Topological Superconductivity in Bilayer Rashba System

We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the heterostructures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity without breaking time-reversal symmetry is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the interlayer interaction is repulsive, both of which can be satisfied in realistic systems. Edge channels are studied in a tight-binding model numerically, and the several predictions on experiments are also given.

Figure 1

(a) (left panel) Schematic view of the model with the interfaces between two kinds of materials $A$ and $B$. An example is that $A$ is ${\mathrm{LaAlO}}_3$ and $B$ is ${\mathrm{SrTiO}}_3$. 2DEGs are formed in the ${\mathrm{SrTiO}}_3$ side and we expect these two hybridize with sufficiently short width of the middle layer. (right panel) Schematic wave functions of bonding and antibonding states along the $z$ direction. The hybridization splits two Rashba bands into bonding and antibonding states with the hybridization gap $\epsilon$. (b) Dispersion of the Hamiltonian of bilayer Rashba model Eq. (1). The position of the Fermi energy ($A\mathrm{\text{−}}C$) is crucial to nontrivial phases. The phase diagrams for each case is shown in Fig. 2.

Figure 2

Phase diagram of superconductivity in the $UV$ plane. Yellow, brown, and orange indicate the region where ${\Delta }_1$, ${\Delta }_2$, and ${\Delta }_3$ show the strongest instability, respectively. Here we take the unit where $m$ is the unity. The white region is nonsuperconducting. Each row corresponds to the Fermi energy at $A$, $B$, and $C$ in Fig. 1b. The system can be topological only when the Fermi energy lies in the hybridization gap, i.e., case $B$, and in this case ${\Delta }_2$ region expands as the SOI increases while ${\Delta }_3$ region is independent of the strength of SOI. However, SOI is indispensable for ${\Delta }_3$. See the text.

Figure 3

Energy spectrum of the cylindrical sample with ${\Delta }_3$ pairing for different positions of the Fermi surface, i.e., case $A$, $B$, and $C$ (from left to right); see Fig. 1b. These figures show that helical edge modes appear at each edge of the sample in the superconducting gap only when the Fermi surface lies within the hybridization gap.