Evidence for surface Andreev bound states in cuprate superconductors from penetration depth measurements

Observation of the non-linear Meissner effect

A long-standing theoretical prediction is that in clean, nodal unconventional superconductors the magnetic penetration depth λ, at zero temperature, varies linearly with magnetic field. This non-linear Meissner effect is an equally important manifestation of the nodal state as the well studied linear-in-T dependence of λ, but has never been convincingly experimentally observed. Here we present measurements of the nodal superconductors CeCoIn5 and LaFePO which clearly show this non-linear Meissner effect. We further show how the effect of a small dc magnetic field on λ(T) can be used to distinguish gap nodes from non-nodal deep gap minima. Our measurements of KFe2As2 suggest that this material has such a non-nodal state.

High-TcCooper-pair injection in a semiconductor-superconductor structure

We observe Andreev reflection in a YBCO-GaN junction through differential conductance spectroscopy. A strong characteristic zero-bias peak was observed and persisted up to the critical temperature of the superconductor with a smaller superconducting order parameter Δ ∼ 1 meV. The presence of Andreev reflection with the small Δ in comparison to its value for high-Tcsuperconductors forms an important milestone toward demonstration of superconducting proximity in high-Tc/semiconductor junctions. Experimental results were then compared to the theoretical model with good agreement. Efficient injection of Cooper pairs into direct bandgap semiconducting structures, together with high transition temperature of YBCO, can pave the way to novel optoelectronics and quantum optical studies of high-Tcmaterials.

Dielectric resonator method for determining gap symmetry of superconductors through anisotropic nonlinear Meissner effect

We present a new measurement method which can be used to image the gap nodal structure of superconductors whose pairing symmetry is under debate. This technique utilizes a high quality factor microwave resonance involving the sample of interest. While supporting a circularly symmetric standing wave current pattern, the sample is perturbed by a scanned laser beam, creating a photoresponse that was previously shown to reveal the superconducting gap anisotropy. Simulation and the measurement of the photoresponse of an unpatterned Nb film show less than 8% anisotropy, as expected for a superconductor with a nearly isotropic energy gap along with expected systematic uncertainty. On the other hand, measurement of a YBa₂Cu₃O_7-δ thin film shows a clear 4-fold symmetric image with ∼12.5% anisotropy, indicating the well-known 4-fold symmetric d_x²-y² gap nodal structure in the ab-plane. The deduced gap nodal structure can be further cross-checked by low temperature surface impedance data, which are simultaneously measured. The important advantage of the presented method over the previous spiral resonator method is that it does not require a complicated lithographic patterning process which limits one from testing various kinds of materials due to photoresponse arising from patterning defects. This advantage of the presented technique, and the ability to measure unpatterned samples such as planar thin films and single crystals, enables one to survey the pairing symmetry of a wide variety of unconventional superconductors.

Topological surface states in nodal superconductors

Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states.

The magnetic penetration depth influenced by the proximity to the surface

The effect of smooth inhomogeneities near a superconductor boundary on the magnetic penetration depth λ is studied with emphasis on the proximity-induced spatial dependence of the Cooper pair amplitude. The influence of surface pair breaking or pair formation on λ is described within the Ginzburg-Landau theory, with no model assumptions, for both strongly type-II and strongly type-I homogeneous superconductors. Generic values of λ, which can differ greatly from the London penetration depth, are identified and demonstrated to be induced by large-scale inhomogeneities, when superconductivity is strongly suppressed on the surface.

Imaging the anisotropic nonlinear meissner effect in nodal YBa2 Cu3 O7-δ thin-film superconductors

We have directly imaged the anisotropic nonlinear Meissner effect in an unconventional superconductor through the nonlinear electrodynamic response of both (bulk) gap nodes and (surface) Andreev bound states. A superconducting thin film is patterned into a compact self-resonant spiral structure, excited near resonance in the radio-frequency range, and scanned with a focused laser beam perturbation. At low temperatures, direction-dependent nonlinearities in the reactive and resistive properties of the resonator create photoresponse that maps out the directions of nodes, or of bound states associated with these nodes, on the Fermi surface of the superconductor. The method is demonstrated on the nodal superconductor YBa2Cu3O7-δ and the results are consistent with theoretical predictions for the bulk and surface contributions.

Low-energy subgap states and the magnetic flux periodicity in d-wave superconducting rings

Wave functions of low-energy quasiparticle subgap states in d-wave superconducting rings, threaded by an Aharonov-Bohm magnetic flux, are found analytically. The respective energies are closest to the midgap position at small magnetic fluxes and deviate from the Fermi surface due to the Doppler shift, produced by the supercurrent. The Doppler-shifted zero-energy states result in a paramagnetic response of the ring at small fluxes. The states exist only for even angular momenta of the center of mass of Cooper pairs, in agreement with recent numerical studies of the problem. This macroscopic quantum effect in d-wave rings results in broken h/2e periodicity, retaining only the h/e periodic behavior of the supercurrent with varying magnetic flux.

Singular current response from isolated impurities in d-wave superconductors

The current response of a d-wave superconductor containing a single impurity is calculated and shown to be singular in the low-temperature limit, leading in the case of strong scattering to a 1/T term in the penetration depth lambda(T) similar to that induced by Andreev surface bound states. For a small number of such impurities, we argue this low-T upturn could be observable in cuprate superconductors.