We study the magnon-mediated pairing between fermions on the surface of a topological insulator (TI) coupled to a ferromagnetic insulator with a tilted mean field magnetization. Tilting the magnetization toward the interfacial plane reduces the magnetic band gap and leads to a shift in the effective TI dispersions. We derive and solve the self-consistency equation for the superconducting gap in two different situations, where we neglect or include the frequency dependence of the magnon propagator. Neglecting the frequency dependence results in $p$-wave Amperean solutions. We also find that tilting the magnetization into the interface plane favors Cooper pairs with center-of-mass momenta parallel to the magnetization vector, increasing $T_c$ compared to the out-of-plane case. Including the frequency dependence of the magnon propagator, and solving for a low number of Matsubara frequencies, we find that the eigenvectors of the Amperean solutions at the critical temperature are dominantly odd in frequency and even in momentum, thus opening the possibility for odd-frequency Amperean pairing.

中文翻译：

---

拓扑绝缘体-铁磁绝缘体双层中可能由奇频安培磁子介导的超导

我们研究了倾斜的平均场磁化强度耦合到铁磁绝缘体的拓扑绝缘体（TI）表面上费米子之间的磁振子介导的配对。使磁化朝向界面平面倾斜会减小磁带隙，并导致有效TI色散发生偏移。我们推导并求解了在两种不同情况下超导间隙的自洽方程，其中忽略或包括了磁振子传播器的频率依赖性。忽略频率依赖性会导致$p$波浪安培方案。我们还发现，将磁化强度倾斜到界面平面有利于Cooper对，其质心矩与磁化矢量平行，增加${Ť}_C$与面外情况相比 包括磁振子的频率依赖性，并求解少量的松原频率，我们发现临界温度下安培解的特征向量在频率甚至动量上主要是奇数，从而为奇频开辟了可能性。安培配对。