Flux Threads Research Articles

Disentangling the Entangled Linkages of Relative Magnetic Helicity

Magnetic helicity, H, measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in V bounded by ∂V . For magnetically closed systems, V∈R3=V+V* , no magnetic flux threads the boundary, nˆ·B∣∂V=0 . Berger & Field and Finn & Antonsen extended the definition of helicity to relative helicity, H , for magnetically open systems where magnetic flux may thread the boundary. Berger expressed this relative helicity as two gauge-invariant terms that describe the self-helicity of the magnetic field that closes inside V and the mutual helicity between the magnetic field that threads the boundary ∂V and the magnetic field that closes inside V . The total magnetic field that permeates V entangles magnetic fields that are produced by current sources J in V with magnetic fields that are produced by current sources J* in V* . Building on this fact, we extend Berger's expressions for relative magnetic helicity to eight gauge-invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents J in V and/or J* in V* , thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy are discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary.

Topological states in a dimerized system with staggered magnetic fluxes

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner states gather at corners in the two-dimensional first-order and second-order topological insulators, respectively. Here, we report two kinds of topological states hosting anomalous bulk-boundary correspondence in the extended two-dimensional dimerized lattice with staggered flux threading. At $\frac{1}{2}$-filling, we observe isolated corner states with no fractional charge as well as metallic near-edge states in the $\mathcal{C}=2$ Chern insulator states. At $\frac{1}{4}$-filling, we find a $\mathcal{C}=0$ topologically nontrivial state, where the robust edge states are well localized along edges but bypass corners. These robust topological insulating states significantly differ from both conventional Chern insulators and usual high-order topological insulators.

A Two‐Spacecraft Study of Mars' Induced Magnetosphere's Response to Upstream Conditions

AbstractThis is a two‐spacecraft study, in which we investigate the effects of the upstream solar wind conditions on the Martian induced magnetosphere and upper ionosphere. We use Mars Express (MEX) magnetic field magnitude data together with interplanetary magnetic field (IMF), solar wind density, and velocity measurements from the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission, from November 2014 to November 2018. We compare simultaneous observations of the magnetic field magnitude in the induced magnetosphere of Mars (|B|IM) with the IMF magnitude (|B|IMF), and we examine variations in the ratio |B|IM/|B|IMF with solar wind dynamic pressure, speed and density. We find that the |B|IM/|B|IMF ratio in the induced magnetosphere generally decreases with increased dynamic pressure and that a more structured interaction is seen when comparing induced fields to the instantaneous IMF, where reductions in the relative fields at the magnetic pile up boundary (MPB) are more evident than in the field strength itself, along with enhancements in the immediate vicinity of the optical shadow of Mars. We interpret these results as evidence that while the induced magnetosphere is indeed compressed and induced field strengths are higher during periods of high dynamic pressure, a relatively larger amount of magnetic flux threads the region compared to that available from the unperturbed IMF during low dynamic pressure intervals.

Quantum phase transitions in a ν=12 bosonic fractional Chern insulator

Interacting quantum many-body systems often generate exotic orders, either topological or conventional competing orders. Understanding these phases and the phase transitions between them are common issues in condensed-matter physics. How to characterize these states in a convincing and convenient way remains ambiguous. Here, we report our numerical study on the interacting $\ensuremath{\nu}=\frac{1}{2}$ hard-core boson system with topological flat bands based on the infinite density matrix group algorithm. We explicitly show that the entanglement spectral flow can be used to diagnose the quantum phases emerging in the hard-core boson systems. In particular, the subsequent charge pumping exhibits a linear, sinelike, and indiscernible dependence by the flux threading in the fractional Chern insulator, supersolid, and solid state, respectively. The real-space boson occupancy in the thermodynamic limit is further calculated for a better understanding of the respective state. We compare the phase diagram obtained here with that obtained by the previously exact diagonalization method, and qualitative differences are observed. Therefore, the infinite density matrix group algorithm provides a convincing and convenient way to study the phase transition in such a strongly correlated topological system.

Semi-annual, annual and Universal Time variations in the magnetosphere and in geomagnetic activity: 3. Modelling

This is the third in a series of papers that investigate the semi-annual, annual and Universal Time variations in the magnetosphere. In this paper, we use the Lin et al. (2010) empirical model of magnetopause locations, along with the assumption of pressure equilibrium and the Newtonian approximation of magnetosheath pressure, to show that the equinoctial pattern arises in both the cross-tail current at the tail hinge point and in the total energy stored in the tail. The model allows us to study the effects of both dipole tilt and hemispheric asymmetries. As a test of the necessary assumptions made to enable this analysis, we also study simulations by the BATSRUS global MHD magnetosphere model. These also show that the reconnection voltage in the tail is greatest when the dipole tilt is small but this only applies at low solar wind dynamic pressurepSWand does not, on its own, explain why the equinoctial effect increases in amplitude with increasedpSW, as demonstrated by Paper 2. Instead, the effect is consistent with the dipole tilt effect on the energy stored in the tail around the reconnection X line. A key factor is that a smaller/larger fraction of the open polar cap flux threads the tail lobe in the hemisphere that is pointed toward/away from the Sun. The analysis using the empirical model uses approximations and so is not definitive; however, because the magnetopause locations in the two hemispheres were fitted separately in generating the model, it gives a unique insight into the effect of the very different offsets of the magnetic pole from the rotational pole in the two hemispheres. It is therefore significant that our analysis using the empirical model does predict aUTvariation that is highly consistent with that found in both transpolar voltage data and in geomagnetic activity.

Dynamical Structure Factor of the J1−J2 Heisenberg Model on the Triangular Lattice: Magnons, Spinons, and Gauge Fields

Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials. However, current theoretical and numerical techniques have limited capabilities, especially in obtaining the dynamical structure factor, which gives a crucial characterization of the ultimate nature of the quantum state and may be directly assessed by inelastic neutron scattering. In this work, we investigate the low-energy properties of the $S=1/2$ Heisenberg model on the triangular lattice, including both nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ super-exchanges, by a dynamical variational Monte Carlo approach that allows accurate results on spin models. For $J_2=0$, our calculations are compatible with the existence of a well-defined magnon in the whole Brillouin zone, with gapless excitations at $K$ points (i.e., at the corners of the Brillouin zone). The strong renormalization of the magnon branch (also including roton-like minima around the $M$ points, i.e., midpoints of the border zone) is described by our Gutzwiller-projected state, where Abrikosov fermions are subject to a non-trivial magnetic $\pi$-flux threading half of the triangular plaquettes. When increasing the frustrating ratio $J_2/J_1$, we detect a progessive softening of the magnon branch at $M$, which eventually becomes gapless within the spin-liquid phase. This feature is captured by the band structure of the unprojected wave function (with $2$ Dirac points for each spin component). In addition, we observe an intense signal at low energies around the $K$ points, which cannot be understood within the unprojected picture and emerges only when the Gutzwiller projection is considered, suggesting the relevance of gauge fields for the low-energy physics of spin liquids.

The influence of the nanostructure geometry on the thermoelectric properties

We discuss the influence of nanostructure geometry on the thermoelectric properties in quantum ring consists of one QD in each arm, each QD connects with side QD. The calculations are based on the time-dependent Hamiltonian model, the steady state is considered to obtain an analytical expression for the transmission probability as a function of system energies. We employed the transmission probability to calculate the thermoelectric properties. We investigate thermoelectric properties through three configurations of this nanostructure. Figure of merit enhanced in configuration (II) when side QD connected to upper arm of quantum ring. The magnetic flux threads quantum ring. The effect of magnetic flux on the thermoelectric properties is examined.

Enhancement of the Cooper-pair splitting in the Fano interferometer

We investigate the Andreev transports through a single-dot Fano interferometer with a side-coupled superconductor. It is found that when a finite magnetic flux threads through this structure, its induced phase factor adjusts the local and crossed Andreev reflections in different manners. Moreover, the crossed Andreev reflection has the opportunity to be enhanced, accompanied by the suppression of the local Andreev reflection. Such a result also exists when the intradot Coulomb interaction is taken into account. Therefore, this structure can be a promising candidate for the enhancement of the Cooper-pair splitting.

Finite size effect of nondegenerate edge states in annulus topological insulators

Topological insulator is promising in spintronics application due to the special properties of its edge states. The requirement is to find efficient ways to fully utilize the well discernible edge states. Using the nature of nondegenerate eigenenergies for the edge states of a topological insulator with annulus geometry, we examine the finite size effect of the system under various conditions, including magnetic flux threading, change of the curvature of the annulus, and implementation in a heterostructure with surrounding barrier materials. The finite size effect manifests itself in two aspects: the energy difference between the edge states and the separation distance between the edge states. The conditions we impose on the system show different tendencies in these two aspects. It is found that a finite size effect indeed can be reduced by lifting the energy degeneracy, and choosing a proper barrier material to localize the edge states is the most effective way to reduce finite size effect. The methodology studied here can be applied to analyze the recently proposed coaxial nanoribbon experiment.

Inflation from flux cascades

When electric-type flux threads compact extra dimensions, a quantum nucleation event can break a flux line and initiate a cascade that unwinds many units of flux. Here, we present a novel mechanism for inflation based on this phenomenon. From the 4D point of view, the cascade begins with the formation of a bubble containing an open Friedmann–Robertson–Walker cosmology, but the vacuum energy inside the bubble is initially only slightly reduced, and subsequently decreases gradually throughout the cascade. If the initial flux number Q0≳O(100), during the cascade the universe can undergo N≳60 efolds of inflationary expansion with gradually decreasing Hubble constant, producing a nearly scale-invariant spectrum of adiabatic density perturbations with amplitude and tilt consistent with observation, and a potentially observable level of non-Gaussianity and tensor modes. The power spectrum has a small oscillatory component that does not decay away during inflation, with a period set approximately by the light-crossing time of the compact dimension(s). Since the ingredients are fluxes threading compact dimensions, this mechanism fits naturally into the string landscape, but does not appear to suffer from the eta problem or require fine-tuning (beyond the usual anthropic requirement of small vacuum energy after reheating).

THERMAL SIGNATURES OF TETHER-CUTTING RECONNECTIONS IN PRE-ERUPTION CORONAL FLUX ROPES: HOT CENTRAL VOIDS IN CORONAL CAVITIES

Using a 3D MHD simulation, we model the quasi-static evolution and the onset of eruption of a coronal flux rope. The simulation begins with a twisted flux rope emerging at the lower boundary and pushing into a pre-existing coronal potential arcade field. At a chosen time the emergence is stopped with the lower boundary taken to be rigid. Then the coronal flux rope settles into a quasi-static rise phase during which an underlying, central sigmoid-shaped current layer forms along the so called hyperbolic flux tube (HFT), a generalization of the X-line configuration. Reconnections in the dissipating current layer effectively add twisted flux to the flux rope and thus allow it to rise quasi-statically, even though the magnetic energy is decreasing as the system relaxes. We examine the thermal features produced by the current layer formation and the associated "tether-cutting" reconnections as a result of heating and field aligned thermal conduction. It is found that a central hot, low-density channel containing reconnected, twisted flux threading under the flux rope axis forms on top of the central current layer. When viewed in the line of sight roughly aligned with the hot channel (which is roughly along the neutral line), the central current layer appears as a high-density vertical column with upward extensions as a "U" shaped dense shell enclosing a central hot, low-density void. Such thermal features have been observed within coronal prominence cavities. Our MHD simulation suggests that they are the signatures of the development of the HFT topology and the associated tether-cutting reconnections, and that the central void grows and rises with the reconnections, until the flux rope reaches the critical height for the onset of the torus instability and dynamic eruption ensues.

Prediction of quantization of magnetic flux in double-layer exciton superfluids

Currently a way is lacking to detect unambiguously the possible phase coherence of an exciton condensate in an electron-hole double layer. Here we show that despite the fact that excitons are charge-neutral, the double layer exciton superfluid exhibits a diamagnetic response. In devices with specific circular geometry the magnetic flux threading between the layers must be quantized in units of $\frac{h}{e} \chi_m$ where $\chi_m$ is the diamagnetic susceptibility of the device. We discuss possible experimental realizations of the predicted unconventional flux quantization.

THE FORMATION OF A MAGNETIC CHANNEL BY THE EMERGENCE OF CURRENT-CARRYING MAGNETIC FIELDS

A magnetic channel - a series of polarity reversals separating elongated flux threads with opposite polarities - may be a manifestation of a highly non-potential magnetic configuration in active regions. To understand its formation we have carried out a detailed analysis of the magnetic channel in AR 10930 using data taken by the Solar Optical Telescope/Hinode. As a result, we found upflows (-0.5 to -1.0 km/s) and downflows (+1.5 to +2.0 km/s) inside and at both tips of the thread respectively, and a pair of strong vertical currents of opposite polarity along the channel. Moreover, our analysis of the nonlinear force-free fields constructed from the photospheric magnetic field indicates that the current density in the lower corona may have gradually increased as a result of the continuous emergence of the highly sheared flux along the channel. With these results, we suggest that the magnetic channel originates from the emergence of the twisted flux tube that has formed below the surface before the emergence.

Measurement of the magnetic field inside the holes of a drilled bulkhigh-Tc superconductor

We use macroscopic holes drilled in a bulk YBCO superconductor to probe its magnetic propertiesin the volume of the sample. The sample is subjected to an AC magnetic flux with a density rangingfrom 30 to 130 mT and the flux in the superconductor is probed by miniature coils inserted in theholes. In a given hole, three different penetration regimes can be observed: (i) theshielded regime, where no magnetic flux threads the hole; (ii) the gradual penetrationregime, where the waveform of the magnetic field has a clipped sine shape whosefundamental component scales with the applied field; and (iii) the flux concentrationregime, where the waveform of the magnetic field is nearly a sine wave, withan amplitude exceeding that of the applied field by up to a factor of two. Thedistribution of the penetration regimes in the holes is compared with that ofthe magnetic flux density at the top and bottom surfaces of the sample, and isinterpreted with the help of optical polarized light micrographs of these surfaces.We show that the measurement of the magnetic field inside the holes can beused as a local characterization of the bulk magnetic properties of the sample.

Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

We carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear current-dependent inductance, inducing an external flux tunable nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive radiation pressure-type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state.

Flux-driven Josephson parametric amplifier

We have developed a Josephson parametric amplifier comprising a superconducting coplanar-waveguide resonator terminated by a dc superconducting quantum interference device (SQUID). An external field (the pump, ∼20 GHz) modulates the flux threading of the dc SQUID and, therefore, the resonant frequency of the cavity field (the signal, ∼10 GHz), which leads to the parametric signal amplification. We operated the amplifier at different band centers and observed amplification (17 dB at maximum) and deamplification depending on the relative phase between the pump and the signal. The noise temperature is estimated to be less than 0.87 K.

Magnetism in SQUIDs at Millikelvin Temperatures

We have characterized the temperature dependence of the flux threading dc SQUIDs cooled to millikelvin temperatures. The flux increases as 1/T as temperature is lowered; moreover, the flux change is proportional to the density of trapped vortices. The data are compatible with the thermal polarization of surface spins in the trapped fields of the vortices. In the absence of trapped flux, we observe evidence of spin-glass freezing at low temperature. These results suggest an explanation for the universal 1/f flux noise in SQUIDs and superconducting qubits.

Does a neutron know that the earth is rotating?

In 1979 we observed the quantum mechanical phase shift of neutron deBroglie waves due to the Earth’s rotation. After the result was published, a number of very nice theoretical papers on the experiment appeared. I have two favorites: The one by M. Dresden and C. N. Yang in which they view the effect as due to the Doppler shift created by reflection from moving mirrors; and the other one by J. J. Sakurai in which he views the origin of the effect as being due to a flux of rotation threading the neutron interferometer loop, in much the same way that magnetic flux threads the electron interferometer loop to create the topological Aharonov-Bohm effect. Here, I would like to place their explanations of the physics of this experiment in juxtaposition with my own understanding of it.

Design and performance of a planar-array MIT system with normal sensor alignment

In this study the performance of a planar array for magnetic induction tomography (MIT) was investigated and the results of measurements to determine the precision and sensitivity of the sensor were undertaken. A planar-array MIT system utilizing flux-linkage minimization for the primary field has been constructed and evaluated. The system comprises 4 printed excitation coils of 4 turns which were shielded, 8 surface-mount inductors of inductance 10 µH as sensor, mounted such that in principle no primary-field flux threads them, and a calibration coil to produce a strong primary field. The excitation current was multiplexed via relays to drive the excitation and reference coils. The noise values were similar in real and imaginary components in the lower frequencies and the factor to which the primary field could be reduced was greatest in the nearest coil. Methods for determining the true real and imaginary components and for flux-linkage minimization for the primary field for variations in channel sensitivities are described and the results of measurements of the system's noise and drift are given. A SNR of 47 dB was observed at 4 MHz when a 0.3 Sm−1 saline filled tank of dimensions 20 cm × 20 cm × 10 cm was placed centrally over the array. Finally, images were reconstructed from measurements of saline samples in a free space background, with the samples moved past the array in 21 1 cm steps to emulate mechanical scanning of the array. The image reconstruction characteristics of the planar array in conjunction with the reconstruction technique employed are discussed.

A primary field compensation scheme for planar array magnetic induction tomography

In biomedical magnetic induction tomography (MIT), measurement precision may be improved by incorporating some form of primary field compensation/cancellation scheme. Schemes which have been described previously include gradiometric approaches and the use of ‘back-off’ coils. In each of these methods, however, the primary field cancellation was achieved only for a single transmitter/receiver combination. For the purpose of imaging, it would be desirable for a fully electronically scanned MIT system to provide a complete set of measurements, all with the primary field cancelled. A single channel suitable for incorporation into an MIT system with planar-array geometry is described. The transmitter is a 6-turn coil of wire 5 cm in diameter. The receiver is a surface mount inductor, of inductance 10 µH, mounted such that, in principle, no net primary field flux threads it. The results of measurements carried out with the single channel system suggest that the signal due to the primary excitation field can be reduced on average by a factor of 298 by the sensor geometry over the operating frequency range 1–10 MHz. The standard deviation and drift of the signal with the system adjusted for maximum primary field cancellation, expressed as a percentage of the signal when the receiver coil was rotated until its axis of sensitivity lay along the primary field, were 0.0009% and 0.009%, respectively. The filter time constant used was 30 ms.