Dynamic structure of the intermediate state was studied in pinning-free thick Pb strips using real-time magneto-optical visualization. It is found that topological hysteresis can be lifted by applying sufficiently large current. Namely, laminar structure that appears on flux exit in a static case is turned into tubular when the sufficiently large transport current is present. Size and distribution of the flux tubes in static and dynamic regimes are different. Temperature, magnetic field and current phase diagram is discussed.
The attenuation of ultrasound (the geometric resonance) in an intermediate state of the type I superconductors at kaN >> 1 is researched. The oscillating dependence of ultrasound attenuation, which has an amplitude modulation as a result of presence of the Andreev reflec-tions by the electronic excitations on the boundaries between the normal metal layer and the superconducting layer in an intermediate state of the type I superconductor, is obtained. The derived theoretical equation explains the nature of experimental results in [1, 2].
Intermediate state (IS) flux structures in mesoscopic type-I superconductors are investigated within the Ginzburg-Landau theory. In addition to well-established tubular and laminar structures, the strong confinement leads to the formation of (i) a phase of singly quantized vortices, which is typical for type-II superconductors and (ii) a ring of a normal domain at equilibrium. The stability region and the formation process of these IS flux structures are strongly influenced by the geometry of the sample.
M. Tinkham and P. G. de Gennes, described in their books the existence of an intermediate type-I superconductor as a consequence of an external surface that affects the well known classification of superconductors into type-I and II. Here we consider the mesoscopic superconductor where the ratio volume to area is small and the effects of the external surface are enhanced. By means of the standard Ginzburg-Landau theory the Tinkham-de Gennes scenario is extended to the mesoscopic type-I superconductor. We find new features of the transition at the passage from the genuine to the intermediate ty…
The magnetic vortices in superconductors usually repel each other. Several cases are discussed when the vortex interaction has an attractive tail and thus a minimum, leading to vortex clusters and chains. Decoration pictures then typically look like in the intermediate state of type-I superconductors, showing lamellae or islands of Meissner state or surrounded by Meissner state, but with the normal regions filled with Abrikosov vortices that are typical for type-II superconductors in the mixed state. Such intermediate-mixed state was observed and investigated in detail in pure Nb, TaN and othe…
Magneto-optical imaging of thick stress-free lead samples reveals two distinct topologies of the intermediate state. Flux tubes are formed upon magnetic field penetration (closed topology) and laminar patterns appear upon flux exit (open topology). Two-dimensional distributions of shielding currents were obtained by applying an efficient inversion scheme. Quantitative analysis of the magnetic induction distribution and correlation with magnetization measurements indicate that observed topological differences between the two phases are responsible for experimentally observable magnetic hysteres…
We consider dynamics of Josephson vortex lattice in layered superconductors with magnetic, charge (electrostatic) and charge-imbalance (quasiparticle) interactions between interlayer Josephson junctions taken into account. The macroscopic dynamical equations for interlayer Josephson phase differences, intralayer charge and electron-hole imbalance are obtained and used for numerical simulations. Different transformations of the vortex lattice structure are observed. It is shown that the additional dissipation due to the charge imbalance relaxation leads to the stability of triangular lattice.
The physics behind the rhombic$\to$square$\to$rhombic flux line lattice transformation in increasing fields is clarified on the basis of Eilenberger theory. We demonstrate that this reentrance observed in LuNi$_2$B$_2$C is due to intrinsic competition between superconducting gap and Fermi surface anisotropies. The calculations reproduce not only it but also predict yet not found lock-in transition to a square lattice with different orientation in higher field. In view of physical origin given, this sequence of transitions is rather generic to occur in four-fold symmetric superconductors.
We present simulations of the intermediate state of type-I superconducting films solving the time dependent Ginzburg-Landau equations, which include the demagnetizing fields via the Biot-Savart law. For small square samples we find that, when slowly increasing the applied magnetic field $H_a$, there is a saw-tooth behavior of the magnetization and very geometric patterns, due to the influence of surface barriers; while when slowly decreasing $H_a$, there is a positive magnetization and symmetry-breaking structures. When random initial conditions are considered, we obtain droplet and laberynthi…
A superconductor in a magnetic field has surface currents that prevent the magnetic field from penetrating its interior. These currents carry kinetic energy and mechanical momentum. When the temperature is raised and the system becomes normal the currents disappear. Where do the kinetic energy and mechanical momentum of the currents go, and how? Here we propose that the answer to this question reveals a key necessary condition for materials to be superconductors, that is not part of conventional BCS-London theory: superconducting materials need to have hole carriers.
Since the discovery of the Meissner effect the superconductor to normal (S-N) phase transition in the presence of a magnetic field is understood to be a first order phase transformation that is reversible under ideal conditions and obeys the laws of thermodynamics. The reverse (N-S) transition is the Meissner effect. This implies in particular that the kinetic energy of the supercurrent is not dissipated as Joule heat in the process where the superconductor becomes normal and the supercurrent stops. In this paper we analyze the entropy generation and the momentum transfer between the supercurr…
Structure of the intermediate state in type-I superconducting lead (Pb) is shown to be very sensitive to the ramp rate of an applied magnetic field. The configurations of resulting static patterns depend sensitively on the shape of the specimen. In particular, geometric barrier, present in the samples with rectangular cross-section, plays an important role in determining the sharp boundary between the phases of different topology. We propose that seemingly laminar (stripe) pattern obtained as a result of the fast field ramp is simply an imprint left behind by the fast-moving flux tubes. Our re…
The geometric structure of an intermediate state in the high pure Gallium single crys-tal at the external magnetic field Hext at the temperature T=0.4 K is researched, using the longi-tudinal ultrasonic signal attenuation method at the ultrasonic signal frequency of 30 MHz. It is experimentally shown that the edge inhomogeneities of the magnetic field distribution have an influence on the structure of an intermediate state in the cylindrical superconductor samples at the transverse orientation of external magnetic field Hext. It is shown that the use of the super-conducting plane screens of Nb…
High-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres and discs. Combined with the measurements of macroscopic magnetization these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to geometric barrier that results in a topological hysteresis -- flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have geometric barrie…
To address unsolved fundamental problems of the intermediate state (IS), the equilibrium magnetic flux structure and the critical field in a high purity type-I superconductor (indium film) are investigated using magneto-optical imaging with a 3D vector magnet and electrical transport measurements. The least expected observation is that the critical field in the IS can be as small as nearly 40% of the thermodynamic critical field $H_c$. This indicates that the flux density in the \textit{bulk} of normal domains can be \textit{considerably} less than $H_c$, in apparent contradiction with the lon…
To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the meltin…
In the intermediate state of a thin type-I superconductor magnetic flux penetrates in a disordered set of highly branched and fingered macroscopic domains. To understand these shapes, we study in detail a recently proposed "current-loop" (CL) model that models the intermediate state as a collection of tense current ribbons flowing along the superconducting-normal interfaces and subject to the constraint of global flux conservation. The validity of this model is tested through a detailed reanalysis of Landau's original conformal mapping treatment of the laminar state, in which the superconducto…
The importance of accounting for the inhomogeneity of the magnetic field distribution and roundness of domain walls near the surface of type-I superconductors in the intermediate state for forming the equilibrium flux structure was predicted by Landau eight decades ago. Further studies confirmed this prediction and extended it to all equilibrium properties of this state. Here we report on direct depth-resolved measurements of the field distribution and shape of domains near the surface of high-purity type-I (indium) films in a perpendicular field using Low-Energy Muon Spin Rotation spectroscop…
The hole doped Fe-based superconductors Ba$_{1-x}$A$_x$Fe$_2$As$_2$ (where A=Na or K) show a particular rich phase diagram. It was observed that an intermediate re-entrant tetragonal phase forms within the orthorhombic antiferromagnetically-ordered stripe-type spin density wave state above the superconducting transition [S. Avci et al., Nature Comm. 5, 3845 (2014), A. E. Böhmer et al., arXiv:1412.7038v2]. A similar intermediate phase was reported to appear if pressure is applied to underdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ [E. Hassinger et al., Phys. Rev. B 86, 140502(R) (2012)]. Here we report d…
By extending the original Anderson singular gauge transformation for static vortices to two mutual flux-attaching singular gauge transformations for moving vortices, we derive an effective action describing the zero temperature quantum phase transition from d-wave superconductor to underdoped regime. Neglecting the charge fluctuation first, we find that the mutual statistical interaction is exactly marginal. In the underdoped regime, the quasi-particles are described by 2+1 dimensional QED; in the superconducting regime, they are essentially free. However, putting back the charge fluctuation c…
Relaxation Dynamics of Superconducting/Normal Interfaces in the Intermediate State of a type-I superconductor
Low Temperature Physics Laboratory, College of Physics & Center of Quantum Materials and Devices, Chongqing University（重庆大学物理学院低温物理实验室与量子材料与器件中心）；Materials Genome Institute, Shanghai University（上海大学材料基因组研究院）
The formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains surrounded by the superconducting phase. The distribution of domain surface areas is found to exhibit a threshold, above which only the lamellar shape is observed. We show that this threshold coincides with the predicted critical surface area for the elongation instability of the circular shape. The partition of the normal phase into circular and lamellar d…
The equations of viscous evolution of 3D arbitrarily shaped vortices in an isotropic type II superconductor and necessary boundary conditions are formulated in the frame of London approximation. The theory is applied to analyse characteristic scenaria of vortex penetration into current-carrying thick plate or bulk samples with another geometry. It is shown that regarding of the surface transport current value a vortex penetrates either as "flexible stick" or as "elastic thread". The latter regime is accompanied by giant stretching of the vortex core along the current-induced surface magnetic f…
A simplified model of c axis transport in the high T_c superconductors is presented. Expressions are found for the c axis optical conductivity, the d.c. resistivity, and the c axis penetration depth. Within the framework of this model, the pseudogap in the optical conductivity arises naturally as a result of the layered band structure of the high T_c materials. We discuss the occurence of the pseudogap in terms of three parameters: a band gap Delta_{ps}, a temperature dependent scattering rate Gamma(T), and the strength of the interlayer coupling t_{perp}. We are also able to find analytic exp…
The calculation of spatial structure of a quantum intermediate state in high pure type I superconductors in external magnetic field at low temperatures is completed. The theoretical model of thermodynamics of intermediate state in type I superconductors was proposed by Andreev. It is shown, that in the quantum case, the period of structure of quantum intermediate state appears to be significantly shorter and it has different dependences on the magnetic field H and temperature T in comparison with the classical intermediate Landau state. The decrease of thickness of normal layers results in the…
We investigate two-dimensional Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to an additional depletion of the superfluid density. We demonstrate the existence of the intermediate superfluid state where the condensate and localized bosons 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 the three dimensiona…
Normal state bubble patterns in Type I superconducting Indium and Lead slabs are studied by the high resolution magneto-optical imaging technique. The size of bubbles is found to be almost independent of the long-range interaction between the normal state domains. Under bubble diameter and slab thickness proper scaling, the results gather onto a single master curve. On this basis, in the framework of the "current-loop" model [R.E. Goldstein, D.P. Jackson and A.T. Dorsey, Phys. Rev. Lett. 76, 3818 (1996)], we calculate the equilibrium diameter of an isolated bubble resulting from the competitio…
A microwave cavity perturbation technique is used to probe the interlayer electrodynamics within the vortex state of the organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2. A Josephson plasma mode is observed which is extremely sensitive to correlations in the locations of vortices in adjacent layers and may, therefore, be used to gauge collective effects between vortices and crystal pinning sites in the title compound. Our previous investigations [M. M. Mola et al., Phys. Rev. B 62 (2000) 5965] revealed a transformation from a correlated quasi-two-dimensional pinned vortex phase, to either a de…
We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anom…
We explore a BCS Bose Einstein crossover scenario for $0 \leq T \leq T_c$ and its implications for the superfluid density and specific heat. The low lying excitations consist of nodal (fermionic) quasi-particles as well as excited (bosonic) pair states. Semi-quantitative comparison with cuprate data is reasonable, with no compelling indications for Landau parameter effects.
Controlled Manipulation of Intermediate State in a Type-I Superconductor
Materials Genome Institute, Shanghai University（上海大学材料基因组研究院）；Department of Physics, Shanghai Key Laboratory for High Temperature Superconductors, Shanghai University（上海大学物理系高温超导上海市重点实验室）；Institute for Quantum Science and Technology, Shanghai University（上海大学量子科学与技术研究院）
The research on the longitudinal ultrasound absorption in an intermediate state of the high pure Gallium single crystal at the frequency of 50-190MHz at the temperatures of 0,37-0,75 K, using the impulse method, is conducted. The new effects in the absorption of ultrasound in an intermediate state of the high pure type I superconductor are discovered. The big oscillations in the dependence of the ultrasound absorption on the magnetic field in an intermediate state of the high pure Gallium single crystal are experimentally observed at the magnitudes of magnetic field below the critical magnetic…
We show that the fully polarized triplet s-wave component is characterized not only by the spin direction, but also by chirality. Interaction of a polarized triplet component and a singlet one results in creation of triplet Cooper pairs with opposite spin direction or of different chiralities. Such spin transformation leads to interesting phenomena in multiterminal magnetic Josephson junctions. We calculate the dc Josephson current $I_{\text{J}}$ in a multiterminal Josephson contact of the S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ type with "magnetic" superconductors S$_{\text{m}}$ that generat…
An exact particle-hole transformation is discovered in a local-moment model for a single layer of heavily electron-doped FeSe. The model harbors hidden magnetic order between the iron d_xz and d_yz orbitals at the wavenumber (pi,pi). It potentially is tied to the magnetic resonances about the very same Neel ordering vector that have been recently discovered in intercalated FeSe. Upon electron doping, the local-moment model successfully accounts for the electron-pocket Fermi surfaces observed experimentally at the corner of the two-iron Brillouin zone in electron-doped FeSe, as well as for isot…
The dependence of the ultrasonic attenuation on the direction of magnetic field in an intermediate state of the very pure Gallium single crystal, in the case, when the magnetic field H is perpendicular to the wave vector k at the temperature T = 0.5 K, is found to be anomalously different from the dependence, observed at the same temperature and the magnitude of magnetic field equal to the critical magnetic field H=Hc in a normal state of superconductor. This new phenomenon can be explained, considering the anisotropy of the Fermi surface in the very pure Gallium single crystal.
The transformation of the vortex lattice in a tetragonal superconductor which consists of its 45 degree reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two successive second order (continuous) phase transitions. The transition magnetic fields are calculated for a range of parameters relevant for borocarbide superconductors in which the reorientation has been observed.
Magnetic relaxation in a type-II superconductor is simulated for a range of temperatures (T) in a simple model of 2D Josephson junction array (JJA) with finite screening. The high-T phase, that is characterised by a single time scale τ_α, crosses over to an intermediate phase at a lower temperature T_{cr} wherein a second time scale τ_β<<τ_α emerges. The relaxation in the time window set by τ_β follows power law which is attributed to self-organization of the magnetic flux during relaxation. Consequently, for T<T_{cr}, a transition from super-critical (current density J>J_{c}) to sub-critical …
We argue that a normal Fermi liquid and a singlet, spin gapped Mott insulator cannot be continuously connected, and that some intermediate phase must intrude between them. By explicitly working out a case study where the singlet insulator is stabilized by orbital degeneracy and an inverted Hund's rule coupling, mimicking a Jahn-Teller effect, we find that the intermediate phase is a superconductor.
In this paper we analyze the structure, phase transitions and some transport properties of the vortex system when the external magnetic field lies parallel to the planes in layered superconductors. We show that experimental results for resistivity are qualitatively consistent with numerical simulations that describe the melting of a commensurate rotated lattice. However for some magnetic fields, the structure factor indicates the occurrence of smectic peaks at an intermediate temperature regime.
Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase like vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg -- Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transitions line. The line however makes a wiggle near the experimentally claimed critical point at 12T.…
By applying an exact unitary transformation to a two-band hamiltonian which also includes the effects due to large pnictogen polarizabilities, we show that an attractive spin-mediated Hubbard term appears in the $d_{xz}$, $d_{yz}$ nearest-neighbour channel. This pairing mechanism implies a singlet superconducting order parameter in iron pnictides.
A three-dimensional lattice of the Josephson junctions with a finite self-conductance is employed to model ceramic superconductors. Using Monte Carlo simulations it is shown that the aging disappears in the strong screening limit. In the weeak screening regime aging is present even at low temperatures. For intermediate values of the self-inductance aging occurs at intermediate temperatures interval but is suppressed entirely at high and low temperatures. Our results are in good agreement with experiments.
Here we show that a pressure of about 8 GPa suppresses both the vacancy order and the insulating phase, and a further increase of the pressure to about 18 GPa induces a second transition or crossover. No superconductivity has been found in compressed insulating 245 phase. The metallic phase in the intermediate pressure range has a distinct behavior in the transport property, which is also observed in the superconducting sample. We interpret this intermediate metal as an orbital selective Mott phase (OSMP). Our results suggest that the OSMP provides the physical pathway connecting the insulatin…
Magnetic hysteresis loops (MHLs) have been comparatively measured on both textured and single crystalline Sc5Ir4Si10 superconductors. Critical current densities and flux pinning forces are calculated from MHLs by Bean model. Three kinds of peaks of the flux pinning force are found at low fields near zero, intermediated fields, and high fields near the upper critical field, respectively. The characters and origins of these peaks are studied in detail.
Cubic Pm-3n Nb3Sn0.92 superconductor (Tc ~ 16 K) was found to exhibit tetragonal instabilities at the superconducting state (T = 10 K). These instabilities are manifested through the appearance of reflections which are forbidden in the Pm-3n symmetry but are compatible with the P42/mmc structure which is observed in the Nb3Sn1-x system for higher Sn content at temperatures lower than ~ 43 K. Nevertheless, the low-temperature structure of Nb3Sn0.92 remains metrically fully cubic, as concluded from single crystal synchrotron radiation diffraction experiments. Subsequent application of external p…
The ThCr2Si2-type arsenide-selenide phase KFe2AsSe is proposed as a parent system for a new "intermediate" group of Fe-based superconducting materials bridging the known families of Fe-pnictides (such as BaFe2As2) and Fe-chalcogenides (such as KxFe2-ySe2) superconductors. The characterization of the proposed charge-balanced phase by means of FLAPW-GGA approach covers the crystal structure, As/Se atomic ordering, stability, electronic bands, Fermi surface, and density of electronic states.
In a type II superconductor in a moderate magnetic field, the superconductor to normal state transition may be described as a phase transition in which the vortex lattice melts into a liquid. In a biaxial superconductor, or even a uniaxial superconductor with magnetic field oriented perpendicular to the symmetry axis, the vortices acquire elongated cross sections and interactions. Systems of anisotropic, interacting constituents generally exhibit liquid crystalline phases. We examine the possibility of a two step melting in homogeneous type II superconductors with anisotropic superfluid stiffn…
Motivated by the recent experimental observation of an intermediate bosonic metallic state in the two-dimensional superconductor-insulator transition at $T=0$, we study an extended Bose Hubbard model in the limit of large number of particles per site. Using a representation of this in terms of two coupled $XY$ models, we find, in addition to an insulating phase and a $(2+1)D$ superfluid phase, two other phases. One phase is a $2D$ superfluid phase where a crossover from $(2+1)D$ to $2D$ has taken place as a result of incipient charge ordering, signaled by $θ$ disordering, and which is closely …
We present high-resolution measurements of the coefficient of thermal expansion $α(T)=\partial \ln l(T)/\partial T$ of the quasi-twodimensional (quasi-2D) salts $κ$-(BEDT-TTF)$_2$X with X = Cu(NCS)$_2$, Cu[N(CN)$_2$]Br and Cu[N(CN)$_2$]Cl. At intermediate temperatures (B), distinct anomalies reminiscent of second-order phase transitions have been found at $T^\ast = 38$ K and 45 K for the superconducting X = Cu(NCS)$_2$ and Cu[N(CN)$_2$]Br salts, respectively. Most interestingly, we find that the signs of the uniaxial pressure coefficients of $T^\ast$ are strictly anticorrelated with those of $…
The experimental research of the longitudinal ultrasound absorption in an intermediate state of the high pure Ga single crystal at the frequencies of 30 - 130 MHz at the temperatures of 0.4 - 0.5 K, using the impulse method, is completed. The new effects in the absorption of ultrasound in an intermediate state of the high pure type I superconductor are discovered. The giant oscillations in the dependence of the ultrasound absorption on the magnetic field at the magnitudes below the critical magnetic field, H < Hc, in an intermediate state of the high pure Ga single crystal are experimentally o…
We present direct imaging of magnetic flux structures in the anisotropic, spin-triplet superconductor Sr$_{2}$RuO$_{4}$ using a scanning $μ$SQUID microscope. Individual quantized vortices were seen at low magnetic fields. Coalescing vortices forming flux domains were revealed at intermediate fields. Based on our observations we suggest that a mechanism intrinsic to the material stabilizes the flux domains against the repulsive vortex-vortex interaction. Topological defects like domain walls can provide this, implying proof for unconventional chiral superconductivity.
The nature of the pseudogap phase remains a major barrier to our understanding of cuprate high-temperature superconductivity. Whether or not this metallic phase is defined by any of the reported broken symmetries, the topology of its Fermi surface remains a fundamental open question. Here we use angle-dependent magnetoresistance (ADMR) to measure the Fermi surface of the cuprate Nd-LSCO. Above the critical doping $p^*$ -- outside of the pseudogap phase -- we fit the ADMR data and extract a Fermi surface geometry that is in quantitative agreement with angle-resolved photoemission. Below $p^*$ -…
The quantization of magnetic flux in superconductors is usually seen as vortices penetrating the sample. While vortices are unstable in bulk type I superconductors, restricting the superconductor causes a variety of vortex structures to appear. We present a systematic study of giant vortex states in type I superconductors obtained by numerically solving the Ginzburg-Landau equations. The size of the vortices is seen to increase with decreasing film thickness. In type I superconductors, giant vortices appear at intermediate thicknesses but they do not form a well-defined vortex lattice. In the …
We consider some properties of odd frequency triplet superconducting condensates. In order to describe fluctuations we construct a supermatrix sigma-model for the superconductor/ferromagnet or superconductor/normal-metal structures. We show that an odd frequency triplet superconductor, when in isolation or coupled to a normal metal, generally displays behaviour comparable to a superconductor with the usual singlet pairings. However, for spin dependent systems such as the superconductor/ferromagnet the two types of superconductor have quite different behaviour. We discuss this difference by con…
