Higher-Order Topological Superconductivity and Electrically Tunable Majorana Corner Modes in Monolayer MnXPb$_2$ (X=Se, Te)-Pb Heterostructure

Higher-order topological superconductors host Majorana zero modes localized at corners or hinges, providing a promising route toward scalable and controllable Majorana networks without vortices or magnetic flux. Here we propose a symmetry-enforced higher-order topological superconductivity based on antiferromagnetic topological insulators, specifically realized in MnXPb$_2$ (X = Se, Te)-Pb heterostructure. We show that the intrinsic boundary dichotomy-gapless Dirac states protected by an effective time-reversal symmetry on antiferromagnetic edges and magnetic gaps on ferromagnetic edges-naturally generates Majorana corner modes as mass domain walls. Superconducting proximity converts the antiferromagnetic edges into one-dimensional topological superconductors, and the intersections between superconducting and magnetic edges bind Majorana zero modes as mass domain walls. Combining first-principles calculations with a calibrated effective boundary theory, we demonstrate robust corner localization and purely electrical control of Majorana fusion and braiding in a triangular geometry. Our results establish MnXPb$_2$ as experimentally promising platform for electrically programmable Majorana networks in two dimensions.

💡 Research Summary

The authors propose a novel route to realize higher‑order topological superconductivity (HOTSC) and electrically programmable Majorana corner modes (MCMs) in a two‑dimensional van‑der‑Waals heterostructure composed of a monolayer antiferromagnetic topological insulator MnXPb₂ (X = Se, Te) and a conventional Pb superconductor. First‑principles calculations show that MnXPb₂ adopts a collinear antiferromagnetic (CAF) ground state with an in‑plane Néel temperature of about 92 K. Including spin‑orbit coupling (SOC) opens an indirect bulk gap of ~190 meV and yields a Z₂ = 1 topological invariant protected by an effective time‑reversal symmetry Θₘ, which combines ordinary time reversal with a half‑lattice translation.

A key insight is the intrinsic “boundary dichotomy” of this antiferromagnetic topological insulator. On edges that preserve the effective Θₘ symmetry (antiferromagnetic edges) the surface Dirac cone remains gapless, whereas on edges that break it (ferromagnetic edges) a magnetic mass term opens a full gap. This dichotomy creates natural mass domain walls at the junctions of antiferromagnetic and ferromagnetic edges, without any external Zeeman field or magnetic flux.

When the MnXPb₂ layer is placed on a Pb film (with an intervening BN buffer to reduce lattice mismatch to –3.4 %), the normal‑state hybridization between MnXPb₂ edge states and Pb bulk bands is weak, preserving the pristine Dirac edge spectrum. Proximity‑induced s‑wave pairing from Pb therefore gaps the antiferromagnetic edges, turning them into one‑dimensional topological superconductors, while the ferromagnetic edges stay insulating. The intersection of a superconducting antiferromagnetic edge and a magnetic ferromagnetic edge thus hosts a zero‑dimensional mass domain wall that binds a single Majorana zero mode.

To capture these physics, the authors construct an 8 × 8 low‑energy effective Hamiltonian in the unfolded Brillouin zone, calibrated against DFT band structures. The model parameters (A ≈ –95 meV, B ≈ 32 meV, m ≈ 266 meV, magnetic exchange M ≈ 7.9 meV, induced pairing Δ ≈ 0.8 meV) faithfully reproduce the bulk gap, edge dichotomy, and the competition between superconducting and magnetic masses. Numerical diagonalization of a finite 40 × 40 cluster yields four zero‑energy states localized exponentially at the four corners, confirming the emergence of MCMs.

Electrical control is achieved by tuning the local chemical potential μ via gate voltages. The system remains in the HOTSC phase as long as |μ| < μ_c = √(3M²/4 – Δ²). By varying μ across μ_c on selected edges, one can switch individual corner modes on or off, effectively moving Majoranas along the perimeter of a triangular island. The authors further propose a minimal braiding architecture consisting of eight isosceles obtuse triangular islands (IOTIs) with independently controllable μ_j and superconducting phases Φ_j. By adiabatically varying μ_j and the phase differences δΦ between islands, they demonstrate numerically that Majorana fusion amplitudes F_φ follow the same functional dependence as in previously studied 1D networks, enabling non‑Abelian braiding without the need for complex wire networks or magnetic vortices.

The heterostructure is experimentally realistic: MnXPb₂ is dynamically stable (no imaginary phonon modes), its lattice constants match well with Pb and BN, and the bulk gap is large enough to suppress bulk‑edge mixing. The magnetic exchange energy (≈ 8 meV) exceeds the induced superconducting gap (≈ 0.8 meV), guaranteeing that the magnetic mass dominates on ferromagnetic edges, a prerequisite for robust corner localization. Moreover, the Néel temperature far exceeds the Pb superconducting transition temperature, ensuring that antiferromagnetic order persists in the superconducting regime.

In summary, the paper introduces a symmetry‑enforced mechanism for higher‑order topological superconductivity that relies solely on the intrinsic magnetic and crystalline symmetries of an antiferromagnetic topological insulator. By coupling MnXPb₂ to a conventional Pb superconductor, the authors realize electrically tunable Majorana corner modes, provide a concrete material platform, and outline a feasible braiding protocol. This work opens a promising pathway toward scalable, gate‑controlled Majorana networks in two dimensions, potentially accelerating the development of fault‑tolerant topological quantum computation.