Absence of zero-energy surface bound states in Cu$_{\mathrm{x}}$Bi$_{2}$Se$_{3}$ via a study of Andreev reflection spectroscopy*

Cu$_{x}$Bi$_{2}$Se$_{3}$ has been proposed as a potential topological superconductor characterized by an odd-parity full bulk superconducting gap and zero-energy surface Andreev bound states (Majorana fermions). A predicted consequence of such Majorana fermions is a peak in the zero-energy density of states which should lead to a persistent zero-bias-conductance-peak (ZBCP) in Andreev reflection (AR) or tunneling experiments. Here we employ a newly developed nanoscale AR spectroscopy method to study normal metal/superconductor (N-S) devices featuring Cu$_{x}$Bi$_{2}$Se$_{3}$. The results show that a ZBCP can be tuned in or out from Cu$_{x}$Bi$_{2}$Se$_{3}$ samples depending on the N-S barrier strength. While the appearance of ZBCP may be traced to different origins, its absence under finite barrier strength represents the absence of zero-energy Majorana fermions. The present observations thus call for a reexamination of the intriguing superconductivity in Cu$_{x}$Bi$_{2}$Se$_{3}$.