Flux Line Lattice Research Articles

Hall anomaly by vacancies in a pinned lattice of vortices: A quantitative analysis based on the thin-film data from Bi2.1Sr1.9CaCu2.0O8+δ

Hall anomaly, as appears in the mixed-state Hall resistivity of type-II superconductors, has had numerous theories but yet a consensus on its origin. In this work, we conducted a quantitative analysis of the magnetotransport measurements on BSCCO thin films by Zhao et al. [Phys. Rev. Lett. 122, 247001 (2019)] and validate a previously proposed vacancy mechanism [cf. J. Phys. Condens. Matter. 10, L677 (1998)] with many-body vortex correlations for the phenomenon. The model attributes the Hall anomaly to the motion of vacancies in pinned fragments of vortex lattice. Its validity is first examined by an exploration on the vortex states near the Kosterlitz-Thouless transition on the vortex crystal. Comparisons are then carried out between the measured activation energies with the calculated creation energy of the vortex-anti-vortex pair and the vacancy energy on the flux-line lattice, with no adjustable parameter. Our analysis elucidates the theoretical basis and prerequisites of the vacancy model. In particular, the vacancy activation energies are an order of magnitude smaller than that of a sole vortex line. The proposed mechanism may provide a macro-theoretical framework for other studies.

Discovery of superconducting quaternary Y–Ni–B–C system, T c ∼ 12 K, and a brief review of superconducting and magnetic properties of RNi2B2C

We give a brief account of the events that led to the discovery of the superconducting system Y–Ni–B–C. In short, several unique properties of the single phase quaternary materials RNi2B2C are briefly discussed, such as certain aspects of coexistence of superconductivity and magnetism in RNi2B2C, flux line lattices in RNi2B2C and the Kondo effect in YbNi2B2C.

Charging in the vortex lattice of type-II superconductors

We study the magnetic-field dependence of the vortex-core charge in the Abrikosov lattice of an $s$-wave superconductor based on the augmented quasiclassical equations, where we incorporate the pair-potential gradient (PPG) terms characteristic of charging in superconductors besides the well-known Lorentz force. Our numerical results at $T=0.2{T}_{\mathrm{c}}$ and $0.5{T}_{\mathrm{c}}$ reveal that periodic charge redistribution is superimposed on the magnetic flux-line lattice with different spatial patterns at different fields. The PPG terms are dominant at weak fields over the Lorentz force for accumulating charge in the vortex cores, whereas the Lorentz force prevails at higher fields to give rise to a peak structure in the core charge around $H\ensuremath{\sim}\frac{1}{2}{H}_{\mathrm{c}2}$. We estimate the peak value of the core charge at $T=0.2{T}_{\mathrm{c}}$ using parameters appropriate for cuprates to obtain a large value of $Q\ensuremath{\sim}{10}^{\ensuremath{-}2}|e|$ in the core region of radius $0.2{\ensuremath{\xi}}_{0}$ in the $ab$ plane and length $1\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ along the $c$ axis.

The vortex lattice in superconductors

Abstract Some properties of the flux-line lattice in conventional and high-T c superconductors are reviewed, with particular stress on phenomenological theories, nonlocal elasticity, irreversible magnetization curves, and influence of the specimen shape on the electromagnetic response.

Thermal fluctuations and vortex lattice structures in chiralp-wave superconductors: Robustness of double-quanta vortices

We use large-scale Monte-Carlo simulations to study thermal fluctuations in chiral $p$-wave superconductors in an applied magnetic field in three dimensions. We consider the thermal stability of previously predicted unusual double-quanta flux-line lattice ground states in such superconductors. In previous works it was shown that, neglecting thermal fluctuations, a chiral $p$-wave superconductor forms an hexagonal lattice of doubly-quantized vortices, except extremely close to the vicinity of $H_{c2}$ where double-quanta vortices split apart. We find dissociation of double-quanta vortices driven by thermal fluctuations. However, our calculations also show that the previous predictions of hexagonal doubly-quantized vortices, where thermal fluctuations were ignored, are very robust in the considered model.

Coexistence of type-I and type-II superconductivity signatures in ZrB12 probed by muon spin rotation measurements

Superconductors usually display either type-I or type-II superconductivity and the coexistence of these two types in the same material, for example at different temperatures is rare in nature. We the employed muon spin rotation (muSR) technique to unveil the superconducting phase diagram of the dodecaboride ZrB12 and obtained clear evidence of both type-I and type-II characteristics. Most importantly, we found a region showing unusual behavior where the usually mutually exclusive muSR signatures of type-I and type-II superconductivity coexist. We reproduced that behavior in theoretical modeling that required taking into account multiple bands and multiple coherence lengths, which suggests that material has one coherence length larger and another smaller than the magnetic field penetration length (the type-1.5 regime). At stronger fields, a footprint of the type-II mixed state showing square flux-line lattice was also obtained using neutron diffraction.

Magnetization of Bi2Sr2CaCu2O8+\u03b4 Micrometer Thin Ring and Its Depinning Line

We demonstrate a geometrical effect on the depinning line (DL) of the flux line lattice of the Bi2Sr2CaCu2O8+δ high-Tc superconductor (HTSC) micrometer ring. The DL shifts to notably lower temperatures in comparison with bulk crystals and thin flakes of the same sample. The shift is attributed to a decrease in the overall pinning potential due to a double size effect, namely (a) the ring thickness sim 1~mu m being smaller than the pinning correlation length and (b) the increase in the effective London penetration depth of the vortices (Pearl vortices). The large shift of the DL to lower temperatures may influence the suitability of this HTSC for applications in microstrip antennas and THz emitters.

Second magnetization peak effect and the vortex phase diagram of V0.0015NbSe2 single crystal

Effect of the weak point disorder on vortex matter phase diagram is studied by incorporation of V atoms through magnetic and magnetoresistance measurement in layered NbSe2 single crystal. We observe that the point disorder introduces fishtail effect and the second magnetization peak (SMP) in the M-H curve of V0.0015NbSe2 at magnetic field far below upper critical field (Hc2). 3D Collective creep of elastic flux line lattice (FLL) support the vortex motion below the onset of SMP. However, the crossover from collective to plastic deformation of FLL support the occurrence of SMP effect. Presence of the peak effect in pinning force density near irreversible magnetic field (Hirr) indicates the 2D to 3D distortion of FLL due to lattice softening associated with the rapid reduction of elastic modulus. Magneto transport measurement shows the glassy transition near the zero resistance region. In the glassy region, the flux line shows 2D characteristics. Above zero resistive region, thermally activated flux flow region is well described by Arrhenius relation. It is seen that the activation energy is decreased significantly by the incorporation of V atoms in NbSe2. The magnetic field dependence of activation energy follows a power law of U0(H) ~ H-α where the exponent α changed from 0.5 to a 0.9 at a crossover field of Hcr = ~ 0.7 T, indicating the transition from weak plastic deformation of FLL to the strong entangled state in vortex liquid phase. Finally a vortex phase diagram is constructed demonstrating all the different phases of vortex lattice of V0.0015NbSe2 at different magnetic fields and temperatures.

Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe.

We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35T applied parallel to the ab plane. At low temperatures, the upper critical field μ_{0}H_{c2}^{ab} shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at μ_{0}H^{*}≈24 T well below μ_{0}H_{c2}^{ab}, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the high-field phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe.

Anisotropy induced vortex lattice rearrangement in CaKFe4As4

The magnetic penetration depth anisotropy $\gamma_\lambda=\lambda_{c}/\lambda_{ab}$ ($\lambda_{ab}$ and $\lambda_{c}$ are the in-plane and the out-of-plane components of the magnetic penetration depth) in a CaKFe$_4$As$_4$ single crystal sample (the critical temperature $T_{\rm c}\simeq 35$ K) was studied by means of muon-spin rotation ($\mu$SR). $\gamma_\lambda$ is almost temperature independent for $T\lesssim 20$ K ($\gamma_\lambda\simeq 1.9$) and it reaches $\simeq 3.0$ by approaching $T_{\rm c}$. The change of $\gamma_\lambda$ induces the corresponding rearrangement of the flux line lattice (FLL), which is clearly detected via enhanced distortions of the FLL $\mu$SR response. Comparison of $\gamma_\lambda$ with the anisotropy of the upper critical field ($\gamma_{H_{\rm c2}}$) studied in Phys. Rev B {\bf 94}, 064501 (2016), reveals that $\gamma_\lambda$ is systematically higher than $\gamma_{H_{\rm c2}}$ at low-temperatures and approaches $\gamma_{H_{\rm c2}}$ for $T \rightarrow T_{\rm c}$. The anisotropic properties of $\lambda$ are explained by the multi-gap nature of superconductivity in CaKFe$_4$As$_4$ and are caused by anisotropic contributions of various bands to the in-plane and the out-of-plane components of the superfluid density.

Orbitally limited pair-density-wave phase of multilayer superconductors

We investigate the magnetic field dependence of an ideal superconducting vortex lattice in the parity-mixed pair-density wave phase of multilayer superconductors within a circular cell Ginzburg-Landau approach. In multilayer systems, due to local inversion symmetry breaking, a Rashba spin-orbit coupling is induced at the outer layers. This combined with a perpendicular paramagnetic (Pauli) limiting magnetic field stabilizes a staggered layer dependent pair-density wave phase in the superconducting singlet channel. The high-field pair-density wave phase is separated from the low-field BCS phase by a first-order phase transition. The motivating guiding question in this paper is: what is the minimal necessary Maki parameter $\alpha_M$ for the appearance of the pair-density wave phase of a superconducting trilayer system? To address this problem we generalize the circular cell method for the regular flux-line lattice of a type-II superconductor to include paramagnetic depairing effects. Then, we apply the model to the trilayer system, where each of the layers are characterized by Ginzburg-Landau parameter $\kappa_0$, and a Maki parameter $\alpha_M$. We find that when the spin-orbit Rashba interaction compares to the superconducting condensation energy, the orbitally limited pair-density wave phase stabilizes for Maki parameters $\alpha_M> 10$.

Probing the superconducting ground state of the rare-earth ternary boride superconductors RRuB2 ( R= Lu,Y) using muon-spin rotation and relaxation

The superconductivity in the rare-earth transition metal ternary borides $R$RuB$_2$ (where $R$ = Lu and Y) has been investigated using muon-spin rotation and relaxation. Measurements made in zero-field suggest that time-reversal symmetry is preserved upon entering the superconducting state in both materials; a small difference in depolarization is observed above and below the superconducting transition in both compounds, however this has been attributed to quasistatic magnetic fluctuations. Transverse-field measurements of the flux-line lattice indicate that the superconductivity in both materials is fully gapped, with a conventional s-wave pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. The electronic properties of the charge carriers in the superconducting state have been calculated, with effective masses $m^*/ m_\mathrm{e} = $ $9.8\pm0.1$ and $15.0\pm0.1$ in the Lu and Y compounds, respectively, with superconducting carrier densities $n_\mathrm{s} = $ ($2.73\pm0.04$) $\times 10^{28}$ m$^{-3}$ and ($2.17\pm0.02$) $\times 10^{28}$ m$^{-3}$. The materials have been classified according to the Uemura scheme for superconductivity, with values for $T_\mathrm{c}/T_\mathrm{F}$ of $1/(414\pm6)$ and $1/(304\pm3)$, implying that the superconductivity may not be entirely conventional in nature.

Field-induced gapless electron pocket in the superconducting vortex phase ofYNi2B2Cas probed by magnetoacoustic quantum oscillations

By use of ultrasound studies we resolved magneto-acoustic quantum oscillation deep into the mixed state of the multiband nonmagnetic superconductor YNi2B2C. Below the upper critical field, only a very weak additional damping appears that can be well explained by the field inhomogeneity caused by the flux-line lattice in the mixed state. This is clear evidence for no or a vanishingly small gap for one of the bands, namely, the spheroidal alpha band. This contrasts de Haas--van Alphen data obtained by use of torque magnetometry for the same sample, with a rapidly vanishing oscillation signal in the mixed state. This points to a strongly distorted flux-line lattice in the latter case that, in general, can hamper a reliable extraction of gap parameters by use of such techniques.

Enhancement of superconductivity under pressure and the magnetic phase diagram of tantalum disulfide single crystals.

In low-dimensional electron systems, charge density waves (CDW) and superconductivity are two of the most fundamental collective quantum phenomena. For all known quasi-two-dimensional superconductors, the origin and exact boundary of the electronic orderings and superconductivity are still attractive problems. Through transport and thermodynamic measurements, we report on the field-temperature phase diagram in 2H-TaS2 single crystals. We show that the superconducting transition temperature (Tc) increases by one order of magnitude from temperatures at 0.98 K up to 9.15 K at 8.7 GPa when the Tc becomes very sharp. Additionally, the effects of 8.7 GPa illustrate a suppression of the CDW ground state, with critically small Fermi surfaces. Below the Tc the lattice of magnetic flux lines melts from a solid-like state to a broad vortex liquid phase region. Our measurements indicate an unconventional s-wave-like picture with two energy gaps evidencing its multi-band nature.

Vortex Matter in Highly Strained Nb $$_{75}$$ 75 Zr $$_{25}$$ 25 : Analogy with Viscous Flow of Disordered Solids

We present the results of magnetization and magneto-transport measurements in the superconducting state of an as-cast Nb$_{75}$Zr$_{25}$ alloy. We also report the careful investigation of the microstructure of our sample at various length scales by using optical, scanning electron and transmission electron microscopies. The information of microstructure is used to understand the flux pinning properties in the superconducting state within the framework of collective pinning. The magneto-transport measurements show a non-Arrhenius behaviour of the temperature and field dependent resistivity in the flux flow region. This non-Arrhenius behaviour is understood in terms of a model, which was originally proposed for viscous flow of disordered solids and is popularly known in the literature as the `shoving' model. The activation energy for flux flow is obtained from magneto-transport measurements and is assumed to be mainly the elastic energy stored in the flux-line lattice. The scaling of pinning force density with respect to reduced field indicates the presence of two pinning mechanisms of different origins. The elastic constants of the flux-line lattice are estimated from magnetization measurements and are used to estimate the length scale of vortex lattice movement, or the volume displaced by the flux-line lattice, during flux flow. It appears that the vortex lattice displacement estimated from elastic energy considerations is of the same order of magnitude as that of the flux-bundle hopping length when a finite resistance appears during flux flow. Our results could provide possible directions for establishing a framework where vortex matter and glass forming liquids or amorphous solids can be treated in a similar manner for understanding the phenomenon of viscous flow in disordered solids or more generally the pinning and depinning properties of elastic manifolds in random media.

Origin of matching effect in anti-dot array of superconducting NbN thin films

We investigate the origin of the matching effect observed in disordered superconducting NbN thin films with a periodic array of holes. In addition to the periodic variation in electrical resistance just above the superconducting transition temperature Tc0, we find pronounced periodic variations with magnetic field in all dynamical quantities that can be influenced by flux-line motion under an external drive, including the magnetic shielding response and the critical current, which survives in some samples down to temperatures as low as 0.09Tc0. In contrast, the superconducting energy gap Δ, which is a true thermodynamic quantity, does not show any periodic variation with magnetic field for the same films. Our results show that commensurate pinning of the flux-line lattice driven by vortex–vortex interaction is the dominant mechanism for the matching effects observed in these superconducting anti-dot films, rather than a Little–Parks-like quantum interference effect.

Dynamic transition in current-driven disordered flux-line lattice in single-crystal of Bi-2212

We have measured the current–voltage characteristics for both as-grown and irradiated Bi2Sr2CaCu2O8+δ single crystals at T=5K in a magnetic field applied parallel to c axis. The results show a variety of dynamical behavior above the depinning threshold, depending on the vortex–vortex interaction (λab/a0) strength and the nature of the quenched disorder (point-like or columnar defects). When the flux lattice is soft, our experimental measurements in both samples have been attributed to plastic flow, including strong metastability and history dependence of the depinning process. The vortex motion in this regime is thought of relatively weakly pinned vortices past more strongly pinned neighbors. A power-law scaling, fit between voltage and applied current can be obtained for the onset of motion in both samples, with different apparent critical exponent depending on defect nature and the strength of interactions. In the plastic regime, the usual scaling ansatz associated with dynamic critical phenomena V scales as (I−Ic)β, where β∼2.2±0.1 and 1.22±0.021 for as-grown and β≈1.49±0.07 for irradiated samples, respectively. Finally, in both cases of defects, with increasing the strength of vortex–vortex interaction a dynamical transition is observed as confirmed by the discontinuity in the vortex–vortex interactions dependence of the critical exponent β. More, our results confirm the important role of the system dimensionnality on vortex dynamics.

How the macroscopic current correlates with the microscopic flux-line distribution in a type-II superconductor: an experimental study

We present a study of the real-space flux-line lattice (FLL) of pristine and neutron irradiated conventional type-II superconductors using scanning tunnelling microscopy. Our work is focused on the magnetic field range, where the critical current density shows a second peak as a result of neutron irradiation. Scanning tunnelling microscopy images, including more than 2000 flux lines, are used to evaluate various microscopic parameters describing the disorder of the FLL, such as the defect density, the nearest neighbour distances and correlation functions. These parameters are compared with the macroscopic critical current density of the samples. The results show a direct correlation of the micro- and macroscopic properties. We observe a clear transition from an ordered to a disordered lattice at the onset of the second peak. Moreover, we discuss the defects of the FLL and their accumulation to large clusters in the second peak region.

Magnetic moment of single vortices in YBCO nano-superconducting particle: Eilenberger approach

Temperature dependence of single vortex magnetic moment in nanosize superconducting particles is investigated in the framework of quasiclassical Eilenberger approach. Such nanoparticles can be used for preparation of high-quality superconducting thin films with high critical current density. In contrast to bulk materials where the vortex magnetic moment is totally determined by flux quantum, in nano-sized specimens (with characteristic size, D, much less than effective penetration depth, λeff) the quantization rule is violated and magnetic moment is proportional to D2/λ2eff(T). Due to strong repulsion between vortices in nanoparticles only a single vortex can be trapped in them. Because of small size of particles the screening current of the vortex is located near the vortex core where the current is quite high and comparable to depairing currents. Therefore, the superconducting electron density, ns, depends on the current value and the distance from the vortex core. This effect is especially important for superconductors having gap nodes, such as YBCO.The current dependence of ns in nanoparticles is analogous to the Volovik effect in flux-line lattice in bulk samples. The magnitude of the effect can be obtained by comparing the temperature dependence of magnetic moment in the vortex and in the Meissner states. In the last case the value of screening current is small and superconducting response to the external field is determined by London penetration depth. Because of importance of nonlinear and nonlocal effects, the quantum mechanical Eilenberger approach is applied for description of the vortex in nanoparticles. The flattening of 1/λ2eff(T) dependence has been found. A comparison of the theoretical results with experimental magnetization data in Meissner and mixed states of YBCO nanopowders has been done. The presence of nonlinear and nonlocal effects in vortex current distribution is clearly visible. The obtained results are important for the description of pining in nanostructured high-Tc thin films.

High field paramagnetic effect in the superconducting state of Ti0.8V0.2 alloy

We report on the superconducting state of Ti0.8V0.2 alloy, highlighting an anomalous magnetic response in the flux-line lattice or the mixed state. The value of magnetization while cooling down the alloy in the presence of high magnetic field is lower than that obtained while warming it up from the lowest temperature in the presence of the same magnetic field. This is just the opposite to the thermo-magnetic hysteresis observed due to homogeneous flux-line pinning. This anomalous effect appears below a characteristic temperature that shifts towards a lower temperature with the increase in applied magnetic field. The value of magnetization measured at a constant temperature after cooling down the sample in the presence of magnetic field increases appreciably with time in the temperature–field domain where this anomalous effect is observed. These results indicate that the present Ti0.8V0.2 alloy exhibits a high field paramagnetic effect resulting from inhomogeneous flux pinning. Optical metallography and x-ray diffraction measurements show the formation of stress induced martensitic phase in the alloy, which could result in the inhomogeneous flux pinning. The temperature dependence of magnetization after annealing the sample after mechanical processing showed the usual properties of a type-II superconductor. This supports the argument that the inhomogeneous distribution of the stress induced martensitic phase is the reason for the existence of the high field paramagnetic effect in Ti0.8V0.2 alloy.