Nematic and chiral superconductivity induced by odd-parity fluctuations

Recent experiments indicate that superconductivity in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ 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.

Figure 1

(a) ${\chi }_p\left(T\right)/{\chi }_s\left(T\right)$ at $U=0$ as a function of ${\gamma }_1$ and ${\gamma }_2$. (b) The surface with rainbow color represents $U_c$ at which ${\chi }_p\left(T\right)={\chi }_s\left(T\right)$. The odd-parity $E_u$ superconductivity supports two different phases: nematic and chiral, which are separated by the gray boundaries. In (a) and (b), we used the normalization ${\gamma }_1^2+{\gamma }_2^2+{\gamma }_3^2=1$ without loss of generality. Therefore, ${\gamma }_1^2+{\gamma }_2^2\le 1$.

Figure 2

Schematic phase diagram as a function of repulsive interaction $U$ ($s$-wave channel) and temperature $T$. In the vicinity of $U_c$ where $s$-wave and nematic superconductivity have the same instability temperature, there is a phase where both types of superconductivity coexist with a relative phase difference $\pm \pi /2$.