Unconventional superconductivity in altermagnets with spin-orbit coupling

Vanuildo S. de Carvalho, Hermann Freire
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Abstract

We investigate some possible symmetries of the superconducting state that emerges in three-dimensional altermagnets in the presence of spin-orbit coupling. We demonstrate within a weak-coupling approach that altermagnetic fluctuations with form factor $\boldsymbol{g}_{\mathbf{k}}$ promote spin-triplet superconductivity described by gap functions $\boldsymbol{d}(\mathbf{k}) = \boldsymbol{u}(\mathbf{k}) \times \boldsymbol{g}_{\mathbf{k}}$, such that $\boldsymbol{u}(\mathbf{k}) = - \boldsymbol{u}(-\mathbf{k})$. Consequently, this singles out $f$-wave spin-triplet superconductivity as the most favorable pairing state to appear in the vicinity of $d$-wave altermagnetism. Furthermore, we obtain that the combination of spin-singlet superconducting states with altermagnetism gives rise to Bogoliubov-Fermi surfaces, which are protected by a $\mathbb{Z}_2$ topological invariant. Using a Ginzburg-Landau analysis, we show that, for a class of spin-orbit coupled altermagnetic models, a superconducting phase is expected to appear at low temperatures as an intertwined $d + if$ state, thus breaking time-reversal symmetry spontaneously.
具有自旋轨道耦合的变磁体中的非常规超导性
我们研究了自旋-轨道耦合存在时三维变磁体中出现的超导态的一些可能的对称性。我们在弱耦合方法中证明,具有形式因子$\boldsymbol{g}_{mathbf{k}}$的变磁波动会促进由间隙函数$\boldsymbol{d}(\mathbf{k}) = \boldsymbol{u}(\mathbf{k})\times\boldsymbol{g}_\{mathbf{k}}$描述的品三重超导性、这样 $\boldsymbol{u}(\mathbf{k}) = -\boldsymbol{u}(-\mathbf{k})$.因此,这就把 $f$-wavespin-triplet 超导性挑出来,作为在 $d$-wave altermagnetism 附近出现的最有利的配对状态。此外,我们还发现,自旋小卫星超导态与变磁性的结合会产生波哥留布夫-费米面,而波哥留布夫-费米面受到$\mathbb{Z}_2$拓扑不变量的保护。我们利用金兹堡-朗道分析表明,对于一类自旋轨道耦合变磁模型,超导相有望在低温下以交织的 $d + if$ 状态出现,从而自发地打破时间反转对称性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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