Altermon: a magnetic-field-free parity protected qubit based on a narrow altermagnet Josephson junction

Abstract

Altermagnets provide a new route to engineer superconducting circuits without magnetic fields. We theoretically study the Andreev bound state (ABS) spectrum of a finite-width altrmagnet-based Josephson junction and show how the $d$-wave altermagnetic symmetry and geometric confinement shape its low-energy excitations. We find a clear distinction between the two $d$-wave symmetries: $d_{x^2-y^2}$ order produces spin splitting, whereas $d_{xy}$ order preserves spin degeneracy and exhibits splitting of the ABS spectrum induced by intermode hybridization. Leveraging these novel features, we propose applying a transverse electric field to tune the system and realize a magnetic-field-free, parity-protected superconducting qubit that we call altermon.

Figures (8)

• Figure 1: Altermagnetic Josephson junction consisting of a semiconductor (SM) nanowire of length $L$ and width $W$, proximitized to superconducting and altermagnetic regions.
• Figure 2: Electronic band structure of a narrow altermagnet with a width of $W=20a$ and a chemical potential $\mu=0.5t$. (a) Pure $d_{x^2-y^2}$-wave magnetization symmetry $(t_1=0, t_2=0.1)$; and (b) Pure $d_{xy}$-wave magnetization symmetry $(t_1=0.4, t_2=0)$. The dotted curves represent the band structure of the system in the absense of altermagnetism $(t_1=t_2=0)$.
• Figure 3: Andreev level spectra in a single-mode ($n=1$) altermagnet Josephson junction with the pure $d$-wave symmetries, $L_S=2000a$, $L=24a$, $W=20a$ and $\mu=0.5t$. Solid curves represent the numerical solution of the BdG equation on a lattice, while dashed curves illustrate the analytical model for the $t_2\neq0$ case (blue for spin up, red for spin down).
• Figure 4: Same as Fig. \ref{['Fig:ABS_sm']}(b), but now for $W=36a$ and showing twice as many Andreev levels. The dashed gray curves illustrate the two-mode ($n=2)$ BdG Hamiltonian model. Dotted black curves: nonmagnetic junction ($t_1=t_2=0$) showing spin- and mode-degenerate levels.
• Figure 5: Altermon low-energy spectrum and frequencies as a function of applied electric field $E_y$; (a) dominant components of the Josephson energy. (b) four lowest energy levels around the transition point $E_y=0.00886 \, t/(4a|e|)$, at which the two lowest levels become nearly degenerate. (c) two lowest frequencies, $hf_{01(12)}/\Delta_0 \equiv E_{01(12)}=E_{1(2)}-E_{0(1)}$. Here we assume $E_J^{k=2}/E_C\approx20$, with $t_1=0$ and $t_2=0.3$ (pure $d_{x^2-y^2}$ altermagnetic symmetry), while all other parameters are set as in Fig. \ref{['Fig:ABS_sm']}.