Nematic and chiral superconductivity induced by odd-parity fluctuations

Recent experiments indicate that superconductivity in Bi$_2$Se$_3$ intercalated with Cu, Nb or Sr is nematic with rotational symmetry breaking. Motivated by this observation, we present a model study of nematic and chiral superconductivity induced by odd-parity fluctuations. We show that odd-parity fluctuations in the two-component $E_u$ representation of $D_{3d}$ crystal point group can generate attractive interaction in both the even-parity $s$-wave and odd-parity $E_u$ pairing channels, but repulsive interaction in other odd-parity pairing channels. Coulomb repulsion can suppress $s$-wave pairing relative to $E_u$ pairing, and thus the latter can have a higher critical temperature. $E_u$ pairing has two distinct phases: a nematic phase and a chiral phase, both of which can be realized in our model. When $s$-wave and $E_u$ pairings have similar instability temperature, we find an intermediate phase in which both types of pairing coexist.