Odd-Parity Topological Superconductors: Theory and Application to ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$

Topological superconductors have a full pairing gap in the bulk and gapless surface Andreev bound states. In this Letter, we provide a sufficient criterion for realizing time-reversal-invariant topological superconductors in centrosymmetric superconductors with odd-parity pairing. We next study the pairing symmetry of the newly discovered superconductor ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ within a two-orbital model, and find that a novel spin-triplet pairing with odd parity is favored by strong spin-orbit coupling. Based on our criterion, we propose that ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ is a good candidate for a topological superconductor. We close by discussing experimental signatures of this new topological phase.

Figure 1

Phase diagram of the two-orbital $U\mathrm{\text{−}}V$ model, showing the highest $T_c$ phase as a function of $m/\mu$ and $U/V$. The arrow shows the experimental estimate for $m/\mu \simeq 1/3$ [18]. The two phases ${\widehat{\Delta }}_1$ and ${\widehat{\Delta }}_2$ are even and odd under inversion, respectively. The insets shows schematically that the Cooper pair wave function in the ${\widehat{\Delta }}_2$ phase consists of two electrons on the top (1) and bottom (2) of the five-atom unit cell.

Figure 2

Phase-sensitive experiments to test ${\Delta }_2$ pairing, which is odd under both inversion ($\mathbf{r}\to -\mathbf{r}$) and reflection about the $yz$ plane ($x\to -x$). A superconducting ring made of either an $s$-wave (a) or $d$-wave (b) superconductor contains a segment of a ${\Delta }_2$ superconductor. The flux through the ring is $nh/4e$ (a) or $(n+\frac{1}{2})h/2e$ (b), where $n$ is an integer.