Andreev bound states at nonmagnetic impurities in superconductor/antiferromagnet heterostructures

Abstract

Andreev bound states can occur at single impurities in superconductors if the impurities suppress superconductivity for a given system. In particular, well-known Yu-Shiba-Rusinov states occur at magnetic impurities in conventional s-wave superconductors. Here we demonstrate that nonmagnetic impurities in S/AF heterostructures with conventional intraband s-wave pairing also produce Andreev bound states. Analogously to the Yu-Shiba-Rusinov bound states the bound states in S/AF bilayers are spin split, but the spin of a particular bound state is determined by the sublattice to which the impurity belongs. The standard decay of the bound state LDOS is superimposed by atomic oscillations related to the staggered character of the exchange field in the host material and by another oscillating pattern produced by finite-momentum Neel triplet pairing generated at the impurity.

Figures (11)

• Figure 1: Sketch of the system under consideration. Insulating two-sublattice antiferromagnet (AF) with staggered magnetization $\bm m_A = -\bm m_B$ induces a staggered exchange field $\bm h_A = -\bm h_B$ via the proximity effect in the adjacent thin superconductor (S). The unit cell is shown by a rectangular. An impurity can occupy site $A$ or $B$ in the S layer. The both possible variants are shown by red balls. The LDOS of Andreev bound states localized at the corresponding impurity is shown schematically. The energy spectrum of the bound states with the appropriate spin structure (red arrows) is also shown above the corresponding impurity.
• Figure 2: LDOS as a function of energy. (a) LDOS at the impurity site. (b) LDOS at the nearest neighbor of the impurity. The inserts show the same LDOS for larger energy range. $2E_g^S$ is a superconducting gap at the Fermi level. The antiferromagnetic gap $2E_g^{AF}$ at $\varepsilon \in [-\mu - h, -\mu+h]$ and the non-superconducting additional bound state inside this gap are also seen. $t=10 \Delta$, $\mu=20\Delta$, $h=15\Delta$, $U_0 = 10\Delta$. The Dynes parameter, describing the level broadening, $\Gamma=0.02\Delta$, see Appendix \ref{['T-matrix']} for description.
• Figure 3: Bound state energies as functions of the impurity strength. $\mu=20\Delta$. Different colors correspond to different $h$. Dashed lines represent bound state energies at a magnetic impurity with the same strength in a conventional $s$-wave superconductor.
• Figure 4: LDOS as a function of energy. At $\mu = 0$ there is the only gap $2E_g = 2(\Delta - h)$. In this case both antiferromagnetic and superconducting gaps are open at the Fermi level and, therefore, $2E_g$ is of mixed origin. $\mu=0$, $h=0.6\Delta$, $U_0 = 10\Delta$.
• Figure 5: Bound state energy $\varepsilon_b$ in the plane $(h,\mu)$. White region corresponds to fully suppressed superconductivity. $U_0N_F = 0.3$.