Chiral topological superconductivity in hole-doped Sn/Si(111)

Abstract

A third monolayer of tin atoms on the semiconductor substrate Si(111) has been shown to become superconducting upon six to ten percent hole doping. Experiments have reported promising results hinting at a superconducting chiral $d$-wave order parameter. Here we examine Sn/Si(111) by combining most recent ab initio results, quasi-particle interference calculations, state-of-the-art truncated-unity functional renormalization group simulations and Bogoliubov-de Gennes analysis. We show remarkable agreement between experimental and theoretical quasi-particle interference data both in the metallic and superconducting regimes. The interacting phase diagram reveals that the superconductivity is indeed chiral $d$-wave with Chern number $C=4$. Surprisingly, magnetically ordered phases are absent, instead we find charge density wave order, as observed in related compounds, as a competing phase. Our results demonstrate that Sn/Si(111) is an outstanding candidate material for chiral topological superconductivity.

Figures (4)

• Figure 1: Metallic regime of Sn/Si(111). (a) Band structure of Sn/Si(111), the surface band of the Sn atoms highlighted in blue marchetti2025. (b) Corresponding Fermi surface of the relevant doping regimes. c) QPI images at 10% hole-doping in momentum space: (Right) Experimental data ming2023 at $\omega=0$mV, $T=9$K; figure reused with permission of the authors reuse.
• Figure 2: Phase diagrams. (a) $U$-$V$ phase diagram at fixed lower van Hove filling $n_{\text{lvH}} = 0.754$ ($\delta_{\text{lvH}} = -0.246$). (b) $\delta$-$V$ phase diagram at fixed Hubbard interaction $U = 0.8W$. The color gradient in a and b shows the critical scale $\Lambda_c$ of the divergence in the TUFRG flow. We find three different phases as shown in the legend. (c) Combination of the strength of the nearest-neighbor $d$-wave pairing $|a_{d,1}|$ (shown as color gradient) and topological invariant $C$ for the superconducting regime, depending on $U$ and $V$. Green area corresponds to extended $s$-wave superconductivity. Grey (black) area displays charge order (a Fermi liquid). (d) Same as c but depending on $\delta$ and $V$. White line corresponds to a topological phase transition, where the BdG gap closes, from $C=4$ to $C=-8$.
• Figure 3: Example of the superconducting order parameter in the $C=4$ phase. The two pairings are doubly degenerate. They are decomposed into the spin singlet pairing $\Psi$ and the spin triplet pairings $\boldsymbol{d}$. While the magnitude of $d_x$ and $d_y$ is roughly 10% of $\Psi$, $d_z$ is smaller by one magnitude. Note the color scale is log normalized to demonstrate this effect. Parameters used: $U = 0.8 W$, $V = 0.1W$, $\delta = -0.1$.
• Figure 4: QPI in the superconducting phase: (Right) experimental data ming2023 for 10% hole doping, $\omega=0.8$mV, $T=0.5$K; figure reused with permission of the authors reuse. (Left) theory for 10% hole doping ($\delta=0.1$) as described in the main text. The intensity of the theory plot has been reduced outside the main structure to highlight the agreement between experiment and theory.