Mesoscopic Rings Research Articles

Stabilizing persistent currents in an atomtronic Josephson junction necklace

Arrays of Josephson junctions are at the forefront of research on quantum circuitry for quantum computing, simulation, and metrology. They provide a testing bed for exploring a variety of fundamental physical effects where macroscopic phase coherence, nonlinearities, and dissipative mechanisms compete. Here we realize finite-circulation states in an atomtronic Josephson junction necklace, consisting of a tunable array of tunneling links in a ring-shaped superfluid. We study the stability diagram of the atomic flow by tuning both the circulation and the number of junctions. We predict theoretically and demonstrate experimentally that the atomic circuit withstands higher circulations (corresponding to higher critical currents) by increasing the number of Josephson links. The increased stability contrasts with the trend of the superfluid fraction – quantified by Leggett’s criterion – which instead decreases with the number of junctions and the corresponding density depletion. Our results demonstrate atomic superfluids in mesoscopic structured ring potentials as excellent candidates for atomtronics applications, with prospects towards the observation of non-trivial macroscopic superpositions of current states.

Mesoscopic ring element growth and deformation induced biofilm streamer evolution in microfluidic channels.

In a fluid environment, biofilms usually form and grow into streamers attached to solid surfaces. Existing research on single streamers studied their formation and failure modes. In the experiment on biofilm growth in a microfluidic channel, we found that rings composed of bacteria and an extracellular matrix are important elements on a mesoscopic scale. In the fluid environment, the failure of these ring elements causes damage to streamers. We simulated the growth and deformation of the ring structure in the micro-channel using multi-agent simulation and fluid-structure coupling of a porous elastic body. Based on this, we simulated the biofilm evolution involving multi-ring deformation, which provides a new length scale to study the biofilm streamer dynamics in fluid environments.

Charge- 4e and Charge- 6e Flux Quantization and Higher Charge Superconductivity in Kagome Superconductor Ring Devices

The flux quantization is a key indication of electron pairing in superconductors. For example, the well-known h/2e flux quantization is considered strong evidence for the existence of charge-2e, two-electron Cooper pairs. Here we report evidence for multicharge flux quantization in mesoscopic ring devices fabricated using the transition-metal kagome superconductor CsV3Sb5. We perform systematic magnetotransport measurements and observe unprecedented quantization of magnetic flux in units of h/4e and h/6e in magnetoresistance oscillations. Specifically, at low temperatures, magnetoresistance oscillations with period h/2e are detected, as expected from the flux quantization for charge-2e superconductivity. We find that the h/2e oscillations are suppressed and replaced by resistance oscillations with h/4e periodicity when the temperature is increased. Increasing the temperature further suppresses the h/4e oscillations, and robust resistance oscillations with h/6e periodicity emerge as evidence for charge-6e flux quantization. Our observations provide the first experimental evidence for the existence of multicharge flux quanta and emergent quantum matter exhibiting higher-charge superconductivity in the strongly fluctuating region above the charge-2e Cooper pair condensate, revealing new insights into the intertwined and vestigial electronic order in kagome superconductors. Published by the American Physical Society 2024

Fractional magnetoresistance oscillations in spin-triplet superconducting rings

Half-quantum vortices in spin-triplet superconductors are predicted to host Majorana zero modes and may provide a viable platform for topological quantum computation. Recent works also suggested that, in thin mesoscopic rings, the superconducting pairing symmetry can be probed via Little-Parks-like magnetoresistance oscillations of periodicity Φ0 = h/2e that persist below the critical temperature. Here we use the London limit of Ginzburg-Landau theory to study these magnetoresistance oscillations resulting from thermal vortex tunneling in spin-triplet superconducting rings. For a range of temperatures in the presence of disorder, we find magnetoresistance oscillations with an emergent fractional periodicity Φ0/n, where the integer n ≥ 3 is entirely determined by the ratio of the spin and charge superfluid densities. These fractional oscillations can unambiguously confirm the spin-triplet nature of superconductivity and directly reveal the tunneling of half-quantum vortices in real-world candidate materials.

Theory of the Little-Parks effect in spin-triplet superconductors

The celebrated Little-Parks effect in mesoscopic superconducting rings has recently gained great attention due to its potential to probe half-quantum vortices in spin-triplet superconductors. However, despite the large number of works reporting anomalous Little-Parks measurements attributed to unconventional superconductivity, the general signatures of spin-triplet pairing in the Little-Parks effect have been less systematically investigated. Here we use Ginzburg-Landau theory to study the Little-Parks effect in a spin-triplet superconducting ring that supports half-quantum vortices; we calculate the field-induced Little-Parks oscillations of both the critical temperature itself and the residual resistance resulting from thermal vortex tunneling below the critical temperature. We observe two separate critical temperatures with a single-spin superconducting state in between and find that due to the existence of half-quantum vortices, each minimum in the upper critical temperature splits into two minima for the lower critical temperature. From a rigorous calculation of the residual resistance, we confirm that these two minima in the lower critical temperature translate into two maxima in the residual resistance below and establish the general conditions under which the two maxima can be practically resolved. In particular, we identify a fundamental trade-off between sharpening each maximum and keeping the overall magnitude of the resistance large. Our results will guide experimental efforts in designing mesoscopic ring geometries for probing half-quantum vortices in spin-triplet candidate materials on the device scale.

Quantum Interference by Vortex Supercurrents

The origin of the parabolic background of magnetoresistance oscillations measured in finite‐width superconducting mesoscopic rings with input and output stubs and in patterned films is analyzed. The transmission model explaining the sinusoidal oscillation of magnetoresistance is extended to address the parabolic background as a function of the magnetic field. Apart from the interference mechanism activated by the ring, pinned superconducting vortices as topological defects introduce a further interference‐based distribution of supercurrents that affects, in turn, the voltmeter‐sensed quasiparticles. The onset of vortices changes the topology of the superconducting state in a mesoscopic ring in such a way that the full magnetoresistance dynamics can be interpreted due to the interference of the constituents of the order parameter induced by both the ring with its doubly connected topology and the vortex lattice in it.

Learning torus PCA-based classification for multiscale RNA correction with application to SARS-CoV-2

Abstract Three-dimensional RNA structures frequently contain atomic clashes. Usually, corrections approximate the biophysical chemistry, which is computationally intensive and often does not correct all clashes. We propose fast, data-driven reconstructions from clash-free benchmark data with two-scale shape analysis: microscopic (suites) dihedral backbone angles, mesoscopic sugar ring centre landmarks. Our analysis relates concentrated mesoscopic scale neighbourhoods to microscopic scale clusters, correcting within-suite-backbone-to-backbone clashes exploiting angular shape and size-and-shape Fréchet means. Validation shows that learned classes highly correspond with literature clusters and reconstructions are well within physical resolution. We illustrate the power of our method using cutting-edge SARS-CoV-2 RNA.

Silicon-Aluminum Phase-Transformation-Induced Superconducting Rings.

The development of devices that exhibit both superconducting and semiconducting properties is an important endeavor for emerging quantum technologies. We investigate superconducting nanowires fabricated on a silicon-on-insulator (SOI) platform. Aluminum from deposited contact electrodes is found to interdiffuse with Si along the entire length of the nanowire, over micrometer length scales and at temperatures well below the Al-Si eutectic. The phase-transformed material is conformal with the predefined device patterns. The superconducting properties of a transformed mesoscopic ring formed on a SOI platform are investigated. Low-temperature magnetoresistance oscillations, quantized in units of the fluxoid, h/2e, are observed.

Effects of Curvature on the Electronic States of a Two-Dimensional Mesoscopic Ring

We study the effects of curvature on an electron in a two-dimensional localized annular region in the presence of external magnetic fields. The approach follows the thin-layer quantization procedure. We verify that the most significant contribution of the mean curvature occurs in the state with \(m=0\), which tends to decrease the energies in null magnetic fields. The effects of curvature are also manifested in the cyclotron frequency as well as in the effective angular momentum through the \(\alpha \) parameter, which can be controlled in such a way that the magnitude of these effects becomes explicit. This is verified in the energies and wave functions of the system. A decrease in the number of occupied states in the Fermi energy is observed, which leads to an alteration in the radial range of the conducting region of the sample. This is confirmed by studying the variations in the radii of the states.

Charge and spin currents in mesoscopic rings: Role of next nearest-neighbors Rashba spin–orbit coupling using the Green’s functions equation of motion technique

The electronic states of a mesoscopic ring are assessed using the Green functions approach and the equation of motion method. We put forward the Green’s function formalism to evaluate precisely persistent charge and spin currents in a ring exhibiting nearest-neighbors (NN) and next-nearest (NNN) neighbors Rashba spin–orbit interactions. Our present scheme circumvents direct diagonalization of the Hamiltonian, allowing to determine numerically persistent currents with both spin–orbit interactions simultaneously. Our results for the spin currents show that the NN Rashba interaction breaks the spin degeneracy producing a square-like shape; while the NNN Rashba interaction creates an energy-dependent splitting of the levels that generates a pattern of small peaks. The merging of both interactions rises a periodic squared-peaked pattern at half integer values of the quantum flux, which suggests the possibility of controlling the spin current magnitude and polarization by modulating the NNN Rashba parameter.

Higher harmonic resistance oscillations in micro-bridge superconducting Nb ring

We studied resistance oscillations in two types of superconducting mesoscopic Nb rings. In a simple superconducting ring device, a resistance oscillation with a period of the quantized magnetic flux was clearly observed. On the other hand, in a micro-bridge ring device where two-narrow parts are embedded in parallel and work as superconductor-normal metal–superconductor junctions, higher harmonic resistance oscillations were obtained when the measurement current was well-tuned. We argue that such higher harmonic resistance oscillations can be detected even in the micro-bridge Nb superconducting ring device where the device size is much larger than the coherence length of Nb.

Quantum interference in finite-size mesoscopic rings

The Ginzburg-Landau theory is used to model the order parameter of a finite-size mesoscopic ring to investigate the effects of the onset of screening currents on the transport of incoming ones. The magnetic flux breaks the symmetry of currents between input and output stubs by means of an induced spatial ordering upon diamagnetic and paramagnetic supercurrents circulating in the ring. The distribution of those screening currents drives the interference of incoming/outgoing supercurrents resulting into a sinusoidal variation of resistance as a function of the magnetic flux even if the density of quasiparticles is not modified by the external magnetic field.

Transmission of a single electron through a Berry ring

A theoretical model of transmission and reflection of an electron with spin is proposed for a mesoscopic ring with rotating localized magnetic moment. This model may be realized in a pair of domain walls connecting two ferromagnetic domains with opposite magnetization. If the localized magnetic moment and the traveling spin is ferromagnetically coupled and if the localized moment rotates with opposite chirality in the double-path, our system is formulated in the model of an emergent spin-orbit interaction in a ring. The scattering problem for the transmission spectrum of the traveling spin is solved both in a single path and a double path model. In the double path, the quantum-path interference changes dramatically the transmission spectrum due to the effect of the Berry's phase. Specifically, the spin-flip transmission and reflection are both strictly forbidden.

Genesis and fading away of persistent currents in a Corbino disk geometry

The detailed analytical and numerical analysis of the electron spectrum, persistent currents, and their densities for an annulus placed in a constant magnetic field (Corbino disk geometry) is presented. We calculate the current density profiles and study their dependence on the inner and outer radii of the annular. We study evolution of the persistent currents and track their emergence and decay for different limiting cases of such a geometry, starting from a nanodot and ending by a macroscopic circle. Our analytical results for the currents are confirmed by the agreement between the integration of the corresponding current densities and the application of the Byers-Yang formula, when it is applicable. Among other results we find the general expression for the persistent current in a narrow annulus, which in the one channel approximation reproduces the well-known result for quasi-one dimensional mesoscopic metallic ring. Moreover it allows to analyze the multi-channel case of a relatively wide annulus. Our study can be used for more accurate treatment and interpretation of the experimental data with measurements of the persistent currents in different doubly-connected systems.

From Macrocycles to Quantum Rings: Does Aromaticity Have a Size Limit?

ConspectusThe ring currents of aromatic and antiaromatic molecules are remarkable emergent phenomena. A ring current is a quantum-mechanical feature of the whole system, and its existence cannot be inferred from the properties of the individual components of the ring. Hückel's rule states that when an aromatic molecule with a circuit of [4n + 2] π electrons is placed in a magnetic field, the field induces a ring current that creates a magnetic field opposing the external field inside the ring. In contrast, antiaromatic rings with 4n π electrons exhibit ring currents in the opposite direction. This rule bears the name of Erich Hückel, and it grew from his molecular orbital theory, but modern formulations of Hückel's rule incorporate contributions from others, particularly William Doering and Ronald Breslow. It is often assumed that aromaticity is restricted to small molecular rings with up to about 22 π electrons. This Account outlines the discovery of global ring currents in large macrocycles with circuits of up to 162 π electrons. The largest aromatic rings yet investigated are cyclic porphyrin oligomers, which exhibit global ring currents after oxidation, reduction or optical excitation but not in the neutral ground state. The global aromaticity in these porphyrin nanorings leads to experimentally measurable aromatic stabilization energies in addition to magnetic effects that can be studied by NMR spectroscopy. Wheel-like templates can be bound inside these nanorings, providing excellent control over the molecular geometry and allowing the magnetic shielding to be probed inside the nanoring. The ring currents in these systems are well-reproduced by density functional theory (DFT), although the choice of DFT functional often turns out to be critical. Here we review recent contributions to this field and present a simple method for determining the ring current susceptibility (in nA/T) in any aromatic or antiaromatic ring from experimental NMR data by classical Biot-Savart calculations. We use this method to quantify the ring currents in a variety of aromatic rings. This survey confirms that Hückel's rule reliably predicts the direction of the ring current, and it reveals that the ring current susceptibility is surprisingly insensitive to the size of the ring. The investigation of aromaticity in even larger molecular rings is interesting because ring currents are also observed when mesoscopic metal rings are placed in a magnetic field at low temperatures. The striking similarity between the ring currents in molecules and mesoscopic metal rings arises because the effects have a common origin: a field-dependent phase shift in the electronic wave function. The main difference is that the magnetic flux through mesoscopic rings is much greater because of their larger areas, so their persistent currents are nonlinear and oscillatory with the applied field, whereas the flux through aromatic molecules is so small that their response is approximately linear in the applied field. We discuss how nonlinearity is expected to emerge in large molecular nanorings at high magnetic fields. The insights from this work are fundamentally important for understanding aromaticity and for bridging the gap between chemistry and mesoscopic physics, potentially leading to new functions in molecular electronics.

Study of electronic properties, magnetization and persistent currents in a mesoscopic ring by controlled curvature

We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We write the Schr\"{o}dinger equation and use the thin-layer quantization procedure to calculate the wavefunctions and the energy spectrum. In such a procedure, it arises a geometry induced potential, which depends on both the mean and the Gaussian curvatures. Nevertheless, since we consider a ring with a mesoscopic size, the effects of the Gaussian curvature on the energy spectrum are negligible. The magnetization and the persistent current are analyzed. In the former, we observed the Aharonov-Bohm (AB) and de Haas-van Alphen (dHvA) types oscillations. In the latter, it is observed only the AB type oscillations. In both cases, the curvature increases the amplitude of the oscillations.

Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices.

We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well () phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L.

Spin Half‐Adder

A new proposal is given to design a spin half‐adder in a nanojunction. It is well known that at finite voltage a net circulating current (known as “circular current”) appears within a mesoscopic ring under the asymmetric ring‐to‐electrode interface configuration. This circular current induces a finite magnetic field at the center of the ring. Herein, this phenomenon is utilized to construct a spin half‐adder. The circular current–induced magnetic field is used to regulate the alignments of local free spins; by their orientations the output states of the “sum” and “carry” are specified. All the outputs are spin based; therefore, the results get atomically stored in the system. The experimental possibilities of the proposed model are also illustrated.

Circular charge and spin currents in a spatially varying Rashba ring in presence of Aharonov-Bohm flux

We investigate magnetic response in a single-channel mesoscopic ring, subjected to Aharonov- Bohm (AB) flux, in presence of spatially varying Rashba spin-orbit (SO) coupling. Simulating the ring system in a tight-binding framework we calculate both charge and spin currents and discuss the interplay between AB flux and SO coupling on these currents. Some anomalous patterns are exhibited following the energy spectrum. Our analysis can be utilized to study the magnetic response in similar kind of spatially varying SO coupled systems and helps us to probe fascinating operations.

Persistent charge and spin currents in the 1D Holstein-Hubbard ring at half filling and at away from half filling by Bethe-ansatz approach

The persistent charge and spin currents are studied by considering the Holstein-Hubbard model for one dimensional mesoscopic ring. Conventional Lang-Firsov transformation is used to eliminate the phonon coordinates and then the zero phonon state is applied to obtain the effective electronic Hamiltonian which is then treated exactly by the Bethe-Ansatz technique. The coupled transcendental equations that arise in this method are solved numerically and the persistent charge and spin currents are studied with respect to the on-site electron-electron Coulomb correlation (U), on-site electron-phonon interaction strength (g0) and inter-site electron-phonon interaction strength (g1) at half-filling and away from half-filling.