Superconductor In Magnetic Field Research Articles

Quantifying the quantum nature of high-spin YSR excitations in transverse magnetic field.

Excitations of individual and coupled spins on superconductors provide a platform to study quantum spin impurity models as well as a pathway toward realizing topological quantum computing. Here, we characterize, using ultralow temperature scanning tunneling microscopy/spectroscopy, the Yu-Shiba-Rusinov (YSR) states of individual manganese phthalocyanine molecules with high spin on an ultrathin lead film in variable transverse magnetic field. We observe two types of YSR excitations, depending on the adsorption geometry. Using a zero-bandwidth model, we detail the role of the magnetic anisotropy, spin-spin exchange, and Kondo exchange. We illustrate that one molecular type can be treated as an individual spin, whereas the other type is best described by a coupled spin system. Using the field dependence of the YSR excitations combined with modeling, we describe the quantum phase of each excitation type. These results provide an insight into the quantum nature of YSR excitations in magnetic field and a platform to study spin impurity models on superconductors in magnetic field.

Nonlinear optical response in superconductors in magnetic field: Quantum geometry and topological superconductivity

Nonlinear optical response in superconductors in magnetic field: Quantum geometry and topological superconductivity

Intrinsic Nature of Spontaneous Magnetic Fields in Superconductors with Time-Reversal Symmetry Breaking.

We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems, and Sr_{2}RuO_{4}. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy, leading to only minimal changes in the charge density on ions close to the muon. Our results imply that the muon-induced perturbation alone is unlikely to lead to the observed spontaneous fields in these materials, whose origin is more likely intrinsic to the time-reversal symmetry-broken superconducting state.

The magnetic and levitation characteristics of single-grain YBaCuO and GdBaCuO-Ag bulk superconductors in high magnetic fields

In principle, high-temperature superconducting (HTS) flux-pinning maglev has the advantage of self-stable levitation and is therefore a good development prospect as a new rail transit technology. The magnetic field intensity is one of the key factors affecting the levitation performance of single-grain bulk superconductors in the HTS maglev system. To date, however, most researchers have focused on the levitation performance of HTS bulk superconductors in magnetic fields within a permanent magnet guideway (PMG) configuration. The magnitude of the external working magnetic field provided by a PMG is limited to about 0.5 T at 77 K, given that the superconductor usually levitates at a typical working height of 10 mm above the PMG. Therefore, the weak magnetic fields generated by the PMG significantly limits the levitation performance of HTS maglev systems to that of the permanent magnet (PM). In this article, a superconducting magnet test bench was utilized to provide a 0–3 T external magnetic field (B) environment for the study of the levitation force in HTS single grains. The difference in levitation performance between YBaCuO (YBCO) and GdBaCuO-Ag (GdBCO-Ag) bulk superconductors under large, changing magnetic fields was studied systematically. The relationships between levitation force and magnetic field characteristics, including vertical magnetic field component (Bz), transverse magnetic field component (Br), and vertical magnetic field variation (ΔBz) were investigated. The result of variation curves about YBCO and GdBCO bulks' levitation forces under different ΔBz shows that the levitation force of the bulk, single-grain superconductors will reach saturation under a varying ΔBz environment (0.72 and 1.5 T). The values of ΔBz corresponding to the saturation positions are found to be independent of the sizes of the HTS samples. At the same time, GdBCO-Ag exhibits a levitation force that is 112.8% greater than YBCO in B = 3 T magnetic environment. As a result, it is demonstrated that the levitation potential of single-grain HTS bulks can be better exploited by optimizing the distribution of the magnetic field.

Direct observation of the scaling relation between density of states and pairing gap in a dirty superconductor* *Project supported by the National Key Research and Development Program of the Ministry of Science and Technology of China (Grant Nos. 2017YFA0302903, 2016YFA0300602, 2016YFA0300604, and 2016YFJC010282), the National Natural Science Foundation of China (Grant Nos. 11227903, 12004416, and U2032204), the Beijing Municipal Science

Theories and experiments on dirty superconductors are complex but important in terms of both theoretical fundamentals and practical applications. These activities are even more challenging when magnetic fields are present because the field distribution, electron density of states, and superconducting pairing potentials become nonuniform. Here, we present tunneling microspectroscopic experiments on NbC single crystals and demonstrate that NbC is a homogeneous dirty superconductor. When applying magnetic fields to the samples, we found that the zero-energy local density of states and the pairing energy gap followed the explicit scaling relation proposed by de Gennes for homogeneous dirty superconductors in high magnetic fields. More significantly, our experimental findings indicate that the validity of the scaling relation extends to magnetic field strengths far below the upper critical field, calling for a new nonperturbative understanding of this fundamental property in dirty superconductors. On the practical side, we used the observed scaling relation to derive a simple and straightforward experimental scheme for estimating the superconducting coherence length of a dirty superconductor in magnetic fields.

Analysis to the Forced Vibration of a High Temperature Superconducting System With Hysteresis

Dynamic behavior with the hysteresis of the levitation force of a high temperature magnet-superconductor system is investigated with application of a displacement harmonic excitation. The dynamic characteristics of the transient stage and the steady stage of forced vibration of the system are discussed in detail. The period-doubling and the natural frequency components are found in forced vibration. It means that the initial frozen magnetic field in superconductor plays an important role on the vibration response. The vibration amplitude vs. excitation frequency is presented. A transition excitation frequency with triple natural frequency is given to distinguish the range of vibration center. The vibration amplitude of the superconducting levitation system shows a linear increasing with the excitation amplitude, which is found to be independent on the critical current density with considerations based on the Bean's critical model. However, the critical current density greatly affects the location of the vibration center. The critical excitation amplitude vs. the field frequency to the superconductor is presented. Levitation is stable most when the sample is exposed to a low-frequency field. In this case large amplitude of the alternating field is needed to break-off of the sample.

Decoding the halo pattern

Superconductivity Magnetic fields can cause the formation of vortices in a superconductor. In cuprate superconductors, the vortex cores are surrounded by “halos,” where the density of electronic states exhibits a checkerboard pattern. Edkins et al. used scanning tunneling spectroscopy to take a closer look into the halos. The results revealed that the patterns correspond to an exotic state called the pair density wave, in which the density of finite momentum Cooper pairs is spatially modulated. Science , this issue p. [976][1] [1]: /lookup/doi/10.1126/science.aat1773

XFEM analysis of the fracture behavior of bulk superconductor in high magnetic field

A bulk superconductor in a high magnetic field is subjected to a large electromagnetic force, which can cause crack propagation and damage the bulk. In this paper, we study the fracture behavior of the GdBCO bulk superconductor under a large electromagnetic force based on the Extended Finite Element Method (XFEM). The critical state Kim model and H-formulations are used to obtain the electromagnetic force of a bulk superconductor in the magnetic field first. Second, the Stress Intensity Factor (SIF) of the bulk superconductor for various cracks under the electromagnetic force is presented. Numerical results show that the SIF depends not only on crack angle and length but also on the width of the bulk. For the inclined crack with a large crack angle, with the crack length increase, the SIFs increase first and decrease, while for a small crack angle, the SIFs decrease with the crack length increase. For the kinked crack, the SIFs decrease with the crack length increase. With the XFEM, the growth of the inclined and kinked cracks in the bulk superconductor during field cooling is presented. The crack propagation paths are dependent on the size of the bulk and different for two crack problems. In the process of crack propagation, the propagation path has a certain degree of deflection angle compared with the initial crack.

AdS-CFT correspondence in noncommutative background, related thermodynamics and holographic superconductor in magnetic field

In this work, we formulate a non-commutative (NC) extension of AdS-CFT correspondence that is manifested in the modification of behavior of a holographic superconductor. The noncommutativity is introduced in the model through the NC corrected AdS charged black hole metric developed by Nicolini, Smailagic and Spallucci. First of all we discuss thermodynamic properties of this black hole in Euclidean formalism. In particular, we compute trace of the boundary energy-momentum tensor which, as expected, is non-zero due to the NC scale introduced in the model. Our findings indicate that the non-commutative effects tend to work against the black hole hair formation. This, in turn, has an adverse effect on the holographic superconductor by making the superconducting phase more fragile. This is reflected in the reduced value of the critical magnetic field and critical temperature. Finally, we comment on a qualitative agreement between our (holographic superconductor) result and that obtained for a conventional superconductor in NC space in a purely condensed matter scenario. In both cases noncommutativity tends to oppose the superconducting phase.

Demagnetization of Cubic Gd-Ba-Cu-O Bulk Superconductor by Crossed-Fields: Measurements and Three-Dimensional Modeling

Superconducting bulks, acting as high-field permanent magnets, are promising for many applications. An important effect in bulk permanent magnets is crossed-field demagnetization, which can reduce the magnetic field in superconductors due to relatively small transverse fields. Crossed-field demagnetization has not been studied in sample shapes such as rectangular prisms or cubes. This contribution presents a study based on both 3D numerical modelling and experiments. We study a cubic Gd-Ba-Cu-O bulk superconductor sample of size 6 mm magnetized by field cooling in an external field of around 1.3 T, which is later submitted to crossed-field magnetic fields of up to 164 mT. Modelling results agree with experiments, except at transverse fields 50\% or above of the initial trapped field. The current paths present a strong 3D nature. For instance, at the mid-plane perpendicular to the initial magnetizing field, the current density in this direction changes smoothly from the critical magnitude, ${J_c}$, at the lateral sides to zero at a certain penetration depth. This indicates a rotation of the current density with magnitude ${J_c}$, and hence force free effects like flux cutting are expected to play a significant role.

Vortex molecules in thin films of layered superconductors

The seminal work of Abrikosov on the vortex lattices in type-II superconductors has triggered the creation and rapid development of the whole new field of condensed matter physics, namely, the physics of vortex matter in a large variety of superfluid and superconducting systems. Among these systems and compounds the layered superconductors are known to form a very important class which is associated with a number of fascinating new discoveries in vortex physics. The phenomenon of the vortex attraction in tilted magnetic fields provides one of the examples of such findings which affected theoretical and experimental research in the field for almost two decades. In our paper we review some recent advances in this direction focusing on the intervortex interaction and equilibrium vortex structures in thin films of layered superconductors in magnetic field tilted with respect to the layers. In such a case the magnetic field penetrates superconductor in the form of tilted vortices or a crossing array of Josephson vortices and pancake stacks. We study the interplay between two different long-range potentials: (i) attraction of tilted vortices or deformed stacks; (ii) the Pearl's repulsion. This interplay is responsible for the formation of the minimum in the total interaction energy and resulting decay of vortex chains in clusters. The number of Abrikosov vortices in these clusters (or vortex molecules) depends on field tilting angle and film thickness.

Landau levels from neutral Bogoliubov particles in two-dimensional nodal superconductors under strain and doping gradients

Motivated by recent work on strain-induced pseudo-magnetic fields in Dirac and Weyl semimetals, we analyze the possibility of analogous fields in two-dimensional nodal superconductors. We consider the prototypical case of a d-wave superconductor, a representative of the cuprate family, and find that the presence of weak strain leads to pseudo-magnetic fields and Landau quantization of Bogoliubov quasiparticles in the low-energy sector. A similar effect is induced by the presence of generic, weak doping gradients. In contrast to genuine magnetic fields in superconductors, the strain- and doping gradient-induced pseudo-magnetic fields couple in a way that preserves time-reversal symmetry and is not subject to the screening associated with the Meissner effect. These effects can be probed by tuning weak applied supercurrents which lead to shifts in the energies of the Landau levels and hence to quantum oscillations in thermodynamic and transport quantities.

Fractal Boundaries of Vortex Pinning Clusters in Copper-oxide Superconductors in Magnetic Field

Fractal Boundaries of Vortex Pinning Clusters in Copper-oxide Superconductors in Magnetic Field

The Suspension of Water Using a Superconductive Magnetic-Field and Its Features

The magnetization of water and its magnetism are experimentally researched and confirmed by virtue of the suspended method of magnetized water droplets in a superconductive magnetic field having a gradient distribution of strength with a maximum value of 16.12 T, generated by the superconductive Nb 3 Zn and NbTi coils. The experiments exhibit that the magnetized and purified water droplets are all suspended in the magnetic-field, the interaction of two suspended water droplets is also observed, and recorded by a camera. Based on these experimental results, we revealed and built the mechanism of suspension of magnetized water droplets using the theory of magnetism, i.e., the balance between the gravity of magnetized water droplet and the magnetic attraction force accepted by it arising from the superconductive magnetic field results in their suspension states. We explained the experimental results using this mechanism and have observed also that the suspended water droplets fall off the bottom of the sample tube if the electric current in the device is broken off. These results verified just the correctness of this mechanism of suspension. On the basis of the mechanism of suspension and these experimental results, we certified and affirmed that the magnetized waters have certain magnetism. This conclusion will promote the development of investigation of magnetized water and its application.

Vortex Flux Dynamics and Harmonic ac Magnetic Response of Ba(Fe0.94 Ni0.06)2As2 Bulk Superconductor

Vortex dynamics and nonlinear ac response are studied in a Ba(Fe0.94 Ni0.06)2As2(T c = 18.5 K) bulk superconductor in magnetic fields up to 12 T via ac susceptibility measurements of the first ten harmonics. A comprehensive study of the ac magnetic susceptibility and its first ten harmonics finds shifts to higher temperatures with increasing ac measurement frequencies (10 to 10,000 Hz) for a wide range of ac (1, 5, and 10 Oe) and dc fields (0 to 12 T). The characteristic measurement time constant t 1 is extracted from the exponential fit of the data and linked to vortex relaxation. The Anderson-Kim Arrhenius law is applied to determine flux activation energy E a /k as a function dc magnetic field. The de-pinning, or irreversibility lines, were determined by a variety of methods and extensively mapped. The ac response shows surprisingly weak higher harmonic components, suggesting weak nonlinear behavior. Our data does not support the Fisher model; we do not see an abrupt vortex glass to vortex liquid transition and the resistivity does not drop to zero, although it appears to approach zero exponentially.

Momentum space imaging of the FFLO state

In a magnetic field superconductors (SC) with small orbital effect exhibit the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase above the Pauli limiting field. It is characterized by Cooper pairs with finite center of mass momentum and is stabilized by the gain in Zeeman energy of depaired electrons in the imbalanced Fermi gas. The ground state is a coherent superposition of paired and depaired states. This concept, although central to the FFLO state lacks a direct experimental confirmation. We propose that STM quasiparticle interference (QPI) can give a direct momentum space image of the depaired states in the FFLO wave function. For a proof of principle we investigate a 2D single orbital tight binding model with a SC s-wave order parameter. Using the equilibrium values of pair momentum and SC gap we calculate the spectral function of quasiparticles and associated QPI spectrum as function of magnetic field. We show that the characteristic depaired Fermi surface parts appear as a fingerprint in the QPI spectrum of the FFLO phase and we demonstrate its evolution with field strength. Its observation in STM experiments would constitute a direct proof for FFLO ground state wave function.

New Theory of Superconductivity. Does the London Equation Have the Proper Solution? No, It Does Not. Self-Generated and External Magnetic Fields in Superconductors

Hereby it studied the fundamental theory created by the London brothers for interpretation of the magnetic field reduction in superconductors. As demonstrated, this theory is not correct. The author of this work has developed the new theory of superconductivity. The equation describing the electron distribution function under the effect of magnetic field explains existence of the Meissner-Ochsenfeld effect. It is shown that the critical field equation matches the width of a potential well in the kinetic energy dependence of mean electron energy. As a result, the supercurrent density formula has been derived. Existence of magnetic fields is explained by two steady-state Maxwell equations. There are magnetic fields that are found to be created in individually shaped metals. Penetration of the external magnetic field in a superconductor has been explained.

New Theory of Superconductivity. Magnetic Field in Superconductor. Effect of Meissner and Ochsenfeld

A new variational method has been proposed for studying the equilibrium states of the interacting particle system to have been statistically described by using the density matrix. This method is used for describing conductivity electrons and their behavior in metals. The electron energy has been expressed by means of the density matrix. The interaction energy of two ekk′ electrons dependent on their wave vectors k and k’ has been found. Energy ekk′ has two summands. The first energy I summand depends on the wave vectors to be equal in magnitude and opposite in direction. This summand describes the repulsion between electrons. Another energy J summand describes the attraction between the electrons of equal wave vectors. Thus, the equation of wavevector electron distribution function has been obtained by using the variational method. Particular solutions of the equations have been found. It has been demonstrated that the electron distribution function exhibits some previously unknown features at low temperatures. Repulsion of the wave vectors k and –k electrons results in anisotropy of the distribution function. This matter points to the electron superconductivity. Those electrons to have equal wave vectors are attracted thus producing pairs and creating an energy gap. It is considered the influence of magnetic field on the superconductor. This explains the phenomenon of Meissner and Ochsenfeld. We consider a new possibility of penetration of the external magnetic field into the superconductor.

Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiralp-wave superconductor

Majorana quasiparticles localized in vortex cores of a chiral p-wave superconductor hybridize with one another to form bands in a vortex lattice. We begin by solving a fully microscopic theory describing all quasiparticle bands in a chiral p-wave superconductor in magnetic field, then use this solution to build localized Wannier wavefunctions corresponding to Majorana quasiparticles. A low-energy tight-binding theory describing the intervortex hopping of these is then derived, and its topological properties---which depend crucially on the signs of the imaginary intervortex hopping parameters---are studied. We show that the energy gap between the Majorana bands may be either topologically trivial or nontrivial, depending on whether the Chern number contributions from the Majorana bands and those from the background superconducting condensate add constructively or destructively. This topology directly affects the temperature-dependent thermal Hall conductivity, which we also calculate.

Berry phases and the intrinsic thermal Hall effect in high-temperature cuprate superconductors.

Bogolyubov quasiparticles move in a practically uniform magnetic field in the vortex state of high-temperature cuprate superconductors. When set in motion by an externally applied heat current, the quasiparticles' trajectories may bend, causing a temperature gradient perpendicular to the heat current and the applied magnetic field, resulting in the thermal Hall effect. Here we relate this effect to the Berry curvature of quasiparticle magnetic sub-bands, and calculate the dependence of the intrinsic thermal Hall conductivity on superconductor's temperature, magnetic field and the amplitude of the d-wave pairing. The intrinsic contribution to thermal Hall conductivity displays a rapid onset with increasing temperature, which compares favourably with existing experiments at high magnetic field on the highest purity samples. Because such temperature onset is related to the pairing amplitude, our finding may help to settle a much-debated question of the bulk value of the pairing strength in cuprate superconductors in magnetic field.