Table 2 Complete set of gap functions for chiral spin-orbit–coupled superconductors.

Complete set of gap functions for chiral spin-orbit–coupled superconductors.. List of allowed gap function components FtJ(k) of Eq. 12 for the chiral pairing channels J = 1,2,3, (pseudo)spin angular momentum j=12,32,52, and crystal rotation symmetries Cn with n = 3,4,6. For each combination (J, j), a complete set of components is given; any other allowed gap function component FtJ(k) is generated by multiplying with fully point group symmetry invariant functions (19). Because angular momenta are only defined mod n, some entries in the table are equivalent, for example, (2,12)(1,12) under C3 symmetry, where (1,12) is the time-reversed partner of (1,12). Recall that s± = sx ±isy and sx,y,z are Pauli matrices acting on the Bloch electron (pseudo)spin.

(J, j)Trigonal (C3)Tetragonal (C4)Hexagonal (C6)
(1,12)k+sz,kzs+,ks,kzk+2s
kzk2sz,(k+3k3)s+
k+sz,kzs+,kz(k+4k4)s+
kzk+2s,kzk2s,k3sz
k+sz,kzs+,kzk+2s
k5sz,kzk4s,kzk6s+
(1,32)k+sz, k+s+, k+skzk2sz,kzk2s+,kzk2sk+sz,kzs,k3sz
kzk2s+,kzk+2s+,kzk+4s
k+sz,kzk2s+,kzk2s
k5sz,kzk+4s+,kzk+4s
(1,52)k+sz, ks+, kzs
k+3s,kzk2sz,kzk+2s+
k+sz,k3sz,kzk+4s+
kzs+,kzk+2s,kzk2s
k+sz,k5sz,kzs
kzk+2s+,kzk4s+,kzk+6s
(2,12)(1,12)k+s+,ks,kzk+2sz
k+3s,k3s+,kzk2sz
k+s+,kzk+2sz,kzk4sz
k+3s,k3s,k5s+
(2,32)(1,32)k+s,kzk+2sz,k+3s+
ks+,kzk2sz,k3s
kzk+2sz,ks+,ks
kzk4sz,k+5s+,k+5s
(2,52)(1,52)kzk+2sz,kzk2sz,k+s+
k3s+,ks,k+3s
kzk+2sz,kzk4sz,k+s
k5s,k3s+,k+3s+
(3,12)(0,12)(1,12)k+3sz,kzk+2s+,kzk+4s
k3sz,kzk2s,kzk4s+
(3,32)(0,32)(1,32)kzs+,kzs,kzk+6s+
k+3sz,k3sz,kzk6s
(3,52)(0,52)(1,52)k+3sz,k3sz,kzk2s+
kzk+4s+,kzk+2s,kzk4s