High-temperature surface superconductivity in topological flat-band systems

We show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.

Figure 1

Spectrum of surface states for different numbers of layers. $N=5$ (left) and $N=50$ (right). The symbols have been calculated by exact diagonalization and the solid lines are computed from Eq. (12) up to the point where the approximation in it is valid. The three cases are: normal case with ${\mu }_n\equiv 0$ (blue circles), $\Delta =0.05t,{\mu }_n\equiv 0$ (red squares), and $\Delta =0.05t,{\mu }_1={\mu }_N=0.03t$ (green crosses).

Figure 2

Zero-temperature gap self-consistently calculated from Eq. (16) for $g=0.01t$. Left panel: $\Delta$ as a function of $p_c$ for various $N$ (solid lines). For $p_c~p_{\Delta }$ the gap saturates at the values given by Eq. (21) which approach Eq. (19) for $N\to \infty$. The dashed lines show the dispersion ${\xi }_p$ for each $N$. Right panel: $\Delta (z)$ profile, $z=\mathit{nd}$. $\Delta (z)$ is symmetric with respect to $z\to W-z$.