Abstract

If the topological insulator Bi$_{2}$Se$_{3}$ is doped with electrons,
superconductivity with $T_{{\rm c}}\approx3-4\:{\rm K}$ emerges for
a low density of carriers ($n\approx10^{20}{\rm cm}^{-3}$) and with
a small ratio of the superconducting coherence length and Fermi wave
length: $\xi/\lambda_{F}\approx2\cdots4$.
These values make fluctuations of the superconducting order parameter
increasingly important, to the extend that the $T_{c}$-value is surprisingly
large. Strong spin-orbit interaction led to the proposal of an odd-parity
pairing state. This begs the question of the nature
of the transition in an unconventional superconductor with strong
pairing fluctuations. We show that for a multi-component order parameter,
these fluctuations give rise to a nematic phase at $T_{{\rm nem}}>T_{c}$.
Below $T_{c}$ several experiments demonstrated a rotational
symmetry breaking where the Cooper pair wave function is locked to
the lattice.
Our theory shows that this rotational symmetry breaking, as vestige of the superconducting state, already occurs
above $T_{c}$. The nematic phase is characterized by vanishing
off-diagonal long range order, yet with anisotropic superconducting
fluctuations. It can be identified through direction-dependent para-conductivity,
lattice softening, and an enhanced Raman response in the $E_{g}$
symmetry channel. In addition, nematic order partially avoids the usual
fluctuation suppression of $T_{c}$.