Engineering Fractional Topological Superconductors: Numerical Bogoliubov-de Gennes Analysis for Parafermion Realization in FCI-Superconductor Heterostructures

TL;DR

The work addresses how to realize Z$_3$ parafermion zero modes in fractional Chern insulator–superconductor heterostructures by combining self-consistent BdG simulations with a full edge-theory treatment. It provides quantitative predictions for MoTe$_2$/NbSe$_2$ systems, including induced gaps $\Delta_{\text{ind}}\sim 45$–$75\ \mu$eV, coherence lengths $\xi\approx360$ nm, and measurable Josephson currents, all within experimentally accessible parameters. The paper derives a complete edge theory mapping to the $\mathbb{Z}_3$ parafermion CFT (central charge $c=4/5$) and shows domain-wall zero modes with a $\

Abstract

We propose a pathway to engineer Z3 parafermion zero modes in fractional Chern insulator-superconductor heterostructures. Using numerical Bogoliubov-de Gennes calculations and edge-theory analysis, we demonstrate how realistic materials such as MoTe2/NbSe2 can host parafermionic excitations with experimentally accessible signatures, including fractional Josephson effects, localized zero modes, interferometry, and thermal transport. Our work outlines concrete strategies for experimentally accessing parafermionic excitations in FCI-superconductor heterostructures.

Figures (4)

• Figure 1: Self-consistent BdG solutions for FCI-SC junction. (a) Spatial profile of induced pairing potential $\Delta_{\text{ind}}(x)$ showing exponential decay with characteristic length $\xi \approx 360\,$nm for transparency $T = 0.5$. (b) Convergence history showing self-consistency achieved within 25 iterations. (c) Induced gap amplitude versus position for three transparency values $T = 0.3, 0.5, 0.8$ demonstrating transparency scaling.
• Figure 2: Transparency scaling of induced gap. Maximum induced gap $\Delta_{\text{max}}$ versus interface transparency $T$, showing saturation behavior described by Eq. \ref{['eq:transparency_scaling']}. Data points represent numerical BdG solutions, solid curve shows fitted function. Shaded region indicates target operating regime $T > 0.4$ for parafermion formation.
• Figure 3: Device schematic for gate-controlled parafermion network. (a) Cross-sectional view showing the seven-layer stack with dimensions labeled. (b) Top-view layout showing patterned NbSe$_2$ superconductor regions (blue), local gate electrodes (gold), and FCI active region (green). Domain walls form at boundaries between gated and ungated regions. (c) Magnified view of single plaquette showing four parafermion positions at domain wall intersections with coupling strengths $J_1, J_2, J_3, J_4$ tunable via gate voltages.
• Figure 4: STM measurement protocol and expected signatures. (a) Spatial map of differential conductance $dI/dV(V=0, x)$ showing exponentially localized zero-bias peaks at domain wall positions. (b) Line cut through domain wall showing exponential decay with fit yielding $\ell_0 = 360 \pm 50$ nm. (c) Splitting energy $E_{\text{split}}$ versus domain wall separation $d$ for parafermions (exponential, solid line) versus Andreev bound states (algebraic, dashed line), demonstrating clear distinction for $d$ in range 0.5 to 2 micrometers.