A central task of condensed matter physics is understanding the relationship between the symmetries of materials and their observable, measurable properties. To this end, a wide range of mathematical tools and many physical approaches are available in the literature. Symmetries play an important role in the formation of magnetic ordering and in classifying the superconducting order parameter of materials.
Muon spin rotation experiments on the superconducting phase of elementary rhenium have revealed that it spontaneously breaks the time-reversal symmetry [T. Shang et al., Phys. Rev. Lett. 121, 257002 (2018)]. A few years later, ab initio calculations were performed to unravel the cause of this anomalous phenomenon [G. Csire et al., Phys. Rev. B 106, L020501 (2022)]. The calculations indicated that finite magnetic moments of opposite directions appear in the superconducting state on the two atoms within the elementary cell of the crystal and that the measured activated specific heat was well-fitted by mixing spin-singlet and spin-triplet Cooper pairs.
In the nonsymmorphic crystal structure of rhenium, the inversion centers and atomic positions do not coincide. Consequently, there is currently no symmetry-based classification of this problem and, thus, no suitable order parameter. The aim of my thesis is to use group theory and representation theory tools to determine the shape of possible order parameters that can explain the experimental results.