Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Besides measurement of the critical current density jc and of creep rates S, the ac magnetic response provides valuable information on the pinscape which is different from that obtained through jc or S, with the Campbell penetration depth λC defining a characteristic quantity well accessible in an experiment. Here, we derive a microscopic expression for the Campbell penetration depth λC using strong pinning theory. Our results explain the dependence of λC on the state preparation of the vortex system and the appearance of hysteretic response. Analyzing different pinning models, metallic or insulating inclusions as well as δTc-and δ -pinning, we discuss the behavior of the Campbell length for different vortex state preparations within the phenomenological H-T phase diagram and compare our results with recent experiments.

The current-carrying capacity of type-II superconductors is decisively determined by how well material defect structures can immobilize vortex lines. In order to gain deeper insights into the fundamental pinning mechanisms, we have explored the case of vortex trapping by randomly distributed spherical inclusions using large-scale simulations of the time-dependent Ginzburg-Landau equations. We find that for a small density of particles having diameters of two coherence lengths, the vortex lattice preserves its structure and the critical current jc decays with the magnetic field following a power-law B −α with α ≈ 0.66, which is consistent with predictions of strong-pinning theory. For a higher density of particles and/or larger inclusions, the lattice becomes progressively more disordered and the exponent smoothly decreases down to α ≈ 0.3. At high magnetic fields, all inclusions capture a vortex and the critical current decays faster than B −1 as would be expected by theory. In the case of larger inclusions with a diameter of four coherence length, the magnetic-field dependence of the critical current is strongly affected by the ability of inclusions to capture multiple vortex lines. We found that at small densities, the fraction of inclusions trapping two vortex lines rapidly grows within narrow field range leading to a peak in jc(B)-dependence within this range. With increasing inclusion density, this peak transforms into a plateau, which then smooths out. Using the insights gained from simulations, we determine the limits of applicability of strong-pinning theory and provide different routes to describe vortex pinning beyond those bounds.

Measuring the ac magnetic response of a type II superconductor provides valuable information on the pinning landscape (pinscape) of the material. We use strong pinning theory to derive a microscopic expression for the Campbell length λC, the penetration depth of the ac signal. We show that λC is determined by the jump in the pinning force, in contrast to the critical current jc which involves the jump in pinning energy. We demonstrate that the Campbell lengths generically differ for zero-field-cooled and field-cooled samples and predict that hysteretic behavior can appear in the latter situation. We compare our findings with new experimental data and show the potential of this technique in providing information on the material's pinscape. 74.25.Op, 74.25.Wx, 74.25.Ha Technologically useful superconductors are of second type and acquire their desired transport and magnetic properties through vortex pinning, i.e., vortices [1] get immobilized by material defects. The characterization of the pinning landscape (or pinscape) is of great importance but presents quite a formidable task. Measurements of dc transport properties, either dynamically through the current-voltage characteristic [2] or statically through magnetization [3], are standard techniques used to gain information on the pinscape. Similarly, the ac magnetic response of superconducting samples [4] provides insight into the shape of pinning potentials. Unfortunately, the relation between the measured penetration depth of the ac signal, the so-called Campbell length λ C , and the parameters of the pinscape is only known on a phenomenological level. In this letter, we present a microscopic derivation of the Campbell length within the framework of strong pinning theory, thereby providing access to microscopic parameters of pinning defects and substantially enlarging the scope of applications of this measurement technique.Probing superconductors via their ac magnetic response goes back to the 60-ies and culminated in Campbell's work [4] which provided the first consistent explanation of the penetration phenomenon (see Refs.[5] for further developments): for small ac magnetic-field amplitudes h ac and frequencies ω, vortices oscillate reversibly within their pinning potentials (described as harmonic wells α x 2 /2), with the external signal h ac penetrating the sample on a distance λ C ∝ B/ √ α of order micrometers. Later work by Lowell [6] and Campbell [7] provided a more quantitative but still phenomenological understanding within a model pinscape. Here, we make use of the strong pinning scenario allowing us to perform a quantitative and microscopic analysis of the ac magnetic response. In particular, we find the dependence of the Campbell penetration depth λ C on the vortex state, e.g., the critical (Bean [3]) state with a linear vortex density gradient supporting the critical current density j c or a field-cooled state with a constant induction B, and predict the occurrence of new hysteretic effects. The comparison with recent experiments [8] confirms...

7 and RbEuFe 4 As 4 8 , and should be contrasted to results on arXiv:1811.00480v2 [cond-mat.supr-con]

Spontaneous rotational-symmetry breaking in the superconducting state of doped Bi2Se3 has attracted significant attention as an indicator for topological superconductivity. In this paper, high-resolution calorimetry of the single-crystal Sr0.1Bi2Se3 provides unequivocal evidence of a twofold rotational symmetry in the superconducting gap by a bulk thermodynamic probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the material's low carrier concentration proving bulk superconductivity. The large basal-plane anisotropy of Hc2 is attributed to a nematic phase of a two-component topological gap structure η = (η1, η2) and caused by a symmetry-breaking energy term δ(|η1| 2 − |η2| 2 )Tc. A quantitative analysis of our data excludes more conventional sources of this two-fold anisotropy and provides the first estimate for the symmetry-breaking strength δ ≈ 0.1, a value that points to an onset transition of the second order parameter component below 2K.arXiv:1807.11136v2 [cond-mat.supr-con]