Double-peak Majorana bound states in altermagnet--superconductor heterostructures

Abstract

We study Majorana bound states in a planar Josephson junction in which the middle channel is a $d$-wave altermagnetic metal deposited on a proximitized two-dimensional electron gas. In the topological regime, the near-zero-energy states reveals a characteristic double-peak spatial profile, with the Majorana wavefunction localized near the altermagnet--superconductor interfaces. Using simplified theoretical models, we show that anisotropic hopping intrinsic to altermagnetism naturally generates interface-localized low-energy states, providing the natural explanation for the double-peak structure. In a nanowire geometry with extended normal metallic regions, the same feature persists but the Majorana bound states become more sensitive to the chemical potential compared to the case in planar Josephson junction. In a T-shaped Josephson junction, multiple near-zero-energy states appear, and the Majorana bound state expected at the crossing point is found to be localized near the interfaces, demonstrating that the localization of the Majorana bound states is primarily governed by interface boundaries rather than by the junction geometry. These results show that anisotropic hopping and interface structure play a central role in altermagnet-based topological superconductors and provide a promising route toward a network of controllable Majorana bound states without external magnetic fields.

Figures (4)

• Figure 1: (a) Schematic of the planar Josephson junction consisting of two $s$-wave superconducting regions separated by a $d$-wave altermagnetic channel deposited on a two-dimensional electron gas. (b) Real-space profile of the normalized local density of states and (c) charge density of states corresponding to the near-zero-energy MBS at $\mu = -0.3$ meV, indicated by the vertical cyan line in (d). (d) Quasiparticle eigenenergy spectrum of the planar Josephson junction as a function of the chemical potential.
• Figure 2: (a) Schematic illustrating the anisotropic hopping for a single-spin channel at the altermagnet/normal-metal interface, where $t_{AM}$ denotes the altermagnetic contribution to the hopping amplitude. (b) Geometry of the $d$-wave altermagnet--normal-metal heterostructure, consisting of a finite altermagnetic region embedded within a larger normal-metal system. (c) Local density of states corresponding to the two lowest-energy degenerate eigenstates of the minimal model $\mathcal{H}_{1}$, showing localization along the interface. The inset displays the corresponding low-energy spectrum indexed by $n$. (d) Local density of states corresponding to the four lowest-energy degenerate eigenstates of the AM/NM heterostructure described by $\mathcal{H}_{\rm AM/NM}$, exhibiting multiple interface-localized regions. The inset shows the corresponding low-energy spectrum. The system dimensions are $L_{AM} = 40a$ and $L_{NM} = 80a$, with $t_{AM} = 0.3\,t$.
• Figure 3: (a) Schematic of the nanowire structure with extended normal metallic regions on both sides of the altermagnetic segment. (b) Real-space profile of the LDOS corresponding to the near-zero-energy MBS at $\mu = -0.3~\mathrm{meV}$ (indicated by the vertical cyan line in panel (c)). (c) Quasiparticle eigenenergy spectrum as a function of chemical potential for the nanowire geometry shown in (a).
• Figure 4: (a) Schematic of a $T$-shaped Josephson junction in which a $d$-wave altermagnetic channel forms the vertical and horizontal arms, separating three $s$-wave superconducting regions on a two-dimensional electron gas. (b) Real-space profile of the LDOS corresponding to the near-zero-energy MBS at $\mu = -0.3~\mathrm{meV}$ (indicated by the vertical cyan line in panel (c)). (c) Quasiparticle eigenenergy spectrum as a function of chemical potential, showing the emergence of two near-zero-energy states well separated from the bulk continuum. The system dimensions are $W_{sc} = 200a$, $W = 8a$, and $H_{sc} = 50a$. All other parameters are identical to those used for the planar Josephson junction in Fig. \ref{['FIG:1']}(a).