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Campbell penetration depth in low carrier density superconductor YPtBi
Magnetic penetration depth, λ m , was measured as a function of temperature and magnetic field in single crystals of low carrier density superconductor YPtBi by using a tunnel-diode oscillator technique. Measurements in zero DC magnetic field yield London penetration depth, λ L ( T ) , but in the applied field the signal includes the Campbell penetration depth, λ C ( T ) , which is the characteristic length of the attenuation of small excitation field, H AC , into the Abrikosov vortex lattice due to its elasticity. Whereas the magnetic field dependent λ C exhibit λ C ~ B p with p = 1 / 2 in most of the conventional and unconventional superconductors, we found that p ≈ 0.23 << 1 / 2 in YPtBi due to rapid suppression of the pinning strength. From the measured λ C ( T , H ) , the critical current density is j c ≈ 40 A / cm 2 at 75 mK. We find that this is orders of magnitude lower than that of conventional superconductors of comparable T c .
Intermediate scattering potential strength in electron-irradiated YBa 2 Cu 3 O 7-δ from London penetration depth measurements
Temperature-dependent London penetration depth, λ(T), of a high quality optimally-doped YBa 2 Cu 3 O 7-δ single crystal was measured using tunnel-diode-resonator technique. Controlled artificial disorder was induced by low-temperature 20 K irradiation by 2.5 MeV electrons at two large doses of 3.8 x 10 19 and 5.3 x 10 19 electrons per cm 2 . The irradiation caused significant suppression of the superconductor's critical temperature, T c , from 94.6 K to 90.0 K, and to 78.7 K, respectively. The low-temperature behavior of λ(T) evolves from a T-linear in pristine state to a T 2 behavior after irradiation, expected for a line-nodal d-wave superconductor. However, the original theory that explained such behavior assumed a unitary limit of the scattering potential, whereas usually in normal metals and semiconductors, Born scattering is sufficient to describe the experiment. To estimate the scattering potential strength, we calculated the superfluid density, ρ s (t = T/T c ) = λ 2 (0)/λ 2 (T), varying the amount and strength of non-magnetic scattering using a self-consistent t-matrix theory. Fitting the obtained curves to a power law, ρ s = 1 - Rt n , and to a polynomial, ρ s = 1 - At - Bt 2 , and comparing the coefficients n in one set and A and B in another with the experimental values, we estimate the phase shift to be around 70 and 65°, respectively. We correlate this result with the evolution of the density of states with nonmagnetic disorder.
London Penetration Depth Measurements Using Tunnel Diode Resonators
The London penetration depth λ is the basic length scale for electromagnetic behavior in a superconductor. Precise measurements of λ as a function of temperature, field and impurity scattering have been instrumental in revealing the nature of the order parameter and pairing interactions in a variety of superconductors discovered over the past decades. Here we recount our development of the tunnel-diode resonator technique to measure λ as function of temperature and field in small single crystal samples. Furthermore, we discuss the principles and applications of this technique to study unconventional superconductivity in the copper oxides and other materials such as iron-based superconductors. The technique has now been employed by several groups world-wide as a precision measurement tool for the exploration of new superconductors.
Quasiparticle spectroscopy in technologically relevant niobium using London penetration depth measurements: experiment and theory
Abstract The London penetration depth, λ ( T ) , was measured in various forms of niobium, including foils, thin films, single crystals, and samples from superconducting radio-frequency (SRF) cavities. We observed a significant difference in λ ( T ) at low temperatures, T < T c / 3 , due to low-energy quasiparticles. In particular, an unusual downturn of λ ( T ) on cooling in the SRF cavity samples required to take into account deep in-gap bound states. Theoretical modeling using the generalized Dynes density of states shows that such in-gap states lead to a downturn or a peak in λ ( T ) upon cooling. Combined, experimental and theoretical findings provide a method for detecting two-level systems or states related to magnetic impurities in the bulk of niobium. This result is particularly relevant for the quantum informatics sciences technologies used in qubits and circuit quantum electrodynamics architecture based on SRF cavities.
London penetration depth of electron-irradiated Ba 0 . 47 K 0 . 53 Fe 2 As 2
We have characterized an electron-irradiated Ba 1-x K x Fe 2 As 2 (x = 0.53) single-crystal using two different experimental techniques: magneto-optic measurements and microwave measurements. The crystal has been measured before as well as after the 2.5 MeV electron irradiation process. After irradiation it was annealed in a number of steps, between 90 °C and 180 °C, and measured after each annealing step. Most microwave measurements were performed by means of a copper cavity, taking advantage of the TE 011 and TM 110 modes, allowing for the determination of the London penetration depths changes δλ ab (T) and δλ c (T), ie perpendicular and parallel to the sample c-axis. Appropriate equations, based on perturbation theory, were derived to calculate the penetration depths changes δλ ab and δλ c for a rectangular prism geometry. The sample showed a full recovery of its T c , however the observed behavior of δλ c and δλ ab was not monotonic vs annealing temperature, displaying a minimum of δλ c and δλ ab at 120 °C. In conclusion, this finding was confirmed by magneto-optic measurements, where besides verifying the sample uniformity and the absence of visible defects, the lower critical field H c1 of the Ba 1-x K x Fe 2 As 2 single-crystal was obtained and the London penetration depth λab(0) was calculated.
Mass accommodation and gas–particle partitioning in secondary organic aerosols: dependence on diffusivity, volatility, particle-phase reactions, and penetration depth
Abstract. Mass accommodation is an essential process for gas–particle partitioning of organic compounds in secondary organic aerosols (SOA). The mass accommodation coefficient is commonly described as the probability of a gas molecule colliding with the surface to enter the particle phase. It is often applied, however, without specifying if and how deep a molecule has to penetrate beneath the surface to be regarded as being incorporated into the condensed phase (adsorption vs. absorption). While this aspect is usually not critical for liquid particles with rapid surface–bulk exchange, it can be important for viscous semi-solid or glassy solid particles to distinguish and resolve the kinetics of accommodation at the surface, transfer across the gas–particle interface, and further transport into the particle bulk. For this purpose, we introduce a novel parameter: an effective mass accommodation coefficient αeff that depends on penetration depth and is a function of surface accommodation coefficient, volatility, bulk diffusivity, and particle-phase reaction rate coefficient. Application of αeff in the traditional Fuchs–Sutugin approximation of mass-transport kinetics at the gas–particle interface yields SOA partitioning results that are consistent with a detailed kinetic multilayer model (kinetic multilayer model of gas–particle interactions in aerosols and clouds, KM-GAP; Shiraiwa et al., 2012) and two-film model solutions (Model for Simulating Aerosol Interactions and Chemistry, MOSAIC; Zaveri et al., 2014) but deviate substantially from earlier modeling approaches not considering the influence of penetration depth and related parameters. For highly viscous or semi-solid particles, we show that the effective mass accommodation coefficient remains similar to the surface accommodation coefficient in the case of low-volatility compounds, whereas it can decrease by several orders of magnitude in the case of semi-volatile compounds. Such effects can explain apparent inconsistencies between earlier studies deriving mass accommodation coefficients from experimental data or from molecular dynamics simulations. Our findings challenge the approach of traditional SOA models using the Fuchs–Sutugin approximation of mass transfer kinetics with a fixed mass accommodation coefficient, regardless of particle phase state and penetration depth. The effective mass accommodation coefficient introduced in this study provides an efficient new way of accounting for the influence of volatility, diffusivity, and particle-phase reactions on SOA partitioning in process models as well as in regional and global air quality models. While kinetic limitations may not be critical for partitioning into liquid SOA particles in the planetary boundary layer (PBL), the effects are likely important for amorphous semi-solid or glassy SOA in the free and upper troposphere (FT–UT) as well as in the PBL at low relative humidity and low temperature.
High-precision measurement of magnetic penetration depth in superconducting films
We report that the magnetic penetration depth (λ) in thin superconducting films is usually measured by the mutual inductance technique. The accuracy of this method has been limited by uncertainties in the geometry of the solenoids and in the film position and thickness, by parasitic coupling between the coils, etc. Here, we present several improvements in the apparatus and the method. To ensure the precise thickness of the superconducting layer, we engineer the films at atomic level using atomic-layer-by-layer molecular beam epitaxy. In this way, we also eliminate secondary-phase precipitates, grain boundaries, and pinholes that are common with other deposition methods and that artificially increase the field transmission and thus the apparent λ. For better reproducibility, the thermal stability of our closed-cycle cryocooler used to control the temperature of the mutual inductance measurement has been significantly improved by inserting a custom-built thermal conductivity damper. Next, to minimize the uncertainties in the geometry, we fused a pair of small yet precisely wound coils into a single sapphire block machined to a high precision. Lastly, the sample is spring-loaded to exactly the same position with respect to the solenoids. Altogether, we can measure the absolute value of λ with the accuracy better than ±1%.
London penetration depth at zero temperature and near the superconducting transition
Herein, a simple relation is established between the zero- T penetration depth λ ( 0 ) and the slope of λ – 2 ( T ) near T c , similar to Helfand-Werthamer's relation for H c 2 ( 0 ) and the slope of H c 2 ( T ) at T c for the isotropic s -wave case with nonmagnetic scattering. When the scattering parameter ρ = ℏ v / 2 π T c ℓ ( v is the Fermi velocity and ℓ is the mean free path) varies from 1 to 10, the coefficient of proportionality between λ – 2 ( 0 ) and T c ( d λ – 2 / d T ) T c changes from 0.43 to 0.38. Combining this relation with the Rutgers thermodynamic identity, one can express λ ( 0 ) in terms of the slope ( d H c 2 / d T ) T c and the density of states.
Probing the superconducting gap symmetry of α - PdBi 2 : A penetration depth study
In this paper, we report measurements of the in-plane London penetration depth λ in single crystals of the α - PdBi 2 superconductor—the α-phase counterpart of the putative topological superconductor β - PdBi 2 , down to 0.35 K using a high-resolution tunnel-diode-based technique. Both λ and superfluid density ρ s exhibit an exponential behavior for T ≤ 0.35T c , with Δ(0) /k B T c ~ 2.0, ΔC/γT c ~ 2.0, and λ(0) ~ 140 nm, showing that α - PdBi 2 is a moderately coupling, fully gapped superconductor. Finally, the values of Δ(0) and ΔC/γT c are consistent with each other via strong-coupling corrections.
Nontrivial Nature and Penetration Depth of Topological Surface States in SmB 6 Thin Films
The nontrivial feature and penetration depth of the topological surface states (TSS) in SmB 6 were studied via spin pumping. The experiments used SmB 6 thin films grown on the bulk magnetic insulator Y 3 Fe 5 O 12 (YIG). Upon the excitation of magnetization precession in the YIG, a spin current is generated in the SmB 6 that produces, via spin--orbit coupling, a lateral electrical voltage in the film. This spin-pumping voltage signal becomes considerably stronger as the temperature decreases from 150 to 10 K, and such an enhancement most likely originates from the spin-momentum locking of the TSS and may thereby serve as evidence for the nontrivial nature of the TSS. The voltage data also show a unique film thickness dependence that suggests a TSS depth of ~32 nm. Finally, the spin--pumping results arc supported by transport measurements and analyses using a tight binding model.
Universal doping evolution of the superconducting gap anisotropy in single crystals of electron-doped Ba(Fe 1– x Rh x ) 2 As 2 from London penetration depth measurements
Doping evolution of the superconducting gap anisotropy was studied in single crystals of 4d-electron doped Ba(Fe 1–x Rh x ) 2 As 2 using tunnel diode resonator measurements of the temperature variation of the London penetration depth Δλ( T ). Single crystals with doping levels representative of an underdoped regime x = 0.039 ( T c = 15.5 K), close to optimal doping x = 0.057 ( T c = 24.4 K) and overdoped x = 0.079 ( T c = 21.5 K) and x = 0.131( T c = 4.9 K) were studied. Superconducting energy gap anisotropy was characterized by the exponent, n, by fitting the data to the power-law, Δλ = AT n . The exponent n varies non-monotonically with x, increasing to a maximum n = 2.5 for x = 0.079 and rapidly decreasing towards overdoped compositions to 1.6 for x = 0.131. This behavior is qualitatively similar to the doping evolution of the superconducting gap anisotropy in other iron pnictides, including hole-doped (Ba,K)Fe 2 As 2 and 3d-electron-doped Ba(Fe,Co) 2 As 2 superconductors, finding a full gap near optimal doping and strong anisotropy toward the ends of the superconducting dome in the T-x phase diagram. The normalized superfluid density in an optimally Rh-doped sample is almost identical to the temperature-dependence in the optimally doped Ba(Fe,Co) 2 As 2 samples. In conclusion, our study supports the universal superconducting gap variation with doping and pairing at least in iron based superconductors of the BaFe 2 As 2 family.
In-plane magnetic penetration depth of superconducting CaKFe 4 As 4
Here, the temperature dependence of the in-plane magnetic penetration depth (λ ab ) in an extensively characterized sample of superconducting CaKFe 4 As 4 (T c ≃35K) was investigated using muon-spin rotation (μSR). A comparison of λ –2 ab (T) measured by μSR with the one inferred from angle-resolved photoemission spectroscopy (ARPES) data confirms the presence of multiple gaps at the Fermi level. An agreement between μSR and ARPES requires the presence of additional bands, which are not resolved by ARPES experiments. These bands are characterized by small superconducting gaps with an average zero-temperature value of Δ 0 =2.4(2)meV. Our data suggest that in CaKFe 4 As 4 the s ± order parameter symmetry acquires a more sophisticated form by allowing a sign change not only between electron and hole pockets, but also within pockets of similar type.
Effective moisture penetration depth model for residential buildings: Sensitivity analysis and guidance on model inputs
Moisture buffering of building materials has a significant impact on the building's indoor humidity, and building energy simulations need to model this buffering to accurately predict the humidity. Researchers requiring a simple moisture-buffering approach typically rely on the effective-capacitance model, which has been shown to be a poor predictor of actual indoor humidity. This paper describes an alternative two-layer effective moisture penetration depth (EMPD) model and its inputs. While this model has been used previously, there is a need to understand the sensitivity of this model to uncertain inputs. In this paper, we use the moisture-adsorbent materials exposed to the interior air: drywall, wood, and carpet. We use a global sensitivity analysis to determine which inputs are most influential and how the model's prediction capability degrades due to uncertainty in these inputs. We then compare the model's humidity prediction with measured data from five houses, which shows that this model, and a set of simple inputs, can give reasonable prediction of the indoor humidity.
Superconducting penetration depth through a Van Hove singularity: Sr 2 RuO 4 under uniaxial stress
A plethora of experiments in Sr 2 RuO 4 have reached conflicting conclusions about the symmetry of the superconducting gap. To probe the gap’s structure in k-space, we use strain to continuously tune the band structure through a Van Hove singularity (VHS) while imaging the superconductivity with scanning SQUID microscopy. We find that the superfluid density peaks at the VHS and that the temperature dependence of the penetration depth is T 2 -quadratic over the entire measured range of strain ε. These results are consistent with a gap structure that has vertical line nodes, experimentally confirming that non-local effects in the Meissner screening can lead to T 2 behavior and clarifying the nature of the low-energy excitations in Sr 2 RuO 4 .
Universal temperature dependence of the London penetration depth in κ - ( ET ) 2 X superconductors
High-precision radio-frequency magnetic susceptibility measurements were performed on single crystals of fully deuterated $κ-(ET)_2Cu[N(CN)_2]\,Br$, hereafter designated as $κ-(ET)_2Cu[N(CN)_2]\,Br$. This material phase separates into superconducting and antiferromagnetic regions, the degree of which depends strongly upon the cooling rate. Here, we show that the screening fraction $η_{sc}$ varies logarithmically with the cooling rate over nearly five decades. The average size of superconducting regions is estimated to vary from 5 to $40μm$, depending upon cooling rate, consistent with previous infrared microscopy measurements. In the region $T≲T_c/3$, the effective magnetic penetration depth exhibits power-law behavior $λ(T)-λ(0)~T^n$ with $n=1.6$, independent of the cooling rate. Changes in cooling rate and the consequent phase separation evidently do not introduce the kind of disorder that would alter the exponent $n$ in a $d$-wave superconductor. The exponent remains close to $n=$ 1.5, reported in single crystals of $κ-(ET)_2Cu[N(CN)_2]\,Br$ and $κ-(ET)_2Cu(NCS)_2$ [A. Carrington et al., Phys. Rev. Lett 83, 4172 (1999)]. The transition temperature fell linearly with $1-η_{sc}$. Measurements were also made on $κ-(ET)_2Cu[N(CN)_2]\,Cl$ of normal isotopic abundance in which a very small amount of superconducting phase $η_{sc}≈10^{-4}$ developed, presumably through the strain-induced sample mounting. This material showed a power-law exponent of $n=1.64$, independent of the cooling rate.
Moisture Modeling: Effective Moisture Penetration Depth Versus Effective Capacitance
This paper compares two moisture models in the context of residential whole-building simulations - the effective moisture penetration depth (EMPD) model and the effective capacitance (EC) model. Previous research has shown that the EMPD model provides a more physically realistic response to humidity-load fluctuations than the EC model. But it is unclear how the choice of moisture model affects overall conclusions informing building design and equipment selection. In this study, the models are evaluated based on their ability to predict relative humidity, predict energy use, and to select HVAC equipment. Whole building simulations indicate that the EC and EMPD models are not equivalent, and that combining the capacitance of the building materials with the indoor air capacitance in the EC model is the root cause of this discrepancy. It means that the EC model cannot dampen humidity loads of different frequencies. This study also showed that a simulation using a certain value of EC in one city can agree with the EMPD results, but that the same EC value in a different city may not agree with the EMPD results. However, the results showed that some conclusions drawn from simulations using the EMPD model and the EC model may often be the same, even if the results differ.
Estimating the Penetration Depth and Orientation of Stress Corrosion Cracks Using Time-Reversal Acoustics
Austenitic stainless steels are known to be susceptible to stress corrosion cracking (SCC), which is an aggressive type of corrosion that exists when a material under tensile stress is placed in a corrosive environment. This is of particular concern as the processing (i.e., cold rolling) and construction (welding) of storage canisters produce an inherent residual stress in metals that can lead to SCC. In this context, our objective is to study the formation of stress corrosion cracks within Type 304L stainless steel, which is frequently used in containers for used nuclear fuel disposal. The conditions present in storage canisters (i.e., elevated temperatures, high residual stresses near welds, and exposure to humidity and chloride) make them susceptible to SCC, potentially leading to critical through-wall failure, and thus loss of containment. The timescales on which through-wall failure is expected in a storage canister under typical conditions is on the order of tens of years. While through-wall flaws are catastrophic (e.g., release of helium and fission gases), the long timescales allow for routine inspection, and potentially mitigation, providing methods exist. This paper is focused on the former problem, i.e. detection of SCC, and the development of a tool for inspection of storage canisters. We will discuss the recent work we did on detecting the presence of SCC as well as imaging on its orientation and penetration depth using an acoustic technique developed at Los Alamos National Laboratory (LANL). This technique has been applied successfully in the laboratory on stainless steel samples with SCC provided by General Electric (GE) and the Electric Power Research Institute (EPRI). Recently, we have also demonstrated that this technique can be deployed for field inspections in tight and confined spaces. (authors)