ( Co 1 - x Ni x ) 2 - y As 2 : A single-crystal neutron diffraction study

Here we report neutron diffraction results for the body-centered-tetragonal series Eu⁢(Co 1-x ⁢Ni x ) 2-y As 2 , x=0.10, 0.20, 0.42, and 0.82, y≤0.10, that detail changes to the magnetic ordering with nominal hole doping. We report the antiferromagnetic (AFM) propagation vectors, magnetic transition temperatures, and the ordered magnetic moments. We find a nonmonotonic change of the AFM propagation vector with x, with a minimum occurring at the tetragonal to collapsed-tetragonal phase crossover. For x=0.10 and 0.82 we find c-axis helix ordering of the Eu magnetic moments (spins) similar to x=0 and 1, with the spins oriented within the ab-plane. For x=0.20 and 0.42 we find higher-temperature c-axis ferromagnetic (FM) order and lower-temperature c-axis cone order. Using the extinction conditions for the space group, we discovered that the Eu spins are ordered in the higher-temperature c-axis FM phase for intermediate values of x, contrary to a previous report suggesting only Co/Ni spin ordering. Although we cannot directly confirm that the Co/Ni spins are also ordered, we suggest that c-axis itinerant-FM ordering of the Co/Ni spins could provide a molecular field that drives FM ordering of the Eu spins, which in turn provides the anisotropy for the lower-temperature c-axis cone order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

How the Universe postpones the evaporation and curtails the quantum spreading of black holes

Black holes are expected to evaporate through the process of Hawking radiation. This process is expected to cause the uncertainty in a black hole’s position to grow to ~ $M^4/M^3_{pl}$ over the course of it’s lifetime, even as its momentum spreads only by ~ $M_{Pl}$ For the black holes that have been observed, which have M ≥ M ⊙ this greatly exceeds the Hubble volume. However, the decay of black holes and their quantum spreading, are delayed in the Universe while the influx of energy into the black holes exceeds their Hawking luminosity. We show that for these M ≥ M ⊙ black holes, their decay outside galaxies and clusters is prevented far longer than it takes the black holes to be dragged well beyond the Hubble horizon, where their eventual decay occurs away from the prying eyes of any observer who has not hitched a ride with them. Meanwhile, black holes in an observer’s galaxy or cluster are themselves prevented from decaying long past the extinction of the last stars, and at least until their galaxy/cluster is swept clean of dark matter, in $\gg$ 10 25 y. Even then, if the black holes become unbound, then they are dragged beyond the Hubble radius before undergoing significant decay; if not, they remain in bound orbits, spreading at most over a subvolume of the galaxy/cluster, and long localized by scatterings to much smaller volumes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Quantum metrology of low-frequency electromagnetic modes with frequency upconverters

We present the RF Quantum Upconverter (RQU) and describe its application to quantum metrology of electromagnetic modes between dc and the very high frequency band (VHF) ( ≲ 300 MHz). The RQU uses a Josephson interferometer made up of superconducting loops and Josephson junctions to implement a parametric interaction between a low-frequency electromagnetic mode (between dc and VHF) and a mode in the microwave C Band ( ∼ 5 GHz), analogous to the radiation pressure interaction between electromagnetic and mechanical modes in cavity optomechanics. We analyze RQU performance with quantum amplifier theory and show that the RQU can operate as a quantum-limited op-amp in this frequency range. It can also use nonclassical measurement protocols equivalent to those used in cavity optomechanics, including back-action evading (BAE) measurements, sideband cooling, and two-mode squeezing. These protocols enable experiments using dc VHF electromagnetic modes as quantum sensors with sensitivity better than the standard quantum limit (SQL). We demonstrate signal upconversion from low frequencies to the microwave C band using an RQU and show a phase-sensitive gain (extinction ratio) of 46.9 dB , which is a necessary step towards the realization of full BAE. Published by the American Physical Society 2025

Kuenstner, Stephen E. (ORCID:0000000346128846)↗

DOE OSTI2024

Nonreciprocal Dissipation Engineering via Strong Coupling with a Continuum of Modes

Optical nonreciprocity plays a key role in almost every optical system, directing light flow and protecting optical components from backscattered light. Controllable forms of on-chip nonreciprocity are needed for the robust operation of increasingly sophisticated photonic integrated circuits (PICs) in the context of classical and quantum computation, networking, communications, and sensing. However, it has been challenging to achieve wideband, low-loss optical nonreciprocity on-chip. In this paper, we demonstrate strong coupling and Rabi-like energy exchange between photonic bands, possessing a continuum of modes, to unlock nonreciprocity and frequency translation over wide optical bandwidths in silicon. Using a traveling-wave phonon field to drive indirect interband photonic transitions, we demonstrate band hybridization that enables an intriguing form of nonreciprocal dissipation engineering. Using the converted mode to create a nonreciprocal dissipation channel, we demonstrate a frequency-neutral, low-loss (less than 1 dB) isolator with high nonreciprocal contrast (more than 14 dB) and broad operating bandwidth (more than 59 GHz). Additionally, through the implementation of complete interband conversion, we demonstrate a high extinction (more than 55 dB) optical frequency translation operation with near-unity efficiency.

Zhou, Yishu↗

DOE OSTI2024

Analysis of heat transfer and AuNPs-mediated photo-thermal inactivation of E. coli at varying laser powers using single-phase CFD modeling

In the wake of the COVID-19 pandemics, the demand for innovative and effective methods of bacterial inactivation has become a critical area of research, providing the impetus for this study. The purpose of this research is to analyze the AuNPs-mediated photothermal inactivation of E. coli. Gold nanoparticles irradiated by laser represent a promising technique for combating bacterial infection that combines high-tech and scientific progress. The intermediate aim of the work was to present the calibration of the model with respect to the gold nanorods experiment. The purpose of this work is to study the effect of initial concentration of E. coli bacteria, the design of the chamber and the laser power on heat transfer and inactivation of E. coli bacteria. Using the CFD simulation, the work combines three main concepts. 1. The conversion of laser light to heat has been described by a combination of three distinctive approximations: a- Discrete particle integration to take into account every nanoparticle within the system, b- Rayleigh-Drude approximation to determine the scattering and extinction coefficients and c- Lambert–Beer–Bourger law to describe the decrease in laser intensity across the AuNPs. 2. The contribution of the presence of E. coli bacteria to the thermal and fluid-dynamic fields in the microdevice was modeled by single-phase approach by determining the effective thermophysical properties of the water-bacteria mixture. 3. An approach based on a temperature threshold attained at which bacteria will be inactivated, has been used to predict bacterial response to temperature increases. The comparison of the thermal fields and temporal temperature changes obtained by the CFD simulation with those obtained experimentally confirms the accuracy of the light-heat conversion model derived from the aforementioned approximations. The results show a linear relationship between maximum temperature and variation in laser power over the range studied, which is in line with previous experimental results. It was also found that the temperature inside the microchamber can exceed 55 °C only when a laser power higher than 0.8 W is used, so bacterial inactivation begins. The experimental data allows to determinate the concentration of nanoparticles. This parameter is introduced into the mathematical model obtaining the same number of AuNPs. However, this assumption introduces a certain simplification, as in the mathematical model the distribution of nanoparticles is uniform. This work is directly connected to the use of gold nanoparticles for energy conversion, as well as the field of bacterial inactivation in microfluidic systems such as lab-on-a-chip. Presented mathematical and numerical models can be extended to the entire spectrum of wavelengths with particular use of white light in the inactivation of bacteria. This work represents a significant advancement in the field, as to the best of the authors’ knowledge, it is the first to employ a single-phase computational fluid dynamics (CFD) approach specifically combined with the thermal inactivation of bacteria. Moreover, this research pioneers the use of a numerical simulation to analyze the temperature threshold of photothermal inactivation of E. coli mediated by gold nanorods (AuNRs). The integration of these methodologies offers a new perspective on optimizing bacterial inactivation techniques, making this study a valuable contribution to both computational modeling and biomedical applications.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Buried-Electrode Hybrid Bonded Thin-Film Lithium Niobate Electro-Optic Mach-Zehnder Modulators

Hybrid bonded silicon nitride thin-film lithium niobate (TFLN) Mach-Zehnder modulators (MZMs) at 1310 nm were designed with metal coplanar waveguide electrodes buried in the silicon-on-insulator (SOI) chip. Here, the MZM devices showed greatly improved performance compared to earlier devices of a similar design, and similar performance to comparable MZM devices with gold electrodes made on top of the TFLN layer. Both devices achieve a 3-dB electro-optic bandwidth greater than 110 GHz and voltage-driven optical extinction ratios greater than 28 dB. Half-wave voltage-length products (VπL) of 2.8 and 2.5 V∙ cm were measured for the 0.5 and 0.4 cm long buried metal and top gold electrode MZMs, respectively.

42 ENGINEERING↗