High Field Limit Research Articles

Identifying capacitive and inductive loss in lumped element superconducting hybrid titanium nitride/aluminum resonators

We present a method to systematically locate and extract capacitive and inductive losses in superconducting resonators at microwave frequencies by use of mixed-material, lumped element devices. In these devices, ultra-low loss titanium nitride was progressively replaced with aluminum in the inter-digitated capacitor and meandered inductor elements. By measuring the power dependent loss at 50 mK as the Al/TiN fraction in each element is increased, we find that at low electric field, i.e., in the single photon limit, the loss is two level system in nature and is correlated with the amount of Al capacitance rather than the Al inductance. In the high electric field limit, the remaining loss is linearly related to the product of the Al area times its inductance and is likely due to quasiparticles generated by stray IR radiation. At elevated temperature, additional loss is correlated with the amount of Al in the inductance, with a power independent TiN-Al interface loss term that exponentially decreases as the temperature is reduced. The TiN-Al interface loss is vanishingly small at the 50 mK base temperature.

Dephasing and hyperfine interaction in carbon nanotubes double quantum dots: Disordered case

We study theoretically the \emph{return probability experiment}, used to measure the dephasing time $T_2^*$, in a double quantum dot (DQD) in semiconducting carbon nanotubes (CNTs) with spin-orbit coupling and disorder induced valley mixing. Dephasing is due to hyperfine interaction with the spins of the ${}^{13}$C nuclei. Due to the valley and spin degrees of freedom four bounded states exist for any given longitudinal mode in the quantum dot. At zero magnetic field the spin-orbit coupling and the valley mixing split those four states into two Kramers doublets. The valley mixing term for a given dot is determined by the intra-dot disorder and therefore the states in the Kramers doublets belonging to different dots are different. We show how nonzero single-particle interdot tunneling amplitudes between states belonging to different doublets give rise to new avoided crossings, as a function of detuning, in the relevant two particle spectrum, crossing over from the two electrons in one dot states configuration, $(0,2)$, to the one electron in each dot configuration, $(1,1)$. In contrast to the clean system, multiple Landau-Zener processes affect the separation and the joining stages of each single-shot measurement and they affect the outcome of the measurement in a way that strongly depends on the initial state. We find that a well-defined return probability experiment is realized when, at each single-shot cycle, the (0,2) ground state is prepared. In this case, valley mixing increases the saturation value of the measured return probability, whereas the probability to return to the (0,2) ground state remains unchanged. Finally, we study the effect of the valley mixing in the high magnetic field limit; for a parallel magnetic field the predictions coincide with a clean nanotube, while the disorder effect is always relevant with a magnetic field perpendicular to the nanotube axis.

Microwave surface resistance of YBCO superconducting thin films under high DC magnetic field

We investigated the dc magnetic field and temperature dependences of the microwave surface resistance (Rs) of YBa2Cu3Oy (YBCO) superconducting thin films with various thicknesses. We used YBCO thin films with 300, 500, and 700nm deposited on a MgO (100) substrate by the thermal co-evaporation method. The Rs was measured using the dielectric resonator method at 21.8GHz, and a high dc magnetic field of up to 12T was applied parallel to the c-axis of the YBCO thin films during Rs measurements. The Rs value of YBCO thin films increased when dc magnetic field was applied. These relationships could be explained by using the two-fluid model for high frequency and low magnetic field limits. We defined the viscous drag coefficient η under the low magnetic limit and the high magnetic field limit as the ηlow (B, T, d) and ηhigh (B, T, d), respectively. The ηlow values were approximately two orders of magnitude greater than ηhigh values. Also, all ηlow and ηhigh value decreased or saturated as the temperature and film thickness increased. These results show that η under the low and high magnetic field limit depended on the temperature and film thickness.

Complete Nuclear Dipolar Line Shapes for High Transverse Field μSR

Abstract It is common in analysis of transverse field TF- μ SR data to assume that the line shape contribution of the nuclear spin lattice is Gaussian. Yet, evaluation of the muon-nuclear dipolar Hamiltonian is trivial in the high field limit subject to conditions of the TF- μ SR experiment. Here we clarify the experimental requirements needed to satisfy the high field limit, and point the reader to previously published calculations in this regime. We describe our calculation method and present line shapes for the tetrahedral and octahedral sites in copper for external magnetic field directions parallel to the method of Van Vleck. As illustrated by the calculated line shapes, dipolar broadening at the muon site is highly sensitive to the direction of the external magnetic field. Judicious choice of the external field direction can be used to minimize dipolar broadening and departures of the line shape from a gaussian character. The calculation is a valuable tool to predict field dependence for a given muon site. Alternatively, it may be used to determine the muon site from experimental data obtained at various field orientations. In situations where the line shape is not well fit by a Gaussian and/or where the muon induces lattice distortion, the calculation is a valuable tool to better fit the μ SR data.

Magnetotransport of Massless Dirac Fermions in Multilayer Organic Conductors

Magnetotransport has been considered in multilayer massless Dirac fermion systems, in which two-dimensional (2D) layers with a pair of Dirac-cone dispersion stack with weak interlayer coupling. The Fermi level is assumed to be fixed at the Dirac point resulting in the zero-gap conductor. At the high-field quantum limit, where only the n = 0 Landau level at the Dirac point is partially occupied, all elements of conductivity tensor have been evaluated by the lowest order contribution of interlayer coupling. We have deduced saturation of in-plane resistance, local maxima of in-plane Hall resistance, negative interlayer magnetoresistance, and cotθ-type unusual angle-dependence of interlayer Hall resistance. These results propose good explanations for mysterious transport features observed in organic zero-gap conductors, α-(BEDT-TTF)2I3 and its related compounds.

An asymptotic preserving scheme for the vlasov-poisson-fokker-planck system in the high field regime

The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects (electrical or gravitational) are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field. We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime, namely, large time steps and coarse meshes can be used, yet the high field limit is still captured. The idea is to combine the two stiff terms and treat them implicitly. Thanks to the linearity of the collision term, using the discretization described in [Jin S, Yan B. J. Comp. Phys., 2011, 230: 6420–6437] we only need to invert a symmetric matrix. This method can be easily extended to higher dimensions. The method is shown to be positive, stable, mass and asymptotic preserving. Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes.

An asymptotic preserving scheme based on a micro-macro decomposition for Collisional Vlasov equations: diffusion and high-field scaling limits

In this work, we extend the micro-macro decomposition based numerical schemes developed in [3]to the collisional Vlasov-Poisson model in the diffusion and high-field asymptotics. In doing so, we first write the Vlasov-Poisson model as a system that couples the macroscopic (equilibrium) part with the remainder part.A suitable discretization of this micro-macro model enables to derive an asymptotic preservingscheme in the diffusion and high-field asymptotics. In addition, two main improvements are presented:On the one hand a self-consistent electric field is introduced, which induces a specific discretizationin the velocity direction, and represents a wide range of applications in plasma physics.On the other hand, as suggested in [30], we introduce a suitable reformulation of the micro-macroscheme which leads to an asymptotic preserving property with the following property: It degenerates into an implicitscheme for the diffusion limit model when $\varepsilon\rightarrow 0$, which makes it free from the usual diffusion constraint$\Delta t=O(\Delta x^2)$ in all regimes.Numerical examples are used to demonstrate the efficiency and the applicability of the schemes for both regimes.

Controllable p-n Junction Formation in Monolayer Graphene Using Electrostatic Substrate Engineering

We investigate electric transport in graphene on SiO2 in the high field limit and report on the formation of p-n junctions. Previously, doping of graphene has been achieved by using multiple electrostatic gates, or charge transfer from adsorbants. Here we demonstrate a novel approach to create p-n junctions by changing the local electrostatic potential in the vicinity of one of the contacts without the use of extra gates. The approach is based on the electronic modification not of the graphene but of the substrate and produces a well-behaved, sharp junction whose position and height can be controlled.

Testing QED in sodium-like gold and xenon: using atomic spectroscopy and an EBIT to probe the quantum vacuum

Electron Beam Ion Traps (EBITs) can strip atoms to their electronic cores, revealing strong perturbations of the quantum vacuum that occur at electric field strengths comparable to those in petawatt lasers focused to their diffraction limit. Wavelengths of the D-lines in sodium-like ions measured previously using the NIST EBIT are discussed in terms of testing quantum electrodynamics in the high-field limit. The accuracy of our measurements in Au68+ (0.03 eV), together with the estimated accuracy of a corresponding calculation (0.02 eV), provide a 0.6% test of QED, the most precise currently available in any sodium-like ion. This measurement tests the predictions of QED for sodium-like ions to more fractional accuracy than even the best results available in hydrogen-like uranium. For the case of Na-like Xe43+, where a modest discrepancy exists between theory and measurements from three independent groups, an apparent collision-energy dependence is revealed which may account for the discrepancy.

Plasma Barodiffusion in Inertial-Confinement-Fusion Implosions: Application to Observed Yield Anomalies in Thermonuclear Fuel Mixtures

The observation of large, self-generated electric fields (≥10(9) V/m) in imploding capsules using proton radiography has been reported [C. K. Li, Phys. Rev. Lett. 100, 225001 (2008)]. A model of pressure gradient-driven diffusion in a plasma with self-generated electric fields is developed and applied to reported neutron yield deficits for equimolar D3He [J. R. Rygg, Phys. Plasmas 13, 052702 (2006)] and (DT)3He [H. W. Herrmann, Phys. Plasmas 16, 056312 (2009)] fuel mixtures and Ar-doped deuterium fuels [J. D. Lindl, Phys. Plasmas 11, 339 (2004)]. The observed anomalies are explained as a mild loss of deuterium nuclei near capsule center arising from shock-driven diffusion in the high-field limit.

Frequency dependence of magnetic ac loss in a five strand YBCO Roebel cable

We have measured the frequency dependent magnetic ac loss in a five strand Roebel cable with2 mm wide non-insulated strands and a transposition length of 90 mm. The cable is made from12 mm wide SuperPower YBCO (yttrium barium copper oxide) coated conductor tape with a20 µm thick surrounding copper stabilizer layer. The ac loss of the Roebel cable is measured in asinusoidally varying external magnetic field in perpendicular orientation, with amplitudesup to 150 mT, in the frequency range of 30–200 Hz, and at a temperature of 77 K. Nomeasurable loss is observed in the parallel orientation. In the perpendicular orientation, thecable loss is predominantly hysteretic in nature. The loss either increases or decreaseswith frequency, in different field ranges. To resolve the origin of the frequencydependence, we measure the loss in a single strand and in standard tape with similarcopper stabilization. The cable and sum of strand losses converge in the highfield limit, indicating that strands are not electrically coupled. We attribute theobserved frequency dependent increase in loss to a sum of the eddy current loss inthe copper stabilizer and the intrinsic frequency dependence of the hysteresisloss. Experimental results and finite element method calculated values for thefrequency dependent contributions to the magnetic ac loss agree well with each other.

Distance-dependent electron transfer rate of immobilized redox proteins: A statistical physics approach

The electron transfer kinetics of redox proteins adsorbed on metal electrodes coated with self-assembled monolayers (SAMs) of mercaptanes shows an unusual distance-dependence. For thick SAMs, the experimentally measured electron transfer rate constant k{exp} obeys the behavior predicted by Marcus theory [R. A. Marcus and N. Sutin, Biochim. Biophys. Acta 811, 265 (1985)], whereas for thin SAMs, k{exp} remains virtually constant [Z. Q. Feng, J. Chem. Soc., Faraday Trans. 93, 1367 (1997)]. In this work, we present a simple theoretical model system for the redox protein cytochrome c electrostatically bound to a SAM-coated electrode. A statistical average of the electron tunneling rate is calculated by accounting for all possible orientations of the model protein. This approach, which takes into account the electric field dependent orientational distribution, allows for a satisfactory description of the "saturation" regime in the high electric field limit. It further predicts a nonexponential behavior of the average electron transfer processes that may be experimentally checked by extending kinetic experiments to shorter sampling times, i.e., 1/k{exp}. For a comprehensive description of the overall kinetics in the saturation regime at sampling times of the order of <<1/k{exp}, it is essential to consider the dynamics of protein reorientation, which is not implemented in the present model.

A phenomenological approach to the anisotropic magnetoresistance and planar Hall effect in tetragonalLa2/3Ca1/3MnO3 thin films

A La2/3Ca1/3MnO3 Hall bar with its long dimension roughly along the hard axis [110]was fabricated on a single-crystal-like tensilely strained film onSrTiO3(001). The anisotropic magnetoresistance (AMR) and planar Hall effect (PHE) have been studied atvarious external magnetic fields and temperatures. A phenomenological model in the highfield limit is developed, and the galvanomagnetic tensor based on a tetragonal symmetry4/mmm (D4h), applicable to epitaxial films on a substrate, has been obtained by expandingthe tensor to the sixth order. The derived in-plane transverse resistanceRxy showsa sin2ϕM angular dependence, while the longitudinalRxx is constituted by notonly a two-fold cos2ϕM term,but also a four-fold cos4ϕM term due to the square symmetry of the lattice. The model is in good agreement withthe experimental results in high fields, while deviations are observed near the⟨100⟩ easy axis with the decreasing field. Close inspection of the fitting parameters reveals theevolution of these term weights with temperature and magnetic field, which is distinct fromconventional ferromagnetic metals and cannot be explained by the phenomenologicalmodel. An alternative mechanism for AMR, stemming from the magnetization-inducedlocal orbit deformation through spin–orbit interaction, as previously proposed byO’Donnell et al, may be prevalent in manganites and other systems of complicated crystalstructure.

Positive magnetic field effect on mutual triplet–triplet annihilation of mixed molecular pairs: Magnetosensitive geterofusion induced by difference of g-factors

The model of magnetic field effect on mutual triplet exciton heteroannihilation under conditions of high field strength has been developed. The increase of the TT-annihilation rate induced by the difference of T-excitons g-factors is obtained in the limit of high magnetic field instead of the usual decrease caused by the intramolecular spin–spin coupling.

Nernst Signal in High-T c Superconductors

The time-dependent Ginzburg-Landau equation with thermal noise is used to calculate the Nernst signal e N , describing the Nernst effect, in type-II superconductor in the vortex-liquid regime. The Gaussian method used is an elaboration of the Hartree-Fock method. An additional assumption often made in analytical calculations that only the lowest Landau level significantly contributes to physical quantities of interest in the high-field limit is lifted by including all the Landau levels. The values of e N are in good quantitative agreement with experimental data for temperature close to T c on Bi 2 Sr 2 CaCu 2 O 8+δ and Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ .

Hyperbolic Conservation Laws

Hyperbolic Conservation Laws

The Ground State of Relativistic Ions in the Limit of High Magnetic Fields

We consider the pseudorelativistic no-pair Brown–Ravenhall operator for the description of relativistic one-electron ions in a homogeneous magnetic field B. It is shown for central charge Z ≤ 87 that their ground state energy decreases according to $${\sqrt{B}}$$ as B → ∞, in contrast to the nonrelativistic behaviour.

Quantum critical dynamics of anS=12antiferromagnetic Heisenberg chain studied byC13NMR spectroscopy

We present a $^{13}\text{C}$ NMR study of the magnetic field driven transition to complete polarization of the $S=\frac{1}{2}$ antiferromagnetic Heisenberg chain system copper pyrazine dinitrate $\text{Cu}({\text{C}}_{4}{\text{H}}_{4}{\text{N}}_{2}){({\text{NO}}_{3})}_{2}$ (CuPzN). The static local magnetization as well as the low-frequency spin dynamics, probed via the nuclear spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$, were explored from the low to the high field limit and at temperatures from the quantum regime $({k}_{B}T⪡J)$ up to the classical regime $({k}_{B}T⪢J)$. The experimental data show very good agreement with quantum Monte Carlo calculations over the complete range of parameters investigated. Close to the critical field, as derived from static experiments, a pronounced maximum in ${T}_{1}^{\ensuremath{-}1}$ is found which we interpret as the finite-temperature manifestation of a diverging density of zero-energy magnetic excitations at the field-driven quantum critical point.

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

We establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized Hydrostatic-Boussinesq equations) to various models involving Optimal Transport (and the related Monge-Ampere equation. This includes the 2D semi-geostrophic equations and some fully non-linear versions of the so-called high-field limit of the Vlasov-Poisson system and of the Keller-Segel for Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology.

Magnetic anisotropy from density functional calculations. Comparison of different approaches: Mn12O12 acetate as a test case

Magnetic anisotropy is the capability of a system in a triplet or higher spin state to store magnetic information. Although the source of the magnetic anisotropy is the zero-field splitting of the ground state of the system, there is a difference between these two quantities that has to be fully rationalized before one makes comparisons. This is especially important for small spins such as triplets, where the magnetic anisotropy energy is only half of the zero-field splitting. Density functional calculations of magnetic anisotropy energies correspond to a high-field limit where the spins are aligned by the external magnetic field. Data are presented for the well-studied molecular magnet Mn(12)O(12) acetate. Both perturbative and self-consistent treatments, different quasirelativistic Hamiltonians (zeroth order regular approximation, Douglas-Kroll, effective core potentials) and exchange-correlation functionals are compared. It is shown that some effects usually considered minor, such as the inclusion of the exchange-correlation potential in the effective one-particle spin-orbit operator, lead to sizable differences when computing magnetic anisotropy energies. Higher-order contributions, that is, the difference between self-consistent and perturbative results, increase the magnetic anisotropy energy somewhat but do not introduce sizeable quartic terms or an in-plane anisotropy. In numerical experiments, on can switch off and on spin-orbit coupling at individual atomic sites. This procedure yields single-site contributions to the overall magnetic anisotropy energy that could be used as parameters in phenomenological spin Hamiltonians. If ferrimagnetic systems are treated with broken symmetry density functional methods where the Kohn-Sham reference function is not a spin eigenfunction, corrections are needed which depend on the size of the exchange couplings in the system and must therefore be evaluated case by case.