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Possible emergence of nematic superconductivity that breaks its underlyinglattice symmetry in doped topological insulator Bi$_2$Se$_3$,establishes thissystem as a unique candidate of topological superconductors. Exclusion ofpossible extrinsic causes for the two-fold superconductivity is essential toclarify its topological nature. Here, we present electrical transport onSr$_x$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 ratiobetween the maximum and minimum in-plane upper critical fields variessignificantly among samples with different shapes. Compared with therectangular sample, the anisotropic ratio is largely suppressed in the circularsample which has higher geometric rotational symmetry. Our results imply thatsample geometry plays a subdominant role, but circular shape is more ideal toreveal the two-fold superconductivity of Sr$_x$Bi$_2$Se$_3$ in the vortexstate.

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