  The recently discovered superconductor CuxBi2Se3 is a candidate for
three-dimensional time- reversal-invariant topological superconductors, which
are predicted to have robust surface Andreev bound states hosting massless
Majorana fermions. In this work, we analytically and numerically find the
linearly dispersing Majorana fermions at k = 0, which smoothly evolve into a
new branch of gapless surface Andreev bound states near the Fermi momentum. The
latter is a new type of Andreev bound states resulting from both the nontrivial
band structure and the odd-parity pairing symmetry. The tunneling spectra of
these surface Andreev bound states agree well with a recent point-contact
spectroscopy experiment[1] and yield additional predictions for low temperature
tunneling and photoemission experiments.
