A new numerical method for quasi-particle spectroscopy around a pair of vortices in triplet superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂·yH₂O are now found to be p-wave (p_x±ip_y) or f-wave ((p_x±ip_y)coscp_z) superconductors. In conventional singlet superconductors, vortices are quantized because phase of order parameter must rotate by 2π around a vortex. But triplet superconductors have a degree of freedom of spin, which is described by d-vector. The d-vector and phase can rotate by π around a vortex, separately. Therefore appearance of HQVs is predicted. Theoretically, it is found that a pair of HQVs is more stable than a singly quantized vortex, for several parameter regions.In this study, in order to investigate quasi-particle bound states around two vortices in s-wave superconductors, we have developed a new numerical method to solve the BdG equation for two vortices state, using Mathieu functions. We confirmed the validity of this method for two vortices state and applied it in case of a pair of vortices. And we solved it.     

Optical and dc conductivities in high-T c superconductors: Spin-fluctuation scattering in the Emery model

On the basis of the Emery model for the CuO₂ plane, the optical conductivity and resistivity due to the inelastic scattering of oxygen holes by antiferromagnetic fluctuations of copper spins are calculated. For moderate hole doping, the electrical conductivity obeys a generalized Drude law. Using a phenomenological model for the dynamic spin susceptibility, the in-plane resistivity reveals a crossover from a quadratic to a linear temperature dependence at the scale of the spin-fluctuation energy. The frequency dependence of the scattering rate changes from a quadratic to a linear increase over a wide frequency range. The theory is compared with experiments on LSCO and YBCO compounds, where the spin dynamics is described within the model by Millis et al. A good quantitative agreement (in particular of the frequency-dependent scattering rate) with experiments is found. We conclude that the spin-fluctuation scattering may play a dominant role in the transport properties of Cu-oxide superconductors.     

Gyroscopic dynamics of antiferromagnetic vortices in the orthoferrite domain wall

The method of generation of antiferromagnetic vortices on the supersound domain wall in the orthoferrites was proposed. Moving antiferromagnetic vortices were accompanied by the solitary deflection waves. These waves were used for investigation of generation and nonlinear dynamics of the antiferromagnetic vortices on a moving domain wall with the help of two- and three-fold digital high-speed photography and Faraday rotation in the orthoferrites plates cut perpendicular to the optical axis. The full velocity of antiferromagnetic vortex nonlinearly increases and saturates on the spin velocity level c. The vortices with smallest topological charges saturate earlier than with big one. The vortices velocity along the domain wall u increases up to the maximum and goes to the dependence u²+v²=c². Vortex dynamics is quasirelativistic on quasirelativistic domain wall. The theory of gyroscopic force in the domain wall of orthoferrites was elaborated by Zvezdin et al. and was confirmed our earlier experimental results.     

Microscopic neutron investigation of the Abrikosov state of high-temperature superconductors

Using small angle neutron scattering we have been able to observe for the first time a well-defined vortex lattice (VL) structure both in the hole-doped LSCO and electron-doped NCCO superconductors. Our measurements on optimally doped LSCO reveal the existence of a magnetic field-induced phase transition from a hexagonal to a square coordination of the VL. Various scenarios to explain such phase transition are presented. In NCCO also a clear square VL could be detected, which is unexpectedly kept down to the lowest measurable magnetic fields.      

High temperature superconductivity in the mixed state and the dynamics of charge carriers

A model to calculate the temperature and magnetic field dependence of the scattering time τ_ν(H, T) of quasiparticles by bound electron states in a vortex in high-temperature superconductors is proposed. In this model, the hydrodynamic interaction of a moving gas of quasiparticles with the discrete states of the vortex velocity field is regarded as quasielastic scattering and the resulting scattering time of quasiparticles is different from scattering of individual vortices. The normalized scattering time was found to decrease exponentially with increasing temperature. This behavior is due to the suppression of the amplitude of the superconducting order parameter as the temperature increases. This model accounts for the observed temperature and field dependence of the scattering time particularly at low-field regime.     

Vortex pinning: A probe for nanoscale disorder in iron-based superconductors

The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density j_c at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to “weak collective pinning” and a magnetic field-independent contribution j_c^coll. The latter allows one to estimate quasiparticle scattering rates.     

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov vortex state of spin-singlet superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in noncentrosymmetric superconductors.     

Direct observations of vortices in a high-Tc superconductor (La1-xSrx)2CuO4 by scanning SQUID microscopy

In order to investigate the behavior of vortices in high-T_c superconductors under low magnetic fields, we have performed scanning SQUID microscopy (SSM) on the ab-surfaces of (La_1-xSr_x)₂CuO₄ (LSCO) single crystals at low temperatures. The observed magnetic images clearly demonstrated vortices in units of K₀ (=hc/2e) below T_c. Vortices trapped inside the overdoped LSCO tended to be arranged in a one-dimensional manner, while those in optimally doped crystals were randomly distributed. From the variable-temperature SSM measurements, it was directly visualized that the normal state with regular magnetic-field distribution gradually changed into the inhomogeneous Meissner state, and finally vortices evolved, with decreasing temperature.     

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate a two-dimensional (2D) Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to a depletion of the superfluid density. We predict the intermediate superfluid state where the condensate and localized bosons are present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto a 3D system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning crossover within the vortex liquid and depinning induced vortex lattice-Bose glass melting.     

Superconductivity in the pseudogap state in the hot spot model: The influence of impurities and the phase diagram

We analyze the peculiarities of the superconducting state (s- and d-wave paring) in the model of the pseudogap state induced by Heisenberg antiferromagnetic short-range order spin fluctuations. The model is based on the pattern of strong scattering near hot spots at the Fermi surface. The analysis is based on the microscopic derivation of the Ginzburg-Landau expansion with the inclusion of all Feynman diagrams of perturbation theory for the interaction of an electron with short-range order fluctuations and in the ladder approximation for the scattering by normal (nonmagnetic) impurities. We determine the dependence of the critical superconducting transition temperature and other superconductor characteristics on the pseudogap parameters and the degree of impurity scattering. We show that the characteristic shape of the phase diagram for high-temperature superconductors can be explained in terms of the model under consideration.     

What does NMR tell us about the electronic state of high-T c superconductors?

An introduction to the models which are usually applied, when interpreting the NMR (nuclear magnetic resonance) parameter Knight shift (K _s) and spin-lattice relaxation rate 1/T ₁ in the normal and the superconducting state of high-temperature superconductors, is given. The different hyperfine interaction parameters involved, as well as the static and dynamic susceptibility χ(q,ω) will be discussed. I will point at those highlights as antiferromagnetic correlations, spin gap and vortex lattice dynamics which have emerged from the analysis of the NMR data.     

Antiferromagnetism and hole pair checkerboard in the vortex state of high T(c) superconductors

We propose a microscopic state for the vortex phase of BSCO superconductors. Around the vortex core or above H(c2), the d wave hole pairs form a checkerboard localized in the antiferromagnetic background. We discuss this theory in connection with recent STM experiments.     

Pnicogen-bridged antiferromagnetic superexchange interactions in iron pnictides

The first-principles electronic structure calculations made substantial contribution to study of high T_c iron-pnictide superconductors. By the calculations, LaFeAsO was first predicted to be an antiferromagnetic semimetal, and the novel bi-collinear antiferromagnetic order was predicted for α-FeTe. Moreover, based on the calculations the underlying mechanism was proposed to be Arsenic-bridged antiferromagnetic superexchange interaction between the next-nearest neighbor Fe moments. In this article, this physical picture is further presented and discussed in association with the elaborate first-principles calculations on LaFePO. The further discussion of origin of the magnetism in iron-pnictides and in connection with superconductivity is presented as well.     

Many-body interactions in hole-doped high-Tc cuprates studied by high-resolution ARPES

We have performed high-resolution angle-resolved photoemission spectroscopy on hole-doped high-T_c cuprate superconductors (HTSCs) to study many-body interaction and the universality of low-energy excitation gap. In Bi₂Sr₂CaCu₂O₈ (Bi2212), we observed a kink in the dispersion in the off-nodal region in the superconducting state, which remarkably weakens on impurity substitution. We also find that the appearance of the kink in the off-nodal region is a common feature of Bi2212 and La_1.85Sr_0.15CuO₄ (LSCO), while the energy scale is remarkably different between two compounds (70 and 20 meV). We discuss universality of the kink in dispersion in the hole-doped HTSCs in terms of the coupling of electrons with spin fluctuations.     

Critical Scaling of Extended Power Law I - V Isotherms near Vortex Glass Transition

In view of the question about the vortex glass theory of the freezing of disordered vortex matter raised by recent experimental observations, we reinvestigate the critical scaling of high Tc superconductors. It is found that the dc current-voltage characteristic of mixed state superconductors has a general form of extended power law which is based on the Ginzburg-Landau （GL） functional in the similar way as the vortex glass theory. Isotherms simulated from this nonlinear equation fit the experimental I- V data of Strachan et al. [Phys. Rev. Left. 87（2001） 067007]. The puzzling question of the derivative plot for the I - V curves and the controversy surrounding the values of critical exponents are discussed.     

Gyroscopic dynamics of antiferromagnetic vortices in domain boundaries of yttrium orthoferrite

It is established experimentally that the magnetic field directed along the b axis has little effect on the velocities of antiferromagnetic vortices in the domain boundary (DB) of yttrium orthoferrite and fails to explain the presence of an appreciable gyroscopic force acting on these vortices. This force is induced by the dynamic canting of magnetic sublattices proportional to the DB velocity. Due to the canting, the velocities of antiferromagnetic vortices depend initially quadratically on the DB velocity, as was experimentally found in this work. The dynamics of antiferromagnetic vortices in the yttrium orthoferrite DBs is gyroscopic and quasi-relativistic, with the limiting velocity of 20 km/s equal to the velocity of spin waves at the linear portion of their dispersion curve.     

Possibility of two-stage flux penetration in antiferromagnetic superconductors

An induced ferromagnetism in antiferromagnetic superconductors is possible, caused by a magnetic structure of vortex lines appearing in an external magnetic field strong enough to “flip over” the spins in the vortex core from their antiferromagnetic configuration. If the magnetic field is less than the “flip over” field the vortex line is entirely in the antiferromagnetic phase. Therefore the vortex interaction with the surface of a sample is altered when an applied magnetic field exceeds the “flip over” field. This mechanism makes the appearance of a new energy barrier that strongly influences the flux penetration possible. An estimation of the second critical entry field is made for DyMo₆S₈.     

Vortex-lattice melting in magnesium diboride in terms of the elastic theory

In the framework of elastic theory, we study the vortex-lattice melting transitions in magnesium diboride for magnetic fields both parallel and perpendicular to the anisotropy axis. Using the parameters from experiments, the vortex-lattice melting lines in the H-T diagram are located systematically by various groups of Lindemann numbers. It is observed that the theoretical result for the vortex melting with parallel and perpendicular fields agrees well with the experimental data. Therefore, it is suggested that the phenomenological elastic theory is universal to various type-II superconductors, including two- and multi-band superconductors.     

Spin waves in the block checkerboard antiferromagnetic phase

Motivated by the discovery of a new family of 122 iron-based superconductors, we present the theoretical results on the ground state phase diagram, spin wave, and dynamic structure factor obtained from the extended J₁-J₂ Heisenberg model. In the reasonable physical parameter region of K₂Fe₄Se₅, we find that the block checkerboard antiferromagnetic order phase is stable. There are two acoustic spin wave branches and six optical spin wave branches in the block checkerboard antiferromagnetic phase, which have analytic expressions at the high-symmetry points. To further compare the experimental data on neutron scattering, we investigate the saddlepoint structure of the magnetic excitation spectrum and the inelastic neutron scattering pattern based on linear spin wave theory.     

Vortex lattice symmetry in hexagonal superconductor CaAlSi probed by small angle neutron scattering

The small angle neutron scattering diffraction patterns from the flux line lattice state in the layered hexagonal superconductor CaAlSi are observed. Under an applied magnetic field (H) parallel to the crystalline c-axis, a hexagonal vortex structure is observed over the entire temperature/field regions. On the other hand, the vortex configuration under H∥a shows an ellipsoidal arrangement of the first-order Bragg peaks due to the anisotropic penetration depth. It was inferred from these results that the vortex state characterized by penetration depth and coherence length in CaAlSi may be described by that of anisotropic uniaxial superconductor using London theory.