Topological Superconductivity in Dirac Semimetals

Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest the possible application of our theory to recently discovered superconducting states in ${\mathrm{Cd}}_3{\mathrm{As}}_2$.

Figure 1

(a) Schematic picture of the Dirac points at $(0,0,\pm k_0)$ and the surface FL in the bulk BZ and the surface BZ, respectively. (b) On the $k_z$ axis, a bulk Dirac point with $Q=-1$ in the left-hand side is decomposed into four chiral modes with different ${\alpha }_p$ in the right-hand side. The bold line is doubly degenerate. (c) Schematic illustration of the surface Majorana quartet in the superconducting Dirac semimetal.

Figure 2

(a) Orbital textures on the Fermi surfaces in the $k_x{k}_y$ plane with $k_z=\pm k_0$ in the $s_z=1$ (left) and $s_z=-1$ (right) sectors. Arrows indicate the direction of the orbit, $(⟨{\sigma }_x⟩,⟨{\sigma }_y⟩)$. A Cooper pair between electrons with opposite spin may realize both of a parallel orbit pair (1) and an antiparallel one (2), depending on the momentum. On the other hand, a Cooper pair between electrons in the same spin state always have the antiparallel orbit configuration (3). (b) Energy spectra at the (100) face. $\mu /t_z=0.5$, $M/t_z=4$, $t_{xy}/t_z=2$, $\eta /t_z=1$, $\beta /t_z=2$, $\gamma /t_z=1$, ${\mathrm{\Delta }}_0/t_z=0.1$, ${\mathrm{\Delta }}_0^{\prime }/t_z=0.01$, and $m_0/t_z=0.2$. The distance between left ($x=0$) and right ($x=L$) surfaces is $L=50$. The red and green lines show the FL-induced MFs.