Abstract
A spin-U(1)-symmetry protected momentum-dependent integer-$Z$-valued topological invariant is proposed to time-reversal-invariant (TRI) superconductivity (SC) whose nonzero value will lead to exactly flat surface band(s). The theory is applied to the weakly spin-orbit coupled quasi-1D A$_2$Cr$_3$As$_3$ (A=Na, K, Rb, Cs) superconductors family with highest $T_c$ up to 8.6 K with $p_z$-wave pairing in the $S_z=0$ 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 regime hosting three flat bands and the remaining part hosting two. Such exactly-flat surface bands will lead to 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.
Highlights
Topological superconductivity (TSC) has aroused great interest in past decades [1,2]
One may worry that the bad quality of the surface and the breaking of mirror-reflection symmetry there might hinder the detection of the surface states
The solution of these problems is shown in Fig. 4(e): when the tip of the scanning tunneling microscope (STM) is put on the side surface near the end of the sample within the localized length ξ ≈ 45c ≈ 20, there would be pronounced
Summary
Topological superconductivity (TSC) has aroused great interest in past decades [1,2]. We propose that the recently synthesized quasi-1D A2Cr3As3 (A=Na, K, Rb, Cs) family [30,31,32,33] with predicted pz-wave pairing symmetry [34,35] belongs to this TSC class, up to the leading SOC. Symmetry analysis suggests that the leading SOC in the A2Cr3As3 family is the atomic SOC conserving the SUS [34], and combined weakand strong-coupling approaches have predicted time-reversalinvariant (TRI) pz-wave triplet pairing with line nodes with the Sz = 0 component [34,35], belonging to the symmetry class required here up to the leading SOC. We provide a topological invariant associated with flat surface band(s) under combined TR+SUS symmetries for TSCs, and apply it to the quasi-1D A2Cr3As3 family. Our proposal provides smoking-gun evidence for experimental identification of such quasi-1D pz-wave superconductors as the A2Cr3As3 with weak SOC conserving the SUS
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