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

Abstract

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.

Figures (5)

• Figure 1: Crystal structure, magnetic ground state, and stability of monolayer MnXPb$_2$ (X = Se, Te). (a) Top and (b) side views of the trigonal crystal structure (space group P3m1), where all Mn atoms lie in a single plane and bond to three neighboring chalcogen atoms. Pink, green and blue balls denote Mn, Te and Pb atoms, respectively. (c) Phonon dispersion without imaginary modes, confirming dynamical stability. (d) Collinear in-plane antiferromagnetic ground state identified from total-energy comparisons among nonmagnetic, ferromagnetic, Néel antiferromagnetic, and collinear antiferromagnetic configurations. $J_1$, $J_2$ denote exchange coupling between first- and second-nearest neighbor Mn atoms. (e) Temperature-dependent magnetic susceptibility fitted by a Curie--Weiss form, yielding a Néel temperature $T_N \approx 92$ K.
• Figure 2: Topological electronic structure and boundary dichotomy in monolayer MnTePb$_2$. (a) Band structure without spin--orbit coupling in the collinear antiferromagnetic state. (b) Band structure with spin--orbit coupling, showing an indirect gap of about 190 meV. (c) Orbital-resolved band character near the Fermi level, indicating SOC-driven band inversion. (d) Evolution of hybrid Wannier charge centers, yielding a nontrivial $Z_2=1$ invariant protected by an effective time-reversal symmetry. (e) Edge spectrum for an antiferromagnetic boundary, hosting a Dirac crossing at the X point. (f) Edge spectrum for a ferromagnetic boundary, exhibiting a full gap.
• Figure 3: MnTePb$_2$--Pb heterostructure and proximity regime. (a) Top and (b) side views of the relaxed stable MnTePb$_2$--Pb--BN heterostructure constructed from commensurate supercells. (c) Band structure of the heterostructure with orbital projections, showing weak normal-state hybridization between MnTePb$_2$ and Pb. (d) Enlarged view near the Fermi level, illustrating that MnTePb$_2$ boundary states remain well separated from Pb bands, a favorable condition for proximity-induced superconductivity.
• Figure 4: Boundary model and Majorana corner modes in the higher-order topological phase. (a) Schematic of the triangular lattice and collinear antiferromagnetic unit cell. (b) Folded Brillouin zone used to construct the effective boundary model. (c) Spectrum of an antiferromagnetic edge without superconductivity, hosting a Dirac mode protected by an effective time-reversal symmetry. (d) Spectrum of a ferromagnetic edge, showing a magnetic mass gap. (e) Low-energy spectrum of a finite cluster in the presence of superconducting proximity, revealing four zero-energy states inside the edge gap. (f) Spatial probability density of the four zero modes, demonstrating exponential localization at the corners. In (c)-(d), the parameters ($A$, $B$, $m$, $M$, $\mu$)=(1, 1, 3, 0.1, 0). In (e)-(f), the parameters ($A$, $B$, $m$, $M$, $\mu$, $\Delta$ )=(1, 1, 3, 0.2, 0, 0.1)
• Figure 5: Electrical control and adiabatic braiding of Majorana corner modes. (a--g) Real-space evolution of Majorana probability densities during an adiabatic braiding cycle implemented by tuning local chemical potentials on three selected triangular islands. The remaining islands are kept fixed. (h) Energy spectrum along the braiding path, showing that the four Majorana modes remain pinned at zero energy and separated from excited states by a finite gap. (i) Time sequence of the chemical-potential protocol used in the braiding operation. During the protocol, $\mu_1$ = $\mu_d$ is fixed. $\mu_2$, $\mu_3$, and $\mu_4$ are varied in time according to (i). The parameters are $\mu_u$ = 0.2$m$, $\mu_d$ = 0.05$m$, M = 0.4$m$, $\Delta$ = 0.25$m$, and A = B = 0.5$m$ = 3; the short-side length of the IRTIs is L = 40a