Intrinsic topological superconductivity with exactly flat surface bands in the quasi-one-dimensional A$_2$Cr$_3$As$_3$ (A=Na, K, Rb, Cs) superconductors

TL;DR

This paper proposes a topological invariant for time-reversal-invariant superconductors, predicting exactly flat surface bands in quasi-1D A$_2$Cr$_3$As$_3$ superconductors, leading to sharp zero-bias conductance peaks.

Contribution

It introduces a new topological invariant protected by spin-U(1) symmetry, explaining flat surface bands in certain superconductors with weak spin-orbit coupling.

Findings

Exactly-flat surface bands cover the entire (001) surface Brillouin zone.

Presence of multiple flat bands (up to three) in some regimes.

Flat bands cause sharp zero-bias conductance peaks in STM spectra.

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.