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At least 163 records · Page 9

Imaging Electrons in Two Dimensional Materials (Final report)

Two-dimensional (2D) materials have extraordinary characteristics that offer promising new approaches for science and technology. Electrons in graphene can move ballistically through a sheet, even though it is only a single atom thick. And transition metal dichalcogenide materials can be cleaved into 2D flakes of all types – metals, semiconductors, insulators, magnetic materials, and superconductors. To benefit from these discoveries, the science needs to be understood to transform 2D materials into useful new devices and systems. The evolution in time of atomic scale graphene structures has been studied in time with a transmission electron microscope (TEM), and ballistic transport of electrons in graphene was been imaged using a cooled scanning probe microscope (SPM), as well as electron motion in MoS 2 . Graphene is only one atom thick but is extremely strong, creating the opportunity to fabricate atomic scale structures in the lateral direction. Using an atomic resolution TEM, a suspended sheet of graphene can be shaped by a Si impurity atom on its surface that acts like a chisel to open up apertures, one atom at a time. The electrons in the TEM provide both the chiseling energy and the ability to image the results. Electrons and holes in graphene form a new type of electronic system with conical conduction and valence bands that meet at the Dirac point, with no energy gap. For moderate densities, the carriers form a Fermi liquid with ballistic transport over micron-scale distances. Using a cooled SPM the cyclotron orbit of electrons in graphene has been imaged. In the magnetic focusing regime, electrons leaving a point contact circle around and leave from a second point contact when the cyclotron diameter is equal to the contact spacing. The paths of electrons are focused - they enter at different angles but converge again at the exiting contact. When the SPM tip knocks an electron out of its orbit, an imaging signal is created. The ballistic motion of carriers in graphene opens the way for ballistic devices that manipulate beams of electrons and holes. Our collaborator Gil-Ho Lee, in Philip Kim's group, created a collimating contact by placing zig-zag absorbers on either side of entering electrons. Our cooled SPM was used to image the electron beam and determine its 9-degree halfwidth. By changing the gate voltage, a collimated beam of holes was also created, opening the way for colliding beam experiments. Coherent beams of carriers are desirable for quantum information processing. Via Andreev reflection, superconducting contacts can covert Cooper pairs in a superconductor to an ingoing and outgoing electrons and holes. Using our cooled SPM, Andreev reflection was imaged from a superconducting contact on a graphene device. Magnetic focusing was used to create an incoming beam of electrons and an outgoing beam of holes, detected by a third point contact. The images show a clear transition from normal reflection above the superconducting transition temperature to Andreev reflection as the device is cooled. Transition metal dichalcogenides offer a wide array of materials that can be exfoliated into ultrathin 2D sheets. A cooled SPM can be used to detect quantum dots as well as to image electron flow. The tip charge capacitively couples to electrons on the dot, acting as a gate to tune the dot conductance. Coulomb blockade peaks appear as a bullseye pattern in an SPM image as the tip is raster scanned above the dot. This approach was used to detect quantum dots in a MoS 2 channel as the carrier density was reduced and electrons pooled in low energy points. Through our DOE supported research, cooled SPM imaging has proven to be a very useful tool to uncover the motion of electrons and holes in the new quantum materials graphene and MoS 2 .

36 MATERIALS SCIENCE↗

Toward a DM Search with Phonon-Mediated MKID Devices at NEXUS

To continue the search for dark matter (DM) into the sub-GeV mass range, the development and characterization of new detectors with sub-eV thresholds is critical. Microwave Kinetic Inductance Detectors (MKIDs) offer an attractive architecture for novel microcalorimeters with the requisite energy resolution and threshold for probing DM down to the fermionic thermal relic mass limit of a few keV. A phonon-sensitive MKID device featuring an aluminum resonator patterned onto a silicon substrate has been operating at the NEXUS low-background facility at Fermilab for characterization and evaluation of its efficacy for a dark matter search. Currently, our estimate of the energy resolution of this device is limited by the efficiency for phonons produced via particle interactions in the substrate to propagate to the superconductor and break Cooper pairs. In this poster, I will present our constraints on the substrate-superconductor coupling and the progress on an absolute energy calibration performed by exposing the rear of the substrate to a pulsed source of 470 nm photons. I will also review the current status and next steps of the phonon-mediated MKID effort at Fermilab.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Sapphire substrate qubit-based detector for light dark matter search

Harnessing sub-eV energy excitations from light dark matter interaction with a target material is one of the challenges in exploring promising novel materials for dark matter searches. In polar materials like sapphire, dark matter interaction can excite sub-eV optical phonon modes. Furthermore, the anisotropy of sapphire crystal could provide a signature of daily modulation of the dark matter scattering rate, making it a promising target material. We plan to utilize superconducting qubits on a sapphire substrate to take advantage of the excitation of phonons, which scatter and further down-convert to lower-energy phonons. A good fraction of these phonons are expected to reach the qubit superconductor on the substrate and break Cooper pairs. Such a process can cause qubit decoherence, which can be measured using standard qubit readout protocol. In this talk, we describe our ongoing attempt to build such a prototype detector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Kinetic Inductance Phonon-Mediated Detectors for Dark Matter: R&D at NEXUS

Superconducting thin films have long been used as phonon sensors, particularly in the field of dark matter (DM) direct detection, due to the meV-scale Cooper-pair binding energy. A novel class of these detectors based on microwave kinetic inductance detectors, dubbed Kinetic Inductance Phonon-Mediated Detectors (KIPMDs), offers an attractive architecture for microcalorimeters to probe DM down to the fermionic thermal relic mass limit of a few keV. Such a device featuring an aluminum resonator patterned onto a silicon substrate was operated at the NEXUS low-background facility at Fermilab for characterization and evaluation of its efficacy for a dark matter search. With this device we have demonstrated a resolution on the energy absorbed by the superconductor of 2.5 eV, a factor of two better than current state-of-the-art. In this talk, I will present our measurement of the energy resolution and phonon collection efficiency performed by exposing the bare substrate to a pulsed source of 470 nm photons. I will also discuss the path forward to obtaining in these devices the sub-eV resolution required to test the “Freeze-in” class of DM models. Finally, I will review other complementary efforts in our group to develop a superconducting qubit-based low-threshold detector.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Investigation of cosmic ray impact on transmon qubits with different materials through fast decay detection at Fermilab’s SQMS laboratory

Noise sources affecting superconducting qubits, such as cosmic rays and ambient gamma radiation, have garnered attention for their potential impact. These radiations deposit energy in the qubit's substrate, generating high-energy phonons that break Cooper pairs, leading to the formation of quasi-particles. When these quasi-particles tunnel across Josephson junctions, they induce qubit de-excitation, causing relaxation errors. In this study, we employ a fast feedback mechanism for performing qubit reset to detect decay events with high time resolution. This capability along with frequency multiplexed readout allows us to explore error correlations across time and space. Transmon qubits, manufactured within the Superconducting Quantum Materials and Systems (SQMS) center [1], are investigated at the above-ground lab. We study the impact of cosmic rays on qubits with different encapsulations, geometries, and locations on the same or different chips. We present preliminary findings and discuss the implications for the performance of contemporary quantum hardware.

Roy, Tanay↗

Search for 3D topological superconductors using laser-based spectroscopy (Final Technical Report)

The three-dimensional topological superconductor (3D TSC) is a novel quantum phase of matter that is predicted to exhibit exotic thermal and electrical properties, which may serve applications ranging from precision thermal management and sensing technologies to fault-tolerant quantum information processing. Over the past decade, there has been an intensive effort to realize 1D and 2D TSCs by artificially engineering them from combinations of already existing materials. For example, coupling conventional superconductors to spin-orbit coupled 1D nanowires or to 2D topological insulator surfaces by the proximity effect provides a route to realizing 1D and 2D TSCs respectively. However no artificial engineering strategy is available for a 3D TSC. Therefore, current searches are limited to intrinsically superconducting compounds whose topological properties are difficult to predict. The overarching goal of this project was to realize and to identify 3D TSCs in bulk single crystals using novel laser-based spectroscopic techniques. One major thrust was to develop ultralow temperature and ultra-high-resolution angle-resolved photoemission spectroscopy (ARPES) to directly measure the dispersion of Majorana excitations that are predicted to exist on the surfaces of 3D TSCs. Another major thrust was to develop a rational route to realize 3D TSCs by identifying their precursor phases. It is theoretically proposed that the critical fluctuations of certain ordered electronic phases can mediate Cooper pairing in odd-parity channels and lead to topological superconductivity. Therefore, 3D TSCs may potentially emerge upon suppressing these inversion symmetry broken precursor phases to a critical point with external perturbations such as pressure, strain or even light. To test this hypothesis, we studied candidate materials using a suite of symmetry-sensitive optical probes including rotational anisotropy optical second harmonic generation (RA-SHG) and time-resolved coherent phonon spectroscopy, all operable under high-pressure and low temperature environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Solid State Quantum Refrigeration Superconducting, Absorption and Measurement Based (Final Technical Report)

During this DOE grant, DE-SC0017890, in place for the past six years, all proposed research was carried out and published in peer-reviewed papers, as well as other projects that emerged during the research. In that effort the research team accomplished all proposed research, as well as many closely related research projects discovered and conceived of during the grant. These works included “Efficient Quantum Measurement Engines”, a work published in Physical Review Letters, giving a theory of quantum measurement-based engines, which uses quantum measurement as a resource. These engines are designed to efficiently convert energy from the stochastic quantum measurement process into useful work. Further publications include “Experimental Realization of a Quantum Dot Energy Harvester”, a joint theory and experimental work in collaboration with the group of Charles Smith in Cambridge, UK, as well as long time theoretical collaborators, Rafael Sánchez and Björn Sothmann. This work, featured as an Editor’s Suggestion in Physical Review Letters, realized an earlier theoretical proposal of ours, whereby two resonant tunneling quantum dots are connected to a central electronic cavity that is heated by a hot energy source. We also published “Superconducting Quantum Refrigerator: Breaking and Rejoining Cooper Pairs with Magnetic Field Cycles” a work done in collaboration with experimentalist Francesco Giazotto from ENS Pisa, Italy, which also resulted in a patent. This paper, published in Phys. Rev. Applied, advanced the concept of a cyclic fridge based on the normal/superconducting phase transition together with layered materials separated by tunnel junctions. We also completed the proposed research on a heat transistor, publishing “Thermal transistor and thermometer based on Coulomb-coupled conductors”, carried out as a collaboration between my group and theorists Splettstoesser (Lund U., Sweden), Sothmann (U. Duisburg-Essen, Germany), and Sánchez (U. Autónoma de Madrid, Spain). We carried out an analysis of a quantum coupled to a quantum point contact as a sensitive thermometer and heat transistor. We found the optimal statistical estimator for the temperature and compared it with experiments on the same type of devices. We also investigated autonomous quantum absorption refrigerators using quantum dots to cool by using a very hot thermal reservoir to drive heat between two other reservoirs. In the article “Quantifying the quantum heat contribution from a driven superconducting circuit”, we demonstrated that for a driven superconducting circuit, we showed heat flow provided by a hot source to the qubit can be switched on and off by varying external parameters, the frequency and the intensity of the driving. In the work “Stochastic thermodynamic cycles of a mesoscopic thermoelectric engine”, we reconsidered the autonomous thermoelectric heat engine in terms of underlying cycles. Rather than periodic behavior, the cycles were stochastic in nature. Nevertheless, by undertaking a graph theoretical analysis of the elementary transport processed, great quantitative and qualitative insight could be found. We also considered the quantum measurement process and showed that a quantum version of Maxwell’s demon could be related to the work extraction of a quantum system, closely related to arrow-of-time measures for quantum measurement, as described in our article “Thermodynamics of quantum measurement and Maxwell's demon's arrow of time”. This work was selected in Phys. Rev. A as an Editor’s Suggestion. A recent preprint titled “Cyclic Superconducting Quantum Refrigerators Using Guided Fluxon Propagation” accomplished an important piece of this grant: to propose a new kind of quantum refrigerator using the dynamics of fluxons in a type II superconductor. This invention envisioned a race-track type geometry where fluxons are confined. By applying a gradient of magnetic field together with electric current in a Corbino geometry, the circulating fluxons can actively cool a cold reservoir, realizing a new type of cyclic superconducting refrigerator. We also investigated the possibility of thermal control from different points of view. The application of quantum measurement to the system gives a new kind of control on the system of interest – we have pioneered this approach and shown that measurement can boost the thermal power of quantum engines as described in “Continuous measurement boosted adiabatic quantum thermal machines”. The ability to have heat flows on demand is an outstanding challenge, and we have provided new solutions to this problem in Thermal control across a chain of electronic nanocavities” for a chain of electron cavities using gating voltage control. The control methods using qubit/qubit coupling to create absorption fridges at their most fundamental level have also been developed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Qubit-Based Detector For Dark Matter Search And Radiation Studies

One of the challenges in exploring promising novel materials for dark matter searches is the detection of sub-eV energy excitations from light-dark matter interaction with a target material. Dark matter interaction can excite sub-eV optical phonon modes in polar materials like sapphire. We plan to utilize superconducting qubits on a sapphire substrate to study their response to energy deposition into the superconducting film and the substrate by irradiating them with photons and particles and also generating phonons in the chip. A fraction of the incident energy is expected to break Cooper pairs in the superconductor, releasing quasiparticles. As the quasiparticles tunnel across the Josephson junction, the charge parity of the qubit changes. The parity switching rate is proportional to the quasiparticle density in the qubit superconductor film and can be measured using standard qubit readout protocol. This presentation describes our ongoing attempt to build such a prototype detector.

Khatiwada, Rakshya↗

Comparative Study of Quasi-Particle Burst Events in Transmon Qubits made with Different Materials and Geometries

Superconducting qubits are susceptible to various noise sources, including cosmic rays. ambient gamma and infrared radiation, which can significantly impact their performance. High-energy radiations deposit energy into the qubit substrate, generating high-energy phonons that disrupt Cooper pairs and create quasi-particles (QPs). Infrared photons, on the other hand can directly create QPs. The tunneling of these quasi-particles across Josephson junctions leads to qubit de-excitation and causes relaxation errors. In this study, we utilize a fast feedback mechanism for qubit reset to detect QP burst events with high time resolution [1]. We investigate transmon qubits fabricated with different encapsulations [2], geometries, and substrates at the above-ground laboratory of the Superconducting Quantum Materials and Systems (SQMS) center at Fermilab. Our preliminary results are presented, with discussions on their implications for the performance of modern quantum hardware. [1] Dominicis and Roy et al.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Cryogenic Muon Tagging System Integrated with a Superconducting Qubit Device for Radiation-Induced Error Mitigation

Superconducting qubits are highly sensitive to ionizing radiation, which can induce correlated errors and limit scalable fault-tolerant quantum computing. In particular, cosmic-ray muons can deposit energy in the substrate, generating phonon bursts that break Cooper pairs and produce quasiparticles, leading to correlated decoherence events across multiple qubits. We present the development of a cryogenic muon tagging system based on Kinetic Inductance Detectors (KIDs) and its integration with superconducting quantum hardware. Originally developed within the ACE-SuperQ project and validated as a standalone detector, the system demonstrated a muon tagging efficiency of approximately 90% and excellent agreement with Monte Carlo simulations. Building on this validation, the tagging system has been integrated with a multi-qubit superconducting chip operated in a dilution refrigerator. The detector configuration consists of a multi-layer KID stack arranged above and below the quantum device, enabling time-coincident identification of muon-induced events within the same cryogenic environment. The integrated setup has been successfully commissioned, enabling simultaneous operation of the qubit chip and the muon tagging system. A first measurement campaign has been carried out, and preliminary data show time-correlated events between the muon tagging detectors and the qubit readout. A quantitative analysis of radiation-induced effects on qubit performance is currently ongoing. This work represents a step toward the implementation of event-level radiation tagging as a tool for characterizing and potentially mitigating correlated errors in superconducting quantum processors, while establishing a modular platform for future studies at the interface between particle physics and quantum information science.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗

Relationship Between Nematicity, Antiferromagnetic Fluctuations, and Superconductivity in FeSe 1-x S x Revealed by NMR

The S-substituted FeSe, FeSe 1-x S x , under pressure (p), provides a versatile platform for studying the relationship among nematicity, antiferromagnetism, and superconductivity. Here we present a short review of the recent experimental evidence showing that nematicity has a remarkable impact on the relationship between antiferromagnetic fluctuations and superconductivity. This has been revealed by several 77 Se nuclear magnetic resonance studies that have tracked the variability of antiferromagnetic fluctuations and superconducting transition temperature (T c ) as a function of x and p. T c is roughly proportional to antiferromagnetic fluctuations in the presence or absence of nematic order suggesting the importance of antiferromagnetic fluctuations in the Cooper pairing mechanism in FeSe 1-x S x . However, the antiferromagnetic fluctuations are more effective in enhancing superconductivity in the absence of nematicity as compared to when it is present. These experimental observations give renewed insights into the interrelationships between nematicity, magnetism, and superconductivity in Fe-based superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electronic Structure Correspondence of Singlet-Triplet Scale Separation in Strained Sr2RuO4

At a temperature of roughly 1 K, Sr 2 RuO 4 undergoes a transition from a normal Fermi liquid to a superconducting phase. Even while the former is relatively simple and well understood, the superconducting state has not even been understood after 25 years of study. More recently, it has been found that critical temperatures can be enhanced by the application of uniaxial strain, up to a critical strain, after which it falls off. In this work, we take an “instability” approach and seek divergences in susceptibilities. This provides an unbiased way to distinguish tendencies to competing ground states. We show that in the unstrained compound, the singlet and triplet instabilities of the normal Fermi liquid phase are closely spaced. Under uniaxial strain, electrons residing on all orbitals contributing to the Fermiology become more coherent, while the electrons of the Ru-dxy character become heavier, and the electrons of the Ru d x z , y z characters become lighter. In the process, Im χ(q,ω) increases rapidly around q = ( 0.3 , 0.3 , 0 ) 2 π / a and q = ( 0.5 , 0.25 , 0 ) 2 π / a , while it gets suppressed at all other commensurate vectors, in particular at q = 0, which is essential for spin-triplet superconductivity. We observe that the magnetic anisotropy under strain drops smoothly, which is concomitant with the increment in singlet instability. Thus, the triplet superconducting instability remains the lagging instability of the system, and the singlet instability enhances under strain, leading to a large energy-scale separation between these competing instabilities. However, since this happens even without spin-orbit coupling, we believe it is primarily the enhancement in the spin fluctuation glue around quasi-anti-ferromagnetic vectors that drives the Cooper pairing instead of the magnetic anisotropy. At large strain, an instability to a spin density wave overtakes the superconducting one. The analysis relies on a high-fidelity, ab initio description of the one-particle properties and two-particle susceptibilities, based on the quasiparticle self-consistent GW approximation augmented by dynamical mean field theory. This approach is described and its high fidelity confirmed by comparing to observed one- and two-particle properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electron Correlation and High-Temperature Superconductivity

Strong electron correlation plays a central role in the high-temperature superconductivity (HTSC) of cuprates. However, to date, research has focused only on its role in spin dynamics and related effects, even though it is becoming increasingly clear that spin alone may not be sufficient to create HTSC. Here, we discuss a possible role of electron correlation in the Bose–Einstein condensation (BEC) of Cooper pairs. Recently, we succeeded in observing dynamic electron correlation via inelastic X-ray scattering through results presented in real space. We discovered that electron correlations are strongly modified in the plasmon, proving that electron dynamics significantly affect electron correlation. Earlier, we found that in 4 He, the atom–atom distance in the BE condensate is 10% longer than that in the non-condensate. These results suggest the possibility that the reduction in electron-repulsion energy upon BEC is driving T c to high values. Thus, electron correlation itself could be the origin of the HTSC phenomenon.

Bose–Einstein condensation↗

Enhancement of Superconductivity in WP via Oxide-Assisted Chemical Vapor Transport

Tungsten monophosphide (WP) has been reported to superconduct below 0.8 K, and theoretical work has predicted an unconventional Cooper pairing mechanism. Here we present data for WP single crystals grown by means of chemical vapor transport (CVT) of WO3, P, and I2. In comparison to synthesis using WP powder as a starting material, this technique results in samples with substantially decreased low-temperature scattering and favors a more three-dimensional morphology. We also find that the resistive superconducting transitions in these samples begin above 1 K. Variation in Tc is often found in strongly correlated superconductors, and its presence in WP could be the result of influence from a competing order and/or a non-s-wave gap.

Chemistry↗

The mechanism of high-T(sub c) superconductivity due to bound hole mediators: Relationship to ferroelectricity

The mediation by bound holes creating Cooper pairing in high T(sub c) superconductors has its origin in charge transfer excitations on the multivalence cation (virtual excitions) and in bound excitions or polarizations associated with the oxygen 2p electrons. These phenomena are produced and/or enhanced by a high internal electric field which is itself created by virtue of the unique crystal structures and polyhedral building blocks of high T(sub c) materials. The polarizations which can create oxygen holes (in addition to excitions) may be due to simply the internal electric field or to polaronic and electron-deficient bond behavior. This gives rise to two energy-dependent oxygen bands near the Fermi level. The magnitude and direction of the internal electric fields were calculated for Y1Ba2Cu3O(7-delta) (1-2-3) and show strong z-direction fields at the Cu(2), O2, and O3 sites and an even stronger -z direction field at the O4 site. The field calculations also show why electrical conductivity in the 1-2-3 material is essentially in the base plane of the CuO5 pyramid (the CuO2 plane).

Vezzoli, G. C.↗

Superconductivity in Russia: Update and prospects

The research projects and new technological developments that have occured in Russia are highlighted in this document. Some of the research discussed includes: x-ray structure analysis of YBCO superconducting single crystals and accompanying phase transformations; the role of electron-electron interaction in High Temperature Superconductors (HTSC); the formation of Cooper pairs in crystals; the synthesis and research on a new family of superconductors based on complex copper and mercury oxides (HgBa2CuO4 + alpha and HgBa2CaCu2O6 + alpha); methods for the extraction of higher (up to C200) fullerenes and metalfullerenides has been developed; and process of production of Josephson junctions and development of SQUID's.

Ozhogin, V.↗

Granular Superconductors and Gravity

As a Bose condensate, superconductors provide novel conditions for revisiting previously proposed couplings between electromagnetism and gravity. Strong variations in Cooper pair density, large conductivity and low magnetic permeability define superconductive and degenerate condensates without the traditional density limits imposed by the Fermi energy (approx. 10(exp -6) g cu cm). Recent experiments have reported anomalous weight loss for a test mass suspended above a rotating Type II, YBCO superconductor, with a relatively high percentage change (0.05-2.1%) independent of the test mass' chemical composition and diamagnetic properties. A variation of 5 parts per 104 was reported above a stationary (non-rotating) superconductor. In experiments using a sensitive gravimeter, bulk YBCO superconductors were stably levitated in a DC magnetic field and exposed without levitation to low-field strength AC magnetic fields. Changes in observed gravity signals were measured to be less than 2 parts in 108 of the normal gravitational acceleration. Given the high sensitivity of the test, future work will examine variants on the basic magnetic behavior of granular superconductors, with particular focus on quantifying their proposed importance to gravity.

Noever, David↗

Static Test for a Gravitational Force Coupled to Type 2 YBCO Superconductors

As a Bose condensate, superconductors provide novel conditions for revisiting previously proposed couplings between electromagnetism and gravity. Strong variations in Cooper pair density, large conductivity and low magnetic permeability define superconductive and degenerate condensates without the traditional density limits imposed by the Fermi energy (approx. 10(exp -6) g cc. Recent experiments have reported anomalous weight loss for a test mass suspended above a rotating type II, YBCO superconductor, with the percentage change (0.05 - 2.1 %) independent of the test mass' chemical composition and diamagnetic properties. A variation of 5 parts per 10' was reported above a stationary (non-rotating) superconductor. In experiments using a sensitive gravimeter, bulk YBCO superconductors were stably levitated in a DC magnetic field. Changes in acceleration were measured to be less than 2 parts in 108 of the normal gravitational acceleration. This result puts new limits on the strength and range of the proposed coupling between static superconductors and gravity.

Li, Ning↗