Magnetic Flux Periodicity Research Articles

Anomalous Fraunhofer-like patterns in quantum anomalous Hall Josephson junctions

The intriguing interplay between topology and superconductivity has attracted significant attention, given its potential for realizing topological superconductivity. In the quantum anomalous Hall insulators (QAHIs)-based junction, the supercurrents are carried by the chiral edge states, characterized by a 2Φ0 magnetic flux periodicity (Φ0=h/2e is the flux quantum, h the Planck constant, and e the electron charge). However, experimental observations indicate the presence of bulk carriers in QAHI samples due to magnetic dopants. In this study, we reveal a systematic transition from edge-state to bulk-state dominant supercurrents as the chemical potential varies from the bulk gap to the conduction band. This results in an evolution from a 2Φ0-periodic oscillation pattern to an asymmetric Fraunhofer pattern. Furthermore, a Fraunhoher-like pattern emerges due to the coexistence of chiral edge states and bulk states caused by magnetic domains, even when the chemical potential resides within the gap. These findings not only advance the theoretical understanding but also pave the way for the experimental discovery of the chiral Josephson effect based on QAHI doped with magnetic impurities. Published by the American Physical Society 2024

Enhancing c‐fosmRNA Expression in Primary Cortical Cell Cultures with a Dynamic Magnetic Fields Device

Magnetic fields have the potential to impact biological systems and trigger various biological responses. However, the mechanisms underlying dynamic magnetic fields (DMFs), which are created by rotating magnets based on Arago's disk principle and include eddy currents, Lorentz forces, and magnetic fields, are not well understood. This study aims to investigate the effects of DMFs on gene expression in primary cultured cortical cells. To simulate DMFs, rotating magnets were used to confirm magnetic flux density, current density, and Lorentz force. Primary cortical cell cultures were then exposed to moderate‐intensity DMFs with a frequency of 40 Hz for 1 h per day over 3 days. The expression of neuroplasticity‐related immediate early genes, including proto‐oncogene c‐fos, activity‐regulated cytoskeleton‐associated protein (Arc) and brain‐derived neurotrophic factor (BDNF) were quantified. The simulation of DMFs generated a periodic magnetic flux density of up to 131 mT, a periodic current density of up to 1.69 A/m2, and a periodic Lorentz force of up to 0.88 nN in the dish. Exposure to DMFs increased c‐fos mRNA expression in primary cortical cell cultures, but did not affect Arc and BDNF expression. The findings suggest that exposure of DMFs in the gamma frequency range, which may be regulated by voltage‐, mechanical‐, and magnetic flux‐sensitive ion channels, could enhance c‐fos expression in primary cortical cell cultures. The device using rotating magnets has the potential to facilitate the development of a cost‐effective and user‐friendly cell culture system based on the principle of Arago's disk. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Magnetic flux periodicity in second order topological superconductors

The magnetic flux periodicity of $\frac{hc}{2e}$ is a well known manifestation of Cooper pairing in typical s-wave superconductors. In this paper we theoretically show that the flux periodicity of a two-dimensional second-order topological superconductor, which features zero-energy Majorana modes localized at the corners of the sample, is $\frac{hc}{e}$ instead. We further show that the periodicity changes back to $\frac{hc}{2e}$ at the transition to a topologically trivial superconductor, where the Majorana modes hybridize with the bulk states, demonstrating that the doubling of periodicity is a manifestation of the non-trivial topology of the state.

Modelling proximity effects in transition edge sensors to investigate the influence of lateral metal structures

The bilayers of transition edge sensors (TESs) are often modified with additional normal-metal features such as bars or dots. Previous device measurements suggest that these features improve performance, reducing electrical noise and altering response times. However, there is currently no numerical model to predict and quantify these effects. Here we extend existing techniques based on Usadel’s equations to describe TESs with normal-metal features. We show their influence on the principal TES characteristics, such as the small-signal electrothermal parameters α and β and the superconducting transition temperature . Additionally, we examine the effects of an applied magnetic field on the device performance. Our model predicts a decrease in , α and β as the number of lateral metal structures is increased. We also obtain a relationship between the length L of a TES and its critical temperature, for a bilayer with normal-metal bars. We predict a periodic magnetic flux dependence of and . Our results demonstrate good agreement with published experimental data, which also show the reduction of α, β and with increasing number of bars. The observed Fraunhofer dependence of critical current on magnetic flux is also anticipated by our model. The success of this model in predicting the effects of additional structures suggests that in the future numerical methods can be used to better inform the design of TESs, prior to device processing.

Robust electron pairing in the integer quantum hall effect regime.

Electron pairing is a rare phenomenon appearing only in a few unique physical systems; for example, superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected electron pairing in the integer quantum Hall effect regime. The pairing takes place within an interfering edge channel in an electronic Fabry-Perot interferometer at a wide range of bulk filling factors, between 2 and 5. We report on three main observations: high-visibility Aharonov-Bohm conductance oscillations with magnetic flux periodicity equal to half the magnetic flux quantum; an interfering quasiparticle charge equal to twice the elementary electron charge as revealed by quantum shot noise measurements, and full dephasing of the pairs' interference by induced dephasing of the adjacent inner edge channel-a manifestation of inter-channel entanglement. Although this pairing phenomenon clearly results from inter-channel interaction, the exact mechanism that leads to electron-electron attraction within a single edge channel is not clear. We believe that substantial efforts are needed in order to clarify these intriguing and unexpected findings.

Determination of time-reversal symmetry breaking lengths in an InGaAs interferometer array

Quantum interference oscillations due to the Aharonov–Bohm phase were measured in a ring interferometer array fabricated on a two-dimensional electron system in an InGaAs/InAlAs heterostructure. Coexisting oscillations with magnetic flux periodicity h/e and h/2e were observed and their amplitudes compared as function of applied magnetic field. The h/2e oscillations originate in time-reversed trajectories with the ring interferometers operating in Sagnac-type mode, while the h/e oscillations result from Mach–Zehnder operation. The h/2e oscillations require time-reversal symmetry and hence can be used to quantify time-reversal symmetry breaking, more particularly the fundamental mesoscopic dephasing length associated with time-reversal symmetry breaking under applied magnetic field, an effective magnetic length. The oscillation amplitudes were investigated over magnetic fields spanning 2.2 T, using Fourier transforms over short segments of 40 mT. As the magnetic field increased, the h/2e oscillation amplitude decreased due to time-reversal symmetry breaking by the local magnetic flux in the interferometer arms. A dephasing model for quantum-coherent arrays was used to experimentally quantify effective magnetic lengths. The data was then compared with analytical expressions for diffusive, ballistic and confined systems.

Explorations of displacement and velocity nonlinearities and their effects to power of a magnetically-excited piezoelectric pendulum

This paper explores the relation of the nonlinearities of displacement and velocity dynamics with the power of a piezoelectric pendulum under a periodic magnetic excitation. Initially, the theoretical formulation including the mechanical, magnetic and electrical terms is realized. Then a simulation study has been done by using the theoretical formulation based on the experimental parameters. Then, a detailed experimental survey has been carried out for some representative system parameters. Results of simulation based on the proposed model are presented and compared with the experimental results. It is observed that the periodic magnetic flux can cause different responses from regular dynamics to chaotic one. Phase space constructions, Poincare sections and FFTs are determined on parameter sets including the excitation frequency f and amplitude Uc of electromagnet. It is proven that the periodic magnetic flux exerts high frequency velocity fluctuations nearby the minimal and maximal values. While the displacement of the tip exhibits a harmonic fluctuation, FFTs prove the high frequency responses in addition to the main frequency. When f differs from the natural frequency of the system f0, the responses become chaotic. It is proven that lower and higher frequency fluctuations in displacement and velocity, which are different from f0 decrease the electrical power harvested by the piezoelectric pendulum. However, in the case of rms values of displacement/velocity, the harvested power is perfectly proportional to the rms values. Therefore, useful relations between power and rms values of displacement/velocity have been determined for the estimation of power output in such systems for the first time. The piezoelectric pendulum harvests much energy when f is closed to f0 and the distance to the magnetic device should be closer in order to decrease the nonlinearities in displacement and velocity.

Quantum Hall effect of Haldane model under magnetic field

Haldane model can realize the anomalous quantum Hall effect (QHE) without Landau levels (LLs) and serves as a prototype of the quantum spin Hall effect. In this paper, we study the QHE of Haldane model under magnetic field with magnitude such that the magnetic flux in a plaquette is commensurate with the lattice structure. First, we show the origin of unconventional QHE in graphene and point out a general rule for the Hall step of Dirac fermions, which strongly depends on the valley degeneracy of each LL. Second, we study the conductance around the neutral point which lies in the gap given by continuous bands, revealing the competition between periodic magnetic flux and uniform magnetic field. Moreover, the redistribution behavior of Chern number is investigated. We find that besides the staggered magnetic flux, the next-nearest-neighbor hopping can also induce the redistribution. We also study the QHE of the extended Haldane model on a square lattice.

Robustness of topological order in semiconductor–superconductor nanowires in the Coulomb blockade regime

Semiconductor–superconductor hybrid systems are promising candidates for the realization of Majorana fermions and topological order, i.e. topologically protected degeneracies, in solid state devices. We show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the excitation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic h/e magnetic flux periodicity in the non-trivial phase. The transition between the trivial and non-trivial phase is reflected in the closing and reopening of an excitation gap. We show that the signatures of topological order are robust against details of the geometry, electrostatic disorder and the existence of additional subbands and only rely on the topology of the nanowire and the existence of a superconducting gap. Finally, we show that the coherence length in the non-trivial phase is much longer than in the trivial phase. This opens the possibility to coat the nanowire with superconducting nanograins and thereby significantly reduce the current due to cotunnelling of Cooper pairs and to enhance the Coulomb charging energy without destroying the superconducting gap.

Photonic realization of the (2+1)-dimensional parity anomaly

We present a photonic realization of the parity anomaly originally found in the (2+1)-dimensional Dirac fermion. We first derive an effective Dirac Hamiltonian around the Brillouin zone corner of triangular-, honeycomb-, and kagome-lattice photonic crystals using group theory. A topological phase transition by broken space-inversion and time-reversal symmetries is derived analytically within the effective theory on the honeycomb lattice. The phase transition is closely related to the Haldane model of the two-dimensional electron system under periodic magnetic flux, which realizes the parity anomaly in a condensed-matter system. We also derive an effective theory around the Brillouin zone center, where quadratic degeneracy in momentum space take places. The effective theory there predicts a similar phenomenon as the parity anomaly. As a result, a topologically nontrivial phase and a chiral edge state are predicted even for staggered configuration of applied magnetic flux. A numerical simulation is also presented to confirm the prediction.

Valley symmetry breaking and gap tuning in graphene by spin doping

We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic singularity appears in the Hall conductivity when the frequency of the external field agrees with the width of the gap.

QUASI-BIENNIAL OSCILLATIONS IN THE SOLAR TACHOCLINE CAUSED BY MAGNETIC ROSSBY WAVE INSTABILITIES

Quasi-biennial oscillations (QBO) are frequently observed in the solar activity indices. However, no clear physical mechanism for the observed variations has been suggested so far. Here we study the stability of magnetic Rossby waves in the solar tachocline using the shallow water magnetohydrodynamic approximation. Our analysis shows that the combination of typical differential rotation and a toroidal magnetic field with a strength > 10^5 G triggers the instability of the m=1 magnetic Rossby wave harmonic with a period of 2 years. This harmonic is antisymmetric with respect to the equator and its period (and growth rate) depends on the differential rotation parameters and the magnetic field strength. The oscillations may cause a periodic magnetic flux emergence at the solar surface and consequently may lead to the observed QBO in the solar activity features. The period of QBO may change throughout the cycle, and from cycle to cycle, due to variations of the mean magnetic field and differential rotation in the tachocline.

Flux periodicities in loops and junctions with d-wave superconductors

The magnetic flux periodicity in superconducting loops is reviewed. Whereas quantization of the magnetic flux with hc/2e prevails in sufficiently thick loops with current free interior, the supercurrent in narrow loops is either hc/2e- or hc/e-periodic with the external magnetic flux. The periodicity depends on the properties of the condensate state, in particular on the Doppler shift of the energy spectrum. For an s-wave superconductor in a loop with diameter larger than the coherence length ξ0, the Doppler shift is small with respect to the energy gap, and the hc/2e-periodic behavior of its flux dependent thermodynamic properties is maintained. However, for smaller s-wave loops and, more prominently, narrow d-wave loops of any diameter R, the Doppler shift has a strong effect on the supercurrent carrying state; as a consequence, the fundamental flux periodicity is in fact hc/e. It is shown analytically and numerically that the hc/e-periodic component in the supercurrent decays only algebraically as 1/R for large d-wave loops. For nodal superconductors the discrete nature of the eigenergies close to the Fermi energy has to be respected in the evaluation of the Doppler shift. Furthermore, we investigate, whether the Doppler shift modifies the supercurrent through Josephson junctions with d-wave superconductors. For transparent junctions, the Josephson current behaves similar to the persistent supercurrent in a loop. These distinct physical phenomena can be compared, if the magnetic flux Φ = φ ⋅ hc/e is identified with the phase variation of the order parameter δϕ through 2πφ = δϕ/2. Correspondingly, the Josephson current can display a 4π-periodicity in δϕ, if the Doppler shift is sufficiently strong which is true for transparent junctions of d-wave superconductors. Moreover, a 4π-periodicity is also valid for the current-flux relation of field-threaded junctions. In the tunneling regime the microscopic theory reproduces the results of the Ginzburg-Landau description for sufficiently wide Josephson junctions.

Magnetic flux periodicity in mesoscopicd-wave symmetric and asymmetric superconducting loops

The magnetic flux dependence of energy and supercurrent in mesoscopic $d$-wave symmetric and asymmetric superconducting loops is investigated by numerically solving the Bogoliubov-de Gennes equations self-consistently. For square loops, we find an $hc/e$-flux periodicity in energy and supercurrent and demonstrate that the flux periodicity is sensitive to the hole size and the superconducting pairing strength as well as temperature. The $hc/2e$-periodic behavior can be restored almost entirely when we displace the central hole sufficiently out of the center of the sample. In rectangular loops, the discrete current-carrying low-energy spectrum can exist for an odd winding number of the order parameter.

Magnetic flux periodicity of h/e in superconducting loops

Superconducting loops exhibit macroscopic quantum phenomena that have far-reaching implications; magnetic flux periodicity and flux quantization are the key to our understanding of fundamental properties of superconductors and are the basis for many applications. In superconducting rings, the electrical current responds to a magnetic flux by having a periodicity of h/2e, where the ratio of Planck’s constant and the elementary charge defines the magnetic flux quantum h/e. The well-known h/2e periodicity is a hallmark for electronic pairing in superconductors and is considered evidence for the existence of Cooper pairs. Here, we show that in contrast to this long-held belief, rings of many superconductors bear an h/e periodicity. These superconductors include the high-temperature superconductors, Sr2RuO4, the heavy-fermion superconductors, as well as all other unconventional superconductors with nodes (zeros) in the energy gap, and conventional s-wave superconductors with small gaps. As we show, the 50-year-old Bardeen–Cooper–Schrieffer theory of superconductivity implies that for loops of such superconductors the ground-state energies and consequently also the supercurrents are generically h/e periodic.

Supercurrent reversal in quantum dots

When two superconductors are electrically connected by a weak link--such as a tunnel barrier--a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of voltage steps in Josephson junctions under microwave irradiation, and in the magnetic flux periodicity of h/2e (where h is Planck's constant) in superconducting quantum interference devices. Here we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Owing to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, that is, in a normal or a pi-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions.

Fractional flux periodicity in doped carbon nanotubes

An anomalous magnetic flux periodicity of the ground state is predicted in two-dimensional cylindrical surface composed of square and honeycomb lattice. The ground state and persistent currents exhibit an approximate fractional period of the flux quantum for a specific Fermi energy. The period depends on the aspect ratio of the cylinder and on the lattice structure around the axis. We discuss possibility of this nontrivial periodicity in a heavily doped armchair carbon nanotube.

Anomalous magnetic flux periodicity of supercurrent in mesoscopic SNS Josephson junctions

We measure the magnetic flux dependence of the supercurrent in diffusive Nb/n-InAs/Nb mesoscopic SNS Josephson junctions with junction length ranging from 220 to 720 nm. In the longer junctions, the modulation periodicity of the maximum supercurrent by magnetic flux is a quantum flux, Φ 0= h/2 e as usual. However, we find that the magnetic flux periodicity becomes twice or 2 Φ 0= h/ e when the junction lengths are shorter than 400 nm.