Vortex Solid State Research Articles

Detection of the vortex-liquid phase in superconducting films by Nernst effect

To clearly detect the vortex-liquid state of a superconducting film, we constructed an experimental system for measuring the Nernst signals in a film sample. We measured Nernst signals N in an amorphous MoxGe1−x film with a thickness of 300 nm. As the field is increased in the vortex-solid phase, N rises from zero at the boundary between the vortex-solid state and the vortex-liquid state, showing a peak in the middle of the liquid phase, and finally decreases. From a linear extrapolation of N after the peak to N = 0, we roughly estimated the upper bound of the liquid state. These results imply that the Nernst measurement could be an alternative to a resistivity measurement for detecting the vortex-liquid state. It would be helpful when the resistivity measurement is inconclusive in detecting vortices such as in an insulator phase in the vicinity of the superconductor-insulator transition in two dimensions.

L X-ray fluorescence cross-sections measurements for elements Ba, La and Ce at synchrotron radiation energies 7, 8, 9 and 10 keV

Ll, Lα, Lβ and Lγ1 X-ray fluorescence cross-sections have been measured for the elements Ba, La and Ce at 7, 8, 9 and 10 keV synchrotron radiations. A Peltier cooled Vortex solid state detector (SII Nano Technology, USA) with an energy resolution of 138 eV at 5.96 keV X-rays was employed for the analysis. The experimental results were compared with the theoretical values estimated from the data of Puri et al. (1993) and Campbell (2003). Two different models Dirac-Hartree-Slater (DHS) and Dirac-Fock (DF) were used to compare the theoretical and experimental results. Most of the experimental measurements were found in good agreement with the theoretical values of Puri et al. (1993) based on DF model.

Magnetic phase diagram of underdoped YBa2Cu3Oy inferred from torque magnetization and thermal conductivity

Strong evidence for charge-density correlation in the underdoped phase of the cuprate YBa2Cu3O y was obtained by NMR and resonant X-ray scattering. The fluctuations were found to be enhanced in strong magnetic fields. Recently, 3D charge-density-wave (CDW) formation with long-range order (LRO) was observed by X-ray diffraction in [Formula: see text] 15 T. To elucidate how the CDW transition impacts the pair condensate, we have used torque magnetization to 45 T and thermal conductivity [Formula: see text] to construct the magnetic phase diagram in untwinned crystals with hole density p = 0.11. We show that the 3D CDW transitions appear as sharp features in the susceptibility and [Formula: see text] at the fields [Formula: see text] and [Formula: see text], which define phase boundaries in agreement with spectroscopic techniques. From measurements of the melting field [Formula: see text] of the vortex solid, we obtain evidence for two vortex solid states below 8 K. At 0.5 K, the pair condensate appears to adjust to the 3D CDW by a sharp transition at 24 T between two vortex solids with very different shear moduli. At even higher H (41 T), the second vortex solid melts to a vortex liquid which survives to fields well above 41 T. de Haas-van Alphen oscillations appear at fields 24-28 T, below the lower bound for the upper critical field [Formula: see text].

Measurement of L-XRF cross-sections and Coster–Kronig enhancement factors for 62Sm at excitation energies 6.8, 7.4 and 8 KeV

Lℓ, Lα and Lβ XRF production cross-sections were measured for 62Sm at excitation energies i.e. 6.8KeV, 7.4KeV and 8KeV using synchrotron radiations. Experimental measurements were also carried out to examine the effect of Coster–Kronig transitions (non-radiative transitions) on fluorescence cross section for the Li (i=1, 2, 3) X-ray lines. The experimental cross-sections with greater accuracy and better signal to noise ratio can be measured using a polarized monoenergetic excitation beam and a high resolution detector system. A Peltier cooled vortex solid state detector with energy resolution of 138eV at 5.959keV X-ray was employed. Experimentally measured cross-sections have been compared with the theoretical predictions with the data of M.O. Krause [J. Phys. Chem. Ref. Data 8 (1979) 307], J.L. Campbell [At. Data Nucl. Data Tables 85 (2003) 291] and S. Puri et al. [X-Ray Spectrom. 22 (1993) 358]. The measured enhancement factors were found to be smaller than the theoretically calculated values.

Phase diagrams of the Bose-Hubbard model and the Haldane-Bose-Hubbard model with complex hopping amplitudes

In this paper, we study Bose-Hubbard models on the square and honeycomb lattices with complex hopping amplitudes, which are feasible by recent experiments of cold atomic gases in optical lattices. To clarify phase diagrams, we use an extended quantum Monte-Carlo simulations (eQMC). For the system on the square lattice, the complex hopping is realized by an artificial magnetic field. We found that vortex-solid states form for certain set of magnetic field, i.e., the magnetic field with the flux quanta per plaquette $f=p/q$, where $p$ and $q$ are co-prime natural numbers. For the system on the honeycomb lattice, we add the next-nearest neighbor complex hopping. The model is a bosonic analog of the Haldane-Hubbard model. By means of the eQMC, we study the model with both weak and strong on-site repulsions. Numerical study shows that the model has a rich phase diagram. We also found that in the system defined on the honeycomb lattice of the cylinder geometry, an interesting edge state appears.

Magnetization properties and vortex phase diagram of CuxTiSe2single crystals

We have investigated the magnetization properties and flux dynamics of superconducting Cu${}_{x}$TiSe${}_{2}$ single crystals within a wide range of copper concentrations. We find that the superconducting anisotropy is low and independent on copper concentration ($\ensuremath{\gamma}\ensuremath{\sim}1.7$), except in the case of strongly underdoped samples ($x\ensuremath{\le}0.06$) that show a gradual increase in anisotropy to $\ensuremath{\gamma}\ensuremath{\sim}1.9$. The vortex phase diagram in this material is characterized by a broad region of vortex liquid phase that is unusual for such a low-${T}_{c}$ superconductor with low anisotropy. Below the irreversibility line the vortex solid state supports relatively low critical current densities as compared to the depairing current limit (${J}_{c}/{J}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}7}$). All this points out that local fluctuations in copper concentration have little effect on bulk pinning properties in this system.

Quantized Vortex State in hcp Solid 4He

The quantized vortex state appearing in the recently discovered new states in hcp 4He since their discovery is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state and its transition into the supersolid (SS) state. Its features are described. The historical expla- nations for the SS state in quantum solids such as solid 4He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as va- cancies, interstitials and other possible excitations in the quantum solids which are expected because of the large zero-point motions. The SS state was proposed as a new state of matter in which real space ordering of the lattice structure of the solid coexists with the momentum space ordering of superfluidity. A new type of superconductors, since the discovery of the cuprate high Tc superconductors, HTSCs, has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high Tcs of these materials are being discussed in connection to the large fluctuations associated with some other phase transitions like the antiferromagnetic transition in addition to that of the low dimensionality. The supersolidity in the hcp solid 4He, in contrast to the new superconductors which have multiple degrees of freedom of the Cooper pairs with spin as well as angular momentum freedom, has a unique feature of possessing possibly only the momentum fluctuations and vortex ring excitations associated with the possible low dimensional fluctuations of the subsystem(s). The high onset temperature of the VF state can be understood by considering thermally excited low D quantized vortices and it may be necessary to seek low dimensional sub-systems in hcp He which are hosts for vortices.

Crossover from crossing to tilted vortex phase in Bi2Sr2CaCu2O8+δ single crystals near ab-plane

In extremely anisotropic layered superconductors of Bi2Sr2CaCu2O8+δ the stacks of vortex pancakes (PV) and the Josephson vortex (JV) interpenetrate, and due to PV–JV mutual pinning energy, weakly interact and form various tilted and crossing lattice structures including vortex chains, stripes, mixed chain+lattice phases, etc. In order to study these phenomena, it is decisive to have excellent quality of samples and the ideal experimental techniques. The vortex phases in high-quality Bi2Sr2CaCu2O8+δ single crystals were studied by in-plane resistivity measurement and local ac magnetic permeability. The sharp crossover was shown by both techniques, deep in the vortex solid state separating the Abrikosov dominant ‘strong pinning’ phase from the Josephson dominant ‘weak pinning’ phase. Those two vortex states were recognized as the mixed chain+lattice vortex phase and chains (tilted) vortex phase, respectively.

Sliding of a vortex solid with self-generated randomness in a frustrated Josephson junction array

A class of Josephson junction arrays under external magnetic field with anisotropic Josephson couplings realizes a gapless band of metastable vortex solid states with self-generated randomness. Each of the metastable states is characterized by a frozen pattern of transverse undulation of vortex stripes which run along the direction of weaker Josephson coupling. The vortex stripes can slide into the direction of stronger Josephson coupling even at zero temperature, eliminating the pinning effects of the underlying lattice structure of the array, but blocked into the direction of weaker coupling. Because of the sliding of the vortex matter, the phase of superconducting order parameter remain disordered at macroscopic level even at zero temperature. This is an extremely strong version of the spin-chirality decoupling which should be manifested in electric transport properties.

Probable Observation of Quantized Vortex Lines Through Solid He Under DC Rotation

We report how one can detect quantized vortices in superfluids contained in cylindrical vessels in well-designed torsional oscillator (TO) experiments under DC rotation. We show the case of an artificial 3D superfluid (Fukuda et al. in Phys. Rev. B 71:212502, 2005) which is made of Kosterlits-Thouless 2D He film condensed on a porous glass substrate with a 3D connected surface of well-controlled pore size. We understand the TO experimental results with an extra energy dissipation peak under DC rotation by considering the circular quantized superflow around each of the vortex lines and interaction with thermally excited 2D vortices as discussed in Fukuda et al. (Phys. Rev. B 71:212502, 2005) and in Nemirovskii and Sonin (Phys. Rev. B 76: 224507, 2007). We discuss here the case of hcp solid 4He (see for ex. Balibar and Caupin in J. Phys., Condens. Matter 20:173201-1-19, 2008) and show the evidence of observation of the vortex lines penetration below a supersolid transition temperature (Kubota et al. in J. Low Temp. Phys. 158:572, 2010), Tc, where macroscopic phase coherence is realized. It is found at exactly the same temperature Tc, below which the hysteresis occurrs (Shimizu et ail. in arXiv:0903.1326, 2009). For hcp solid 4He we have reported the vortex fluid (VF) state onset temperature (Penzev et al. in Phys. Rev. Lett. 101:065301, 2008) To=∼500 mK, by detailed drive velocity, Vac dependence study using TO technique. The TO response of the hcp 4He is characterized by the energy dissipation peaked at Tp near 100 mK similar to the behavior in a KT transition. The real supersolid (SS) state occurs at Tc below Tp and much lower than To. Our observation of the evidence of vortex lines penetration just below Tc together with the VF state properties gives support for the idea that hcp 4He shares some features with the “new type of superconductors”, where the vortex state, involving the VF as well as various vortex solid states, has been commonly discussed (Fisher et al. in Phys. Rev. B 43(1):130, 1991; Leggett in Quantum Liquids, Oxford University Press, London, 2006).

Quenching quantum vortex fluctuations in order to achieve higher critical current densities in [formula omitted] coated conductors

The relationship between the issue of obtaining higher critical current densities in textured M Ba 2 Cu 3 O 7 films and the boundary between the electrically dissipation-less vortex solid state and the dissipative vortex liquid state is explored in the context of a recently developed phenomenological melting line expression. Based on an extension of the Lindemann melting theory of Blatter and Ivlev, the temperature-field H – T dependence of this expression for H g ( T ) depends upon three parameters, a quantum fluctuation parameter Q, the Lindemann number c L , and an exponent s, for which the value of each is relevant to understanding the problem of increasing the critical current density over an extended H – T region. The importance of minimizing the value of the quantum parameter Q as a means of achieving higher critical current densities is demonstrated by examining the H g ( T ) lines of YBa 2 Cu 3 O x with various levels of Pr, Ca, and oxygen doping.

A boomerang-shaped reduction in interlayer phase coherence in Bi2Sr2CaCu208+y with splayed columnar defects

We present evidence for entangled solid vortex matter in a glassy state in a layered superconductor Bi2Sr2CaCu2O8+y containing randomly splayed linear defects. The interlayer phase coherence(IPC)—probed by the Josephson plasma resonance—is enhanced at high temperatures, reflecting the recoupling of vortex liquid by the defects. At low temperatures in the vortex solid state, the interlayer coherence follows a boomerang-shaped reentrant temperature path with an unusual low field decrease in coherence, indicative of meandering vortices. This behavior suggests strongly suppressed IPC in this system, which may be explained by the vortex entanglement induced by the columnar defects in the "splayed-glass" state.

Magnetothermal instability in the organic layered superconductorκ−(BEDT-TTF)2Cu(NCS)2

We have studied the magnetothermal instability in $\ensuremath{\kappa}\text{\ensuremath{-}}{(\text{BEDT-TTF})}_{2}\text{Cu}{(\text{NCS})}_{2}$ by means of measuring the temperature change in the sample. We report the remarkable temperature spikes due to the flux jumps and the preceding temperature oscillations in the vortex solid state. These dependences on the sweep rate are almost consistent with the conventional theory based on the Bean model. The temperature dependences of the flux jump suggest that the melting transition from the vortex solid to the liquid phase at low temperatures is not driven by thermal fluctuations, but rather by quantum ones. The small temperature fluctuations observed at very low temperatures imply the dendritic vortex distribution in this salt.

Entanglement of Solid Vortex Matter: A Boomerang-Shaped Reduction Forced by Disorder in Interlayer Phase Coherence inBi2Sr2CaCu2O8+y

We present evidence for entangled solid vortex matter in a glassy state in a layered superconductor Bi2Sr2CaCu2O8+y containing randomly splayed linear defects. The interlayer phase coherence--probed by the Josephson plasma resonance--is enhanced at high temperatures, reflecting the recoupling of vortex liquid by the defects. At low temperatures in the vortex solid state, the interlayer coherence follows a boomerang-shaped reentrant temperature path with an unusual low-field decrease in coherence, indicative of meandering vortices. We uncover a distinct temperature scaling between in-plane and out-of-plane critical currents with opposing dependencies on field and time, consistent with the theoretically proposed "splayed-glass" state.

VORTEX STATES AND PEAK EFFECT AT LOW TEMPERATURE IN THICK AMORPHOUS FILMS WITH WEAK PINNING

We report on the dynamic as well as static properties of vortices in the low-temperature (T) solid phase of a thick amorphous Mo x Ge 1-x film with weak pinning. The vortex-solid state is considered to be a weakly disordered vortex lattice, which is inferred from the mode-locking resonance over the broad field region. The peak effect of the critical current Ic with magnetic field is clearly visible down to the lowest T measured (0.2 K), which corresponds to 3.3% of the superconducting transition temperature. We find that largest voltage noise originating from current-driven vortices appears in the field region just prior to the peak field at which Ic takes a peak. This is in accord with the result reported in NbSe 2 single crystals.

Vortex phase diagram and dynamics at low temperature in a thick a-MoxGe1−x film

We study the vortex phase diagram and dynamics in the low-temperature liquid phase of a thick amorphous a-MoxGe1−x film with weak pinning. The vortex solid state is ordered vortex lattice or Bragg glass, which is different from the disordered vortex glass of a-MoxSi1−x films with stronger pinning. We find, however, that the vortex liquid state is similar to that for the a-MoxSi1−x films, involving the quantum-vortex-liquid phase at low temperature, where we again detect the unusual vortex flow.

Interlayer coherence in Bi2Sr2CaCu2O8+y with splayed columnar defects

By using the Josephson plasma resonance, we investigate the interlayer phase coherence (IPC) in the vortex states of GeV-proton-irradiated Bi2Sr2CaCu2O8+y crystals containing splayed columnar defects, which are introduced by Bi fission. At high temperatures in the vortex liquid state, we observe an enhancement of IPC in a field range beginning well below the matching field BΦ, in close correspondence with the recoupling crossover observed near BΦ/3 in the heavy-ion irradiated Bi2Sr2CaCu2O8+y. At low temperatures in the vortex solid state, a reentrant behavior of the resonance field is found in the zero-field-cooling condition, which has not been observed in pristine samples. This behavior suggests strongly suppressed IPC in this system, which may be explained by the vortex entanglement induced by the columnar defects in the splayed glass state.

Angle-resolvedI−Vcharacteristics measurements inBi1.8Pb0.2Sr2CaCu2O8+δsingle crystals with inclined columnar defects

Current-voltage $(I\text{\ensuremath{-}}V)$ characteristics have been measured over a wide temperature range in a ${\mathrm{Bi}}_{1.8}{\mathrm{Pb}}_{0.2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ single crystal with tilted columnar defects (CDs). This configuration was compared to a crystal irradiated along the $c$ axis. Above $40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and in the vortex solid state, angular measurements reveal a pronounced dip in the dissipation when a magnetic field is applied parallel to the CDs. At $T\ensuremath{\leqslant}40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the measured $I\text{\ensuremath{-}}V$ characteristics showed that besides the persistence of the directional pinning at low temperatures, there is a shift from the CDs toward the $c$ axis. Our samples showed, in the high temperature range $(T\ensuremath{\geqslant}40\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and for ${B}_{\ensuremath{\phi}}∕10<\mathbf{H}<{B}_{\ensuremath{\phi}}$ (where ${B}_{\ensuremath{\phi}}$ is the matching field) applied parallel to the CDs, a three-dimensional Bose-glass transition with the same critical exponents as ${z}^{\ensuremath{'}}=5.3\ifmmode\pm\else\textpm\fi{}0.1$ and ${v}^{\ensuremath{'}}=1.1\ifmmode\pm\else\textpm\fi{}0.1$ which are in very good agreement with numerical simulations. Our findings support the existence of the Bose-glass-to-liquid transition at ${T}_{\mathrm{BG}}({\ensuremath{\mu}}_{0}H)$ in the case of tilted columnar defects.

Low-temperature vortex dynamics in (Bi,Pb)2212 single crystals with columnar defects aligned at 45° to the c-axis

The focus of the present report is the comparison of pinning properties between a Bi 1.8Pb 0.2Sr 2CaCu 2O 8+ δ single crystal irradiated at 45° and the one irradiated along c-axis. At temperatures T⩾40 K, and in the vortex solid state, angular measurements reveal for both samples a pronounced dip in the dissipation when a magnetic field is applied parallel to the tracks. In contrast, at low temperature the dip shifts from inclined columnar defects towards the c-axis direction. The dip shift observed with decreasing T can be associated to a partially pinned staircase vortex structure.

Electronic compressibility and charge imbalance relaxation in cuprate superconductors

In the material SmLa 1− x Sr x CuO 4− δ with alternating intrinsic Josephson junctions we explain theoretically the relative amplitude of the two plasma peaks in transmission by taking into account the spatial dispersion of the Josephson Plasma Resonance in c-direction due to charge coupling. From this and the magnetic field dependence of the plasma peaks in the vortex solid and liquid states it is shown that the electronic compressibility of the CuO 2 layers is consistent with a free electron value. Also the London penetration depth λ ab ≈1100 Å near T c can be determined. The voltage response in the IV-curve of a Bi 2Sr 2CaCu 2O 8 mesa due to microwave irradiation or current injection in a second mesa is related to the nonequilibrium charge imbalance of quasiparticles and Cooper pairs and from our experimental data the relaxation time ∼100 ps is obtained.