Néel proximity effect at antiferromagnet/superconductor interfaces

TL;DR

The paper shows that a compensated antiferromagnet adjacent to a conventional superconductor can induce Néel triplet Cooper pairs in the superconductor, reducing the critical temperature despite zero net spin-splitting. It develops a two-sublattice quasiclassical Green's function formalism to describe both rapid lattice-scale oscillations tied to the AF order and smoother coherence-scale physics, and corroborates these insights with Bogoliubov–de Gennes numerics. The analysis reveals that interband (Néel) pairing arises from the two-sublattice structure and is odd-frequency, with disorder suppressing these triplets and the AF gap, leading to nontrivial, impurity-dependent behavior of Tc. Overall, the work provides a coherent mechanism for AF-induced proximity effects in S/AF bilayers and offers a practical framework for interpreting related experiments.

Abstract

Spin-splitting induced in a conventional superconductor weakens superconductivity by destroying spin-singlet and creating spin-triplet Cooper pairs. We demonstrate theoretically that such an effect is also caused by an adjacent compensated antiferromagnet, which yields no net spin-splitting. We find that the antiferromagnet produces Néel triplet Cooper pairs, whose pairing amplitude oscillates rapidly in space similar to the antiferromagnet's spin. The emergence of these unconventional Cooper pairs reduces the singlet pairs' amplitude, thereby lowering the superconducting critical temperature. We develop a quasiclassical Green's functions description of the system employing a two-sublattice framework. It successfully captures the rapid oscillations in the Cooper pairs' amplitude at the lattice spacing scale as well as their smooth variation on the larger coherence length scale. Employing the theoretical framework thus developed, we investigate this Néel proximity effect in a superconductor/antiferromagnet bilayer as a function of interfacial exchange, disorder, and chemical potential, finding rich physics. Our findings also offer insights into experiments which have found a larger than expected suppression of superconductivity by an adjacent antiferromagnet.

Figures (8)

• Figure 1: (a) Sketch of the antiferromagnetic insulator interfaced via a compensated interface to the thin superconductor, considered in the framework of a tight-binding Bogoliubov-de Gennes Hamiltonian in Sec. \ref{['sec:BdG']}. The system represents a two-dimensional 12 × 100 spatial cluster. Blue points are S sites, red and green points correspond to AF sites with opposite directions of the on-site magnetization $\pm \bm m$. (b) Spatial variation of the triplet correlations amplitude $F_{\bm i}^t$ in the investigated AF/S bilayer. Each colored square codes the value of $F_{\bm i}^t$ at a given site. Only small vertical part of the bilayer is shown, which is marked with a black rectangle in panel (a). An alternating sign of the correlations in S commensurate with the Néel order in the AF can be seen along the interfacial direction. The triplet amplitude is normalized to the hopping amplitude, see appendix.
• Figure 2: Schematic depiction of the setup under consideration. A Néel ordered antiferromagnet (AF) is interfaced via a compensated interface to a superconductor (S). The interface is in the $y-z$ plane and the first superconducting layer is at $i_x=0$. The lattice in both parts of the structure is divided into two sublattices A and B. The red arrows depict localized spins in the AF. The basis vectors of the original (prior to the introduction of A and B sublattices) lattice in the superconductor are $\bm a_x$, $\bm a_y$, $\bm a_z$.
• Figure 3: Normal state LDOS for different values of impurity scattering time $\tau$, which is measured in units of the inverse bulk superconducting critical temperature $T_{c0}^{-1}$. $\varepsilon$ is measured in units of $T_{c0}$. We consider $\mu = 0$ and $h=0.3 T_{c0}$ in this figure.
• Figure 4: Electron dispersion of the normal-state S in the reduced Brillouin zone (BZ) $pa \in [-\pi/2,\pi/2]$ considering a 1D system with two sites in the unit cell $\xi_{\pm}(p) = \mp 2t \cos pa - \mu$. The reciprocal lattice vector due to the periodicity enforced by the AF is $Q_{1D} = \pi/a$. The spectrum branches are doubled in the BZ due to the reduction of the BZ volume. The blue line indicates ordinary pairing between $(p_0, \xi_1 = 0)$(1) and $(- p_0,\xi_2 = 0)$(2) electrons corresponding to the zero total pair momentum. The green line indicates Néel pairing between $p_0$(1) and $- p_0 + Q_{1D}$ (3) corresponding to the total pair momentum $Q_{1D}$. From the point of view of the first BZ it is an interband pairing between electrons (1) and (3'). Taking into account that $p_0$ is defined from the condition $-2 t \cos p_0 a - \mu = 0$ one immediately obtains that $\xi_1 - \xi_{3'} = 2\mu$. That is, the energy difference between (1) and (3') electrons grows with $\mu$ thus reducing the efficiency of pairing. The antiferromagnetic gap opening as discussed in Fig. \ref{['ldos_normal']} has been disregarded in the present simplified figure. $\Delta_0$ is the zero-temperature gap of the bulk S.
• Figure 5: Anomalous Green's function of the Néel triplet correlations summed over positive Matsubara frequencies $F_A^t = \sum \limits_{\omega_m>0} f_t$ as a function of $h_{eff}$ for different values of the mean free time $\tau$. Red line represents the same quantity for an S/F interface with a ferromagnetic insulator producing the same value of the effective exchange field (but homogeneous, not staggered) in the superconductor. The S/F interface is not sensitive to impurities, for this reason only one line is shown for the ferromagnetic case. Each line ends at the critical value of $h_{eff}$ corresponding to the full suppression of superconductivity. We consider $\mu=0$ here.