Muons with 100% spin polarization and whose energy can be continuously varied from 0.5 to 30 keV provide a novel extension of the μSR technique allowing depth dependent studies of thin films and multilayered structures in the range from ∼1 to ∼200 nm. For example it is possible to study magnetic field profiles near the surface of superconductors and directly determine fundamental quantities such as the magnetic penetration depth. Low energy muons (LE-μ + ) also allow mapping the spin polarization in multilayered structures, for instance that of the conduction electrons of a non-magnetic buried layer in between thin ferromagnetic layers.

https://iopscience.iop.org/article/10.1088/0953-8984/16/40/010/pdf

Nano-scale thin film investigations with slow polarized muons

Key questions for any superconductor include: what is its maximum dissipation-free electrical current (its ‘critical current') and can this be used to extract fundamental thermodynamic parameters? Present models focus on depinning of magnetic vortices and implicate materials engineering to maximise pinning performance. But recently we showed that the self-field critical current for thin films is a universal property, independent of microstructure, controlled only by the penetration depth. Here, using an extended BCS-like model, we calculate the penetration depth from the temperature dependence of the superconducting energy gap thus allowing us to fit self-field critical current data. In this way we extract from the T-dependent gap a set of key thermodynamic parameters, the ground-state penetration depth, energy gap and jump in electronic specific heat. Our fits to 79 available data sets, from zinc nanowires to compressed sulphur hydride with critical temperatures of 0.65 to 203 K, respectively, are excellent and the extracted parameters agree well with reported bulk values. Samples include thin films, wires or nanowires of single- or multi-band s-wave and d-wave superconductors of either type I or type II. For multiband or multiphase samples we accurately recover individual band contributions and phase fractions.

Thermodynamic Parameters of Single‐ or Multi‐Band Superconductors Derived from Self‐Field Critical Currents

Quantum transport in GaInAs-AlInAs heterojunctions, and the influence of intersubband scattering

https://repository.ubn.ru.nl/bitstream/handle/2066/115596/115596.pdf

A study of intersubband scattering in GaAs/AlxGa1−xAs heterostructures by means of a parallel magnetic field

Implanting fully polarized low energy muons on the nanometer scale beneath the surface of a superconductor in the Meissner state enabled us to probe the evanescent magnetic field profile $B(z)$ ($0lz\ensuremath{\lesssim}200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ measured from the surface). All the investigated samples [$\mathrm{Nb}:\ensuremath{\kappa}\ensuremath{\simeq}0.7(2)$, $\mathrm{Pb}:\ensuremath{\kappa}\ensuremath{\simeq}0.6(1)$, $\mathrm{Ta}:\ensuremath{\kappa}\ensuremath{\simeq}0.5(2)$] show clear deviations from the simple exponential $B(z)$ expected in the London limit, thus revealing the nonlocal response of these superconductors. From a quantitative analysis within the Pippard and BCS models the London penetration depth ${\ensuremath{\lambda}}_{L}$ is extracted. In the case of Pb the clean limit coherence length ${\ensuremath{\xi}}_{0}$ is obtained. Furthermore we find that the temperature dependence of the magnetic penetration depth follows closely the two-fluid expectation $1∕{\ensuremath{\lambda}}^{2}\ensuremath{\propto}1\ensuremath{-}{(T∕{T}_{c})}^{4}$. While $B(z)$ for Nb and Pb are rather well described within the Pippard and BCS models, for Ta this is only true to a lesser degree. We attribute this discrepancy to the fact that the superfluid density is decreased by approaching the surface on a length scale ${\ensuremath{\xi}}_{0}$. This effect, which is not taken self-consistently into account in the mentioned models, should be more pronounced in the lowest $\ensuremath{\kappa}$ regime consistently with our findings.

/pdf/observation-of-nonexponential-magnetic-penetration-profiles-pfim6tqbdg.pdf

Observation of nonexponential magnetic penetration profiles in the Meissner state: A manifestation of nonlocal effects in superconductors

The transconductance of an accumulation layer on $n$-type InAs is studied in a magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the layer. Structures are observed, nonperiodic in $\frac{1}{H}$, corresponding to mixed electric and magnetic subbands. The effect promises a simple, sensitive method of probing the shape of the self-consistent potential in surface space-charge layers with multiply occupied subbands.

Hybrid Quantum Oscillations in a Surface Space-Charge Layer

Determination of subband populations in tipped magnetic fields

Magnetoabsorption resonances in superconducting Al are studied as a function of magnetic field orientation and temperature in the (100) and (110) crystal planes. Using a recent theoretical calculation describing the quasiparticle energy levels, we extract from the experimental data the variation of penetration depth lambda with crystal plane and field orientation. The overall anisotropy in lambda at T = 0 is found to be about 10%, with values in the range 460--510 A. Our lambda variation is compared with that predicted by simple tensor analysis.

Quasiparticle magnetospectroscopy and penetration-depth anisotropy in superconducting aluminum

Microwave magnetoabsorption peaks in single-crystal superconducting Al have been identified by comparison with a detailed calculation of quasiparticle energy levels. The peaks correspond to resonant transitions between states bound in the magnetic-field penetration layer as predicted by Pincus. By fitting the observed spectra to the calculations, we are able to extract the penetration length lambda and a second parameter describing the shape of the nonlocal-field penetration.

S. Whitmore

Papers

Hybrid Quantum Oscillations in a Surface Space-Charge Layer

Determination of subband populations in tipped magnetic fields

Quasiparticle magnetospectroscopy and penetration-depth anisotropy in superconducting aluminum

Quasiparticle Magnetospectroscopy in Superconductors: A Detailed Look at the Shape of the Penetration Layer