Intrinsic topological superconductivity with exactly flat surface bands in the quasi-one-dimensional A2Cr3As3 (A=Na, K, Rb, Cs) superconductors

A spin-U(1)-symmetry protected momentum-dependent integer-Z-valued topological invariant is proposed to time-reversal-invariant superconductivity whose nonzero value will lead to exactly flat surface band(s). The theory is applied to the weakly spin-orbit-coupled quasi-1D A2Cr3As3 (A=Na, K, Rb, Cs) superconductors family with highest Tc up to 8.6 K with pz-wave pairing in the Sz=0 channel. It's found that up to the leading atomic spin-orbit coupling (SOC), the whole (001) surface Brillouin zone is covered with exactly flat surface bands, with some of the regime hosting three flat bands and the remaining part hosting two. Such exactly flat surface bands will lead to a very sharp zero-bias conductance peak in the scanning tunneling microscopic spectrum. When a tiny subleading spin-flipping SOC is considered, the surface bands will only be slightly split. The application of this theory can be generalized to other unconventional superconductors with weak SOC, particularly to those with mirror-reflection symmetry.