By Ji L.

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**Additional info for 2-idempotent 3-quasigroups with a conjugate invariant subgroup consisting of a single cycle of length four**

**Example text**

In this case, the temperature dependence of the thermodynamic properties is quantitatively related to the density of states and shows power laws depending on the position and form of the line or point nodes of the superconducting gap. If the scattering phase shift is near the Born limit δ = 0 no clear predictions can be made. Unitary scattering leads to virtual bound states on the impurity sites. For the typical concentration of impurities, these bound states overlap and lead to a small “normal state-like” contribution (linear in T ) to κ.

Therefore, the measured ﬁeld distribution is a convolution of the distribution due to the Knight shift and the ﬂux-line lattice [21]. The line broadening due to the presence of the ﬂux-line lattice is traditionally assumed to be Gaussian. The muon depolarization rate then is given by σ ∝ 1/λ2 ∝ n s , where λ is the magnetic penetration depth and n s the superﬂuid density. Therefore, such studies yield information on the absolute value of λ, its anisotropy, and the temperature dependence λ(T ) which gives information about the gap nodes (see Sect.

Together with neutron scattering and NMR, it is one of the very few microscopic methods investigating the bulk of the material, as the muons penetrate tenth of a millimetre into the sample. In recent years, µSR has become a primary method for the study of type-II superconductors, because muons are an ideal tool to investigate weak-magnetism phenomena in zero external ﬁeld, and can be utilized to search for the occurrence of spontaneous magnetism below T c , which would signal a possible breakdown of the time-reversal symmetry invariance.

### 2-idempotent 3-quasigroups with a conjugate invariant subgroup consisting of a single cycle of length four by Ji L.

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