  Unconventional superconductivity is characterized by the spontaneous symmetry
breaking of the macroscopic superconducting wavefunction in addition to the
gauge symmetry breaking, such as rotational-symmetry breaking with respect to
the underlying crystal-lattice symmetry. Particularly, superconductivity with
spontaneous rotational-symmetry breaking in the wavefunction amplitude and thus
in bulk properties, not yet reported previously, is intriguing and can be
termed "nematic" superconductivity in analogy to nematic liquid-crystal phases.
Here, based on specific-heat measurements of the single-crystalline
Cu$_x$Bi$_2$Se$_3$ under accurate magnetic-field-direction control, we report
thermodynamic evidence for nematic superconductivity, namely, clear
two-fold-symmetric behavior in a trigonal lattice. The results indicate
realization of an "odd-parity nematic" state, feasible only by macroscopic
quantum condensates and distinct from nematic states in liquid crystals. The
results also confirm topologically non-trivial superconductivity in
Cu$_x$Bi$_2$Se$_3$.
