Engineering subgap states in superconductors by the symmetry of altermagnetism

Abstract

Combining superconducting and magnetic materials is a promising path to generate exotic interface subgap states. In this regard, altermagnetism is particularly interesting because it lifts spin degeneracy while providing tailored anisotropy of spin splittings. Here, we investigate the realization and control of subgap states by using the symmetry contrast between altermagnetic fields and unconventional pairings. When the symmetries of altermagnetism and unconventional superconductivity align, we demonstrate the emergence of bulk zero-energy flat bands as the Bogoliubov Fermi surface, giving rise to a zero-bias conductance peak. The symmetry and strength of $d$-wave altermagnets strongly affect the surface Andreev states from $d$-wave and chiral $d$- and $p$-wave superconductors. As a result, distinct types of subgap states are realized, including curved and flat bands, that can be detected by tunneling spectroscopy. Our results offer a solid route for designing and manipulating subgap states in superconducting systems, which can be useful for functionalizing superconducting devices.

Figures (4)

• Figure 1: (a) An altermagnet (AM, orange) is placed on top of a superconductor (SC, green) to engineer subgap states. A normal metal probe (N, blue) is coupled to SC at $x=0$ near the AM-SC interface, achieved by adjusting the thickness of the insulating substrate (grey) beneath N. (b) Illustrations of the selected AM orderings in momentum space where the red and blue colors indicate up and down spins. (c) Table listing the type of emergent subgap states for several AM-SC combinations. Labels "flat", "split", and "curved" indicate when the dispersion of subgap states is respectively zero, spin-split, or drastically varying.
• Figure 2: Conductance for a junction with various combinations of $d$-wave SCs and $d$-wave AMs. The AM is $d_{x^{2}-y^{2}}$-wave in panels (a-c) and $d_{xy}$-wave in (d). SC pairing is $d_{x^{2}-y^{2}}$-wave in (a), (b) and $d_{xy}$-wave in (c), (d). Panel (a) show angle-resolved conductance at $h_{0}=\Delta_{0}$. For all panels $Z=2$.
• Figure 3: Conductance for junctions with chiral $p$-wave SCs. AM is $d_{x^{2}-y^{2}}$ in (a)(c) and $d_{xy}$ in (b)(d). (a)(b) angle-resolved charge conductance at $h_{0}=\Delta_{0}$. (c)(d) total conductance for distinct values of $h_{0}$. $Z=2$ for all panels.
• Figure 4: Conductance for junctions with chiral $d$-wave SCs with a $d$-wave AM. (a) angle-resolved charge conductance at $h_{0}=\Delta_{0}$ and (b) total conductance for distinct values of $h_{0}$ for a $d_{x^2-y^2}$-wave AM. (c) zero bias conductance vs $\alpha$ and $h_0$ where $\alpha$ denotes the crystal orientation of AM. (d) Same junction with (c) but the total conductance as a function of $eV$ and $\alpha$ at $h_0=\Delta_0$. $Z=2$ for all panels.