  Non-centrosymmetric superconductors, whose crystal structure is absent of
inversion symmetry, have recently received special attentions due to the
expectation of unconventional pairings and exotic physics associated with such
pairings. The newly discovered superconductors A2Cr3As3 (A=K, Rb), featured by
the quasi-one dimensional structure with conducting CrAs chains, belongs to
such kind of superconductor. In this study, we are the first to report the
finding that the superconductivity of A2Cr3As3 (A=K, Rb) has a positive
correlation with the extent of non-centrosymmetry. Our in-situ high pressure ac
susceptibility and synchrotron x-ray diffraction measurements reveal that the
larger bond angle of As-Cr-As in the CrAs chains can be taken as a key factor
controlling superconductivity. While the smaller bond angle and the distance
between the CrAs chains also affect the superconductivity due to their
structural connections with the angle. We find that the larger value of the
difference between the larger and samller angles, which is associated with the
extent of the non-centrosymmetry of the lattice structure, is in favor of
superconductivity. These results are expected to shed a new light on the
underlying mechanism of the superconductivity in these Q1D superconductors and
also to provide new perspective in understanding other non-centrosymmetric
superconductors.
