Relevance of sample geometry on the in-plane anisotropy of SrxBi2Se3 superconductor

Possible emergence of nematic superconductivity that breaks its underlying lattice symmetry in doped topological insulator Bi$_2$Se$_3$,establishes this system as a unique candidate of topological superconductors. Exclusion of possible extrinsic causes for the two-fold superconductivity is essential to clarify its topological nature. Here, we present electrical transport on Sr$_x$Bi$_2$Se$_3$ superconductors with rectangular and circular geometries. The occurrence of the two-fold symmetric in-plane upper critical field $H_{c2}$ is found to be weakly geometry dependent. However, the anisotropic ratio between the maximum and minimum in-plane upper critical fields varies significantly among samples with different shapes. Compared with the rectangular sample, the anisotropic ratio is largely suppressed in the circular sample which has higher geometric rotational symmetry. Our results imply that sample geometry plays a subdominant role, but circular shape is more ideal to reveal the two-fold superconductivity of Sr$_x$Bi$_2$Se$_3$ in the vortex state.