Singlet s± -wave pairing in quasi-one-dimensional ACr3As3(A=K,Rb,Cs) superconductors

The recent discovery of quasi-one-dimensional chromium-based superconductivity has generated much excitement. We study in this work the superconducting instabilities of a representative compound, the newly synthesized ${\mathrm{KCr}}₃{\mathrm{As}}₃$ superconductor. Based on inputs from density functional theory calculations, we first construct an effective multiorbital tight-binding Hamiltonian to model its low-energy band structure. We then employ standard random-phase approximation calculations to investigate the superconducting instabilities of the resultant multiorbital Hubbard model. We find various pairing symmetries in the phase diagram in different interaction parameter regimes, including the triplet $f$-wave, ${p}_z$-wave, and singlet ${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave pairings. We argue that the singlet ${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave pairing, which emerges at intermediate interaction strength, may be realized in this material. This singlet pairing is driven by spin-density wave fluctuations enhanced by Fermi-surface nesting. We point out that phase-sensitive measurement can distinguish the $s$-wave pairing in ${\mathrm{KCr}}₃{\mathrm{As}}₃$ from the ${p}_z$ wave previously proposed for a related compound ${\mathrm{K}}₂{\mathrm{Cr}}₃{\mathrm{As}}₃$. The ${s}^{\ifmmode\pm\else\textpm\fi{}}$-wave pairing in ${\mathrm{KCr}}₃{\mathrm{As}}₃$ shall also exhibit a subgap spin resonance mode near the nesting vector, which can be tested by inelastic neutron scattering measurements. Another intriguing property of the ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing is that it can induce time-reversal invariant topological superconductivity in a semiconductor wire with large Rashba spin-orbit coupling via proximity effect. Our study shall be of general relevance to all superconductors in the family of $A{\mathrm{Cr}}₃{\mathrm{As}}₃\phantom{\rule{4pt}{0ex}}(A=\text{K},\text{Rb},\text{Cs})$.