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The superconductivity in the rare-earth transition-metal ternary borides RRuB2 (where R = Lu and Y) has been investigated using muon-spin rotation and relaxation. Measurements made in zero field suggest that time-reversal symmetry is preserved upon entering the superconducting state in both materials; a small difference in depolarization is observed above and below the superconducting transition in both compounds, however, this has been attributed to quasistatic magnetic fluctuations. Transverse-field measurements of the flux-line lattice indicate that the superconductivity in both materials is fully gapped, with a conventional s-wave pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. The electronic properties of the charge carriers in the superconducting state have been calculated, with effective masses m∗/me = 9.8 ± 0.1 and 15.0 ± 0.1 in the Lu and Y compounds, respectively, with superconducting carrier densities ns = (2.73 ± 0.04) × 10^28 m^(−3) and (2.17 ± 0.02) × 10^28 m^(−3). The materials have been classified according to the Uemura scheme for superconductivity, with values for Tc/TF of 1/(414 ± 6) and 1/(304 ± 3), implying that the superconductivity may not be entirely conventional in nature.

The discovery of new families of unconventional superconductors is important both experimentally and theoretically, especially if it challenges current models and thinking. By using muon spin relaxation in zero field, time-reversal symmetry breaking has been observed in Re6Hf. Moreover, the temperature dependence of the superfluid density exhibits s-wave superconductivity with an enhanced electron-phonon coupling. This, coupled with the results from isostructural Re6Zr, shows that the Re6X family is indeed a new and important group of unconventional superconductors.

We systematically investigate the normal and superconducting properties of noncentrosymmetric Re6Zr using magnetization, heat capacity, and electrical resistivity measurements. Resistivity measurements indicate Re6Zr has poor metallic behavior and is dominated by disorder. Re6Zr undergoes a superconducting transition at Tc = (6.75 ± 0.05) K. Magnetization measurements give a lower critical field, μ0Hc1 = (10.3 ± 0.1) mT. The Werthamer-Helfand-Hohenberg model is used to approximate the upper critical field μ0Hc2 = (11.2 ± 0.2) T, which is close to the Pauli limiting field of 12.35 T and which could indicate singlet-triplet mixing. However, low-temperature specific-heat data suggest that Re6Zr is an isotropic, fully gapped s-wave superconductor with enhanced electron-phonon coupling. Unusual flux pinning resulting in a peak effect is observed in the magnetization data, indicating an unconventional vortex state.

The superconductivity of the noncentrosymmetric compound La7Ir3 has been investigated using muon spin rotation and relaxation (μSR). Zero-field measurements reveal the presence of spontaneous static or quasi-static magnetic fields below the superconducting transition temperature Tc = 2:25 K - a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic, and that the pairing symmetry of the superconducting electrons is predominantly s-wave with an enhanced binding strength. The results indicate that the superconductivity in La7Ir3 may be unconventional, and paves the way for further studies of this family of materials.

The superconductivity in the rare-earth transition metal ternary borides $R$RuB$_2$ (where $R$ = Lu and Y) has been investigated using muon-spin rotation and relaxation. Measurements made in zero-field suggest that time-reversal symmetry is preserved upon entering the superconducting state in both materials; a small difference in depolarization is observed above and below the superconducting transition in both compounds, however this has been attributed to quasistatic magnetic fluctuations. Transverse-field measurements of the flux-line lattice indicate that the superconductivity in both materials is fully gapped, with a conventional s-wave pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. The electronic properties of the charge carriers in the superconducting state have been calculated, with effective masses $m^*/ m_\mathrm{e} = $ $9.8\pm0.1$ and $15.0\pm0.1$ in the Lu and Y compounds, respectively, with superconducting carrier densities $n_\mathrm{s} = $ ($2.73\pm0.04$) $\times 10^{28}$ m$^{-3}$ and ($2.17\pm0.02$) $\times 10^{28}$ m$^{-3}$. The materials have been classified according to the Uemura scheme for superconductivity, with values for $T_\mathrm{c}/T_\mathrm{F}$ of $1/(414\pm6)$ and $1/(304\pm3)$, implying that the superconductivity may not be entirely conventional in nature., Comment: 8 pages, 8 figures

This thesis presents muon spin rotation and relaxation (μSR) studies of various superconducting materials. μSR studies have been complemented with laboratory measurements of heat capacity, resistivity, and magnetization. This work contributes to the body of work surrounding noncentrosymmetric superconductors (NCS) and unconventional superconductivity.\ud \ud The intermetallic compound La₇Ir₃ is found to break time-reversal symmetry upon transitioning into the superconducting state, elucidated by muon spin relaxation. The pairing symmetry appears fully gapped, and is well described by an isotropic s-wave model. Further theoretical analysis of the point group symmetry could investigate the allowed superconducting states potentially existing here.\ud \ud The physical properties of the NCS Re₃Ta are well described by the conventional BCS theory of superconductivity. μSR suggests unusual narrowing of the vortex lattice signal in a region close to Tc, interpreted as motional narrowing due to thermal motion of vortices. This is supported by irreversible magnetization in a sizable region in the phase diagram. Ginzburg number and quantum resistance calculations place Re₃Ta intermediate between the high-Tc and conventional low-Tc superconductors.\ud \ud LuRuB₂ and YRuB₂, superconducting members of the ternary boride family of materials, are studied using μSR. Zero-field measurements detect spin fluctuations exhibiting critical slowing down as the temperature is lowered, suggesting that these materials lie near a quantum phase transition. These weak fluctuations coexist with the superconductivity, which is well described by an isotropic, s-wave model for the pairing symmetry.\ud \ud The semi-metal Lu₃Os₄Ge₁₃ is investigated using transverse-field and zerofield μSR. The superfluid density is well described by a model containing two superconducting gaps, supporting previously reported heat capacity measurements. Zero-field measurements below Tc reveal a signal hinting at broken time-reversal symmetry, however, it does not coincide with the bulk superconducting transition. Further theoretical work could determine whether this is the first observation of a novel three-gap multiband superconducting ground state.