Superconductors: A new route to tunable quantum states

A study led by Professor Guo-qing Zheng and PhD student Seiji Ogawa at Okayama University has identified three distinct spin-triplet superconducting phases within the chromium-based superconductor K₂Cr₃As₃

Published in Physical Review Letters, the research demonstrates how temperature and magnetic fields can tune distinct topological states capable of hosting Majorana excitations for fault-tolerant quantum computing.

Spin-Triplet Superconductivity in K₂Cr₃As₃

Unlike conventional superconductors, where paired electrons have anti-parallel spins, spin-triplet superconductors feature electron pairs with parallel spins, retaining an internal spin degree of freedom.

While spin-triplet states are primary candidates for hosting topological Majorana zero modes, previous bulk material candidates suffered from extremely low transition temperatures (T_c) or competing magnetic orders.

K₂Cr₃As₃ addresses these limitations by offering a bulk spin-triplet platform with a transition temperature of T_c ≈ 6.2 K without long-range magnetic ordering. Using 75As nuclear magnetic resonance (NMR), including Knight-shift and spin-lattice relaxation rate measurements, the team mapped how the order parameter’s d(k)-vector and gap symmetry evolve under external magnetic fields applied along the crystalline c-axis.

Discovery of three distinct superconducting phases

The NMR measurements revealed three field- and temperature-dependent superconducting phases:

• Phase A (Low field, high temperature):

  • Emerges near Tc under low magnetic fields. Characterised as a helical spin-triplet state featuring point-nodal gap structures.

• Phase B (Low field, low temperature):

  • As cooling continues, the material transitions to a chiral state where the d(k)-vector rotates by 90°, altering the paired-spin orientation while retaining point nodes.

• Phase C (High field):

  • At elevated magnetic fields, the system transitions into a state defined by a line-nodal pz-wave gap structure. Below ~7 T, the phase boundary splits into two successive transitions during cooling: an initial reorientation of the gap symmetry followed by a 90° rotation of the d(k)-vector.

Implications for topological quantum computing

The multi-phase behaviour of K₂Cr₃As₃ provides a versatile physical platform for topological quantum processing:

• Phase B breaks time-reversal symmetry, analogous to the superfluid ³He-A phase, and its magnetic vortex cores are predicted to host localised Majorana zero modes.
• Phase A possesses topological properties that could support boundary Majorana edge states when fabricated into thin-film geometries.

By demonstrating that magnetic fields and temperature can drive transitions between distinct topological phases in a bulk crystal, the researchers establish K₂Cr₃As₃ as an adaptable platform for studying Majorana physics and engineering stable quantum states.