An unusual material hosts even and odd superconducting phases

Most unconventional superconductors have a single superconducting phase. That’s surprising because their conduction electrons have a variety of theorized ways to couple up. Conceivably, they could transition between different sorts of superconducting orders. But so far, only uranium ditelluride and two other uranium compounds have shown such transitions.

Now Elena Hassinger of the Technical University of Munich and the Max Planck Institute for Chemical Physics of Solids in Dresden, Germany, and her colleagues have observed two superconducting phases in crystals of CeRh₂As₂. Unlike the two phases in UTe₂, the ones in CeRh₂As₂ seem to have different parities as a result of the material’s unusual structure.

The CeRh₂As₂ crystal is a heavy-fermion material. Like other members of the class, its interesting electronic behavior arises from the partially filled 4f and 5f orbitals of its rare-earth or actinide ions. Electrons in those orbitals hybridize with conduction electrons to produce quasiparticles of large effective mass—anywhere from 50- to 1000-fold that of an electron.

Hassinger and her collaborators grew CeRh₂As₂ crystals and performed an extensive series of measurements of their specific heat and AC magnetic susceptibility, among other properties. The researchers noticed an unexpected spike in the specific heat at 0.3 K that indicated a phase transition. A drop in the resistivity and susceptibility around the same temperature led the researchers to conclude that the transition marked the onset of superconductivity.

The team assembled a full phase diagram by subjecting samples to temperatures down to 40 mK and magnetic fields up to 15 T. When the magnetic field was applied in the plane of the material’s layers, CeRh₂As₂ didn’t show signs of multiple superconducting phases, and a magnetic field of less than 2 T forced it out of the superconducting phase.

When the field was applied out of the plane, despite the material’s fairly low transition temperature, it remained superconducting under extremely strong fields of up to 14 T. Typically, a superconducting state that’s easily destroyed by thermal energy will likewise be sensitive to the energy from a magnetic field. The critical temperature decreased with increasing field, but around 4 T, the rate at which it decreased suddenly slowed down (as shown in the figure above).

The researchers wondered if that abrupt change signaled the transition between two superconducting phases. Applying a suite of experimental techniques—including susceptibility, magnetization, and magnetostriction—supported that conclusion because they, too, showed a kink at 4 T, whereas the resistivity stayed zero throughout.

The researchers attribute the superconducting behavior in CeRh₂As₂ to the structure locally breaking inversion symmetry, despite the material’s overall inversion symmetry. The layers of Ce atoms (blue in the image to the right) are separated by two types of Rh–As layers (green and gray) with the same structure but the atom sites swapped. Because those Rh–As layers are different, inversion symmetry is absent in the vicinity of any given Ce atom.

The CeRh₂As₂ crystal’s orientation-dependent magnetic response somewhat resembles that of noncentrosymmetric materials. Breaking inversion symmetry leads to commingling spin-singlet (even-parity) and spin-triplet (odd-parity) superconducting states. That mixed state is suppressed by in-plane fields but not by out-of-plane fields. However, such materials lack multiple superconducting phases.

Centrosymmetric materials, on the other hand, have either even- or odd-parity superconducting phases, and a transition between the phases should be possible. Because of its unusual structure, CeRh₂As₂ combines the magnetic anisotropy of noncentrosymmetric materials with the single-parity phases of centrosymmetric materials.

Calculations using a model Hamiltonian that captured the Ce ion’s local symmetry replicated the experimentalists’ findings and indicated that one of the superconducting phases is even parity and the other is odd parity, a rare type of superconductivity found in some ferromagnetic superconductors and UTe₂. Odd-parity states are interesting in part because they may be topological and thus potentially useful for topological quantum computing. (S. Khim et al., Science 373, 1012, 2021 .)