Multiquanta Vortices Research Articles

Quasi-one-dimensional vortex matter in superconducting nanowires

It is well known that superconducting films made of a type-I material can demonstrate a type-II magnetic response, developing stable vortex configurations in a perpendicular magnetic field. Here we show that the superconducting state of a type-I nanowire undergoes more complex transformations, depending on the nanowire thickness. Sufficiently thin nanowires deviate from type I and develop multiquantum vortices and vortex clusters similar to intertype (IT) vortex states in bulk superconductors between conventional superconductivity types I and II. When the nanowire thickness decreases further, the quasi-one-dimensional vortex matter evolves towards type II so that the IT vortex configurations gradually disappear in favor of the standard Abrikosov lattice (chain) of single-quantum vortices. However, type II is not reached. Instead, an ultrathin nanowire re-enters abruptly the type-I regime while vortices tend to be suppressed by the boundaries, eventually becoming one-dimensional phase-slip centers. Our results demonstrate that arrays of nanowires can be used to construct composite superconducting materials with a widely tunable magnetic response.

Microscopic Theory of Pinning of Multiquantum Vortex in Cylindrical Cavity

We have proposed and developed a microscopic model of depinning (escape) of a multiquantum vortex in a superconductor with a cylindrical nonconducting cavity with the transverse size smaller than or on the order of the superconducting coherence length ξ0 at zero temperature. The spectrum of subgap quasiparticle excitations in two- and three-quantum vortices trapped by a cylindrical cavity has been calculated in the quasiclassical approximation. It is shown that the transformation of the spectrum is accompanied by break of anomalous spectral branches due to normal reflection of quasiparticles from the surface of a defect. A microscopic (spectral) criterion for multiquantum vortex pinning has been proposed; according to this criterion, the multiquantum vortex can be trapped in the cavity during the formation of a minigap in the elementary excitation spectrum near the Fermi level. Self-consistent calculations of density of states N(r, e) for two- and three-quantum vortices trapped by a cylindrical cavity of radius on the order of ξ0 have been performed using quasiclassical Eilenberger equations. In the pure limit and for low temperatures T ≪ T c , peculiarities observed in the N(r, e) distribution reflect the presence of M anomalous spectral branches in the M-quantum vortex and confirm the correctness of the spectral criterion of pinning (depinning) of a multiquantum vortex.

Solitons and Vortex Lattices in the Gross–Pitaevskii Equation with Spin–Orbit Coupling under Rotation

The Gross–Pitaevskii equation for two-component rotating Bose–Einstein condensates with the Rashba-type spin–orbit (SO) coupling is studied with numerical simulations and variational analyses. A multiquantum vortex state becomes a ground state in a harmonic potential when mutual interaction is absent. When the attractive interaction is strong, the multiquantum vortex state exhibits modulational instability in the azimuthal direction, and a soliton-like state appears. When the repulsive interaction is strong, a vortex lattice state with a multiquantum vortex at the center is created. We find that the vortex lattice state is approximated at a linear combination of multiquantum vortex states.

Field effects on the vortex states in spin–orbit coupled Bose–Einstein condensates

Multi-quantum vortices can be created in the ground state of rotating Bose–Einstein condensates with spin–orbit couplings. We investigate the effects of external fields, either a longitudinal field or a transverse field, on the vortex states. We reveal that both fields can effectively reduce the number of vortices. In the latter case we further find that the condensate density packets are pushed away in the horizontal direction and the vortices finally disappear to form a plane wave phase.

Ground-state multiquantum vortices in rotating two-species superfluids

We show numerically that a rotating, harmonically trapped mixture of two Bose-Einstein-condensed superfluids can---contrary to its single-species counterpart---contain a multiply quantized vortex in the ground state of the system. This giant vortex can occur without any accompanying single-quantum vortices, may either be coreless or have an empty core, and can be realized in a $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{41}\mathrm{K}$ Bose-Einstein condensate. Our results not only provide a rare example of a stable, solitary multiquantum vortex but also reveal exotic physics stemming from the coexistence of multiple, compositionally distinct condensates in one system.

Evidence of surface superconductivity and multi-quanta vortex states in a weakly-pinned single crystal of Ca3Ir4Sn13

We report here the observation of anomalous paramagnetic signal(s) in the isofield field-cooled cool-down magnetization scans (MFCC(T)) recorded for a single crystal of a low Tc superconductor Ca3Ir4Sn13. Novel features emanating from the MFCC(T) response include an oscillatory magnetization behavior below Tc and a rich multiplicity (non-uniqueness) in magnetization ranging from diamagnetism to paramagnetism at a given H,T value. The metastability in MFCC(T) has been ascribed to non-unique coexistence of multi-quanta vortex states (LΦ0,Φ0=hc/2e, L>1) and single quantum (L=1, Abrikosov) vortices. Additionally, the isothermal M(H) scans recorded across a short window of temperature just below Tc show evidence for only the multi-quanta vortex states in the domain of surface superconductivity, with no fingerprint(s) of pinned Abrikosov lattice.

Counter-rotating vortices in miscible two-component Bose-Einstein condensates

Counter-rotating vortices in miscible two-component Bose-Einstein condensates, in which superflows counter-rotate between the two components around the overlapped vortex cores, are studied theoretically in a pancake-shaped potential. In a linear stability analysis with the Bogoliubov--de Gennes model, we show that counter-rotating vortices are dynamically unstable against splitting into multiple vortices. The instability shows characteristic behaviors as a result of counter-superflow instability, which causes relaxation of relative flows between the two components in binary condensates. The characteristic behaviors are completely different from those of multiquantum vortices in single-component Bose-Einstein condensates; the number of vortices generated by the instability can become larger than the initial winding number of the counter-rotating vortex. We also investigate the nonlinear dynamics of the instability by numerically solving the Gross-Pitaevskii equations. The nonlinear dynamics drastically changes when the winding number of counter-rotating vortices becomes larger, which lead to nucleation of vortex pairs outside of the vortex core. The instability eventually develops into turbulence after the relaxation of the relative rotation between the two components.

Self-consistent electronic structure of multiquantum vortices in superconductors at T ≪ Tc

We investigate the multiquantum vortex states in a type-II superconductor in both ‘clean’ and ‘dirty’ regimes defined by impurity scattering rate. Within a quasiclassical approach we calculate self-consistently the order parameter distributions and electronic local density of states (LDOS) profiles. In the clean case we find the low temperature vortex core anomaly predicted analytically by Volovik (1993 JETP Lett. 58 455) and obtain the patterns of LDOS distributions. In the dirty regime multiquantum vortices feature a peculiar plateau in the zero energy LDOS profile, which can be considered as an experimental hallmark of multiquantum vortex formation in mesoscopic superconductors.

Impurity scattering effect on the zero-energy peak of the local density of states in a multi-quantum vortex core

We theoretically study a non-magnetic impurity effect on the vortex bound states of a multi-quantum vortex. The zero-energy peak of the local density of states is investigated for vortex cores with the winding numbers 2 and 4 within the framework of the quasiclassical theory of superconductivity. We find that the zero-energy peaks, which appear away from the vortex center in the clean limit, move towards the vortex center with increasing the impurity scattering rate, resolving a contradiction between an experimental result and previous theoretical predictions.

Abnormal magnetoresistance behavior in Nb thin films with rectangular arrays of antidots

Magnetoresistance in superconducting Nb films perforated with rectangular arrays of antidots (holes) is investigated at various temperatures and currents. Normally, the magnetoresistance increases with the increasing magnetic field. In this paper, we report a reverse behavior in a certain range of high fields after vortex reconfiguration transition, where the resistances at non-matching fields are smaller than those in the low field regime. This phenomenon is due to a strong caging effect, in which the interstitial vortices are trapped among the pinned multiquanta vortices. This effect is temperature and current dependent.

Vortex interaction enhanced saturation number and caging effect in a superconducting film with a honeycomb array of nanoscale holes

The electrical transport properties of a MoGe thin film with a honeycomb array of nanoscale holes are investigated. The critical current of the system shows nonmatching anomalies as a function of applied magnetic field, enabling us to distinguish between multiquanta vortices trapped in the holes and interstitial vortices located between the holes. The number of vortices trapped in each hole is found to be larger than the saturation number predicted for an isolated hole and shows a nonlinear field dependence, leading to the caging effect as predicted from the Ginzburg-Landau (GL) theory. Our experimental results are supplemented by numerical simulations based on the GL theory.

Formation of Multiple-Flux-Quantum Vortices in Mesoscopic Superconductors from Simulations of Calorimetric, Magnetic, and Transport Properties

Because of strong flux confinement in mesoscopic superconductors, a "giant" vortex may appear in the ground state of the system in an applied magnetic field. This multiquanta vortex can then split into individual vortices (and vice versa) as a function of, e.g., applied current, magnetic field, or temperature. Here we show that such transitions can be identified by calorimetry, as the formation or splitting of a giant vortex results in a clear jump in measured heat capacity versus external drive. We attribute this phenomenon to an abrupt change in the density of states of the quasiparticle excitations in the vortex core(s), and further link it to a sharp change of the magnetic susceptibility at the transition--proving that the formation of a giant vortex can also be detected by magnetometry.

Local Current Injection into Mesoscopic Superconductors for the Manipulation of Quantum States

We perform strategic current injection in a small mesoscopic superconductor and control the (non)equilibrium quantum states in an applied homogeneous magnetic field. In doing so, we realize a current-driven splitting of multiquanta vortices, current-induced transitions between states with different angular momenta, and current-controlled switching between otherwise degenerate quantum states. These fundamental phenomena form the basis for the electronic and logic applications discussed, and are confirmed in both theoretical simulations and multiple-small-tunnel-junction transport measurements.

Fractional matching effect in single-crystal films of [formula omitted] with antidot lattice

To study the vortex behavior in 2D periodic pinning potentials, we measured field dependence of the vortex-flow resistance and the critical current in single-crystal Bi 2 Sr 2 CaCu 2 O 8 + y (Bi2212) films with an equilateral triangular array of antidots. Fractional matching effect was observed in 1/4, 1/3, 1/2, 2/3, 3/4, and 6/7 of the first matching field H 1 , and even above H 1 . While the most of fractional numbers except 1/2 can be explained from commensurability between triangular lattices of antidots and vortices, the matching effect in 1/2 H 1 suggests the existence of the interstitial vortices in comparison with the results of a reported numerical simulation. The fractional matching effect above H 1 can be explained as a matching effect by multi-quanta vortices.

Topologically trapped vortex molecules in Bose-Einstein condensates

In a numerical experiment based on Gross-Pitaevskii formalism, we demonstrate unique topological quantum coherence in optically trapped Bose-Einstein condensates (BECs). Exploring the fact that vortices in a rotating BEC can be pinned by a geometric arrangement of laser beams, we show the parameter range in which vortex-antivortex molecules or multiquantum vortices are formed as a consequence of the optically imposed symmetry. Being low-energy states, we discuss the conditions for spontaneous nucleation of these unique molecules and their direct experimental observation, and provoke the potential use of the phase print of an antivortex or a multiquantum vortex when realized in unconventional circumstances.

Electronic structure and heat transport of multivortex configurations in mesoscopic superconductors

On the basis of the Bogoliubov--de Gennes theory we study the transformation of the quasiparticle spectrum in the mixed state of a mesoscopic superconductor, governed by an external magnetic field. We analyze the low-energy part of the excitation spectrum and investigate the field dependent behavior of anomalous spectral branches crossing the Fermi level. Generalizing the Caroli--de Gennes--Matricon approach, we present an analytical solution describing the anomalous branches in a vortex with an arbitrary winding number. We also study the spectrum transformation caused by the splitting of a multiquantum vortex into a set of well separated vortices focusing mainly on a generic example of a two-vortex system. For vortices positioned rather close to the sample surface we investigate the effect of the quasiparticle reflection at the boundary on the spectrum and the density of states at the Fermi level. Considering an arbitrary surface curvature, we study the disappearance of an anomalous spectral branch for a vortex leaving the sample. The changes in the vortex configuration and resulting transformation of the anomalous branches are shown to affect strongly the density of states and the heat conductance along the magnetic-field direction.

Formation of vortex clusters and giant vortices in mesoscopic superconducting disks with strong disorder

Merged, or giant, multi-quanta vortices (GVs) appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters/GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.

Pinning-Induced Formation of Vortex Clusters and Giant Vortices in Mesoscopic Superconducting Disks

Merged, or giant, multiquanta vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualize vortices in small Nb disks with varying degrees of disorder, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.

Vortex states in mesoscopic superconductors

The results of theoretical investigations of the electronic structure and transport properties of vortex states in mesoscopic superconductors with sizes of several coherence lengths are reviewed. The features of the electronic spectra of multiquantum vortices and vortex molecules, as well as mechanisms of thermal transport along vortex lines, are considered by taking into account boundary effects.

Dynamically stable multiply quantized vortices in dilute Bose-Einstein condensates

Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.