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Majorana Fermions and Exotic Surface Andreev Bound States in Topological Superconductors: Application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Cu</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Se</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>
The recently discovered superconductor ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ 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 …