AI 中文总结
本研究针对多轨道超导体，通过求解线性化Eliashberg方程修正了超导配对的粒子置换对称性规则，揭示了内禀时间反演对称性破缺配对的可能性，并指出Sr₂RuO₄中洪特耦合是关键因素。
AI 中文摘要
我们通过求解Sr$_2$RuO$_4$的线性化Eliashberg方程数值解，研究了超导配对态中粒子置换的基本对称性规则。我们发现，一般的多带、频率相关超导能隙函数，在两个配对电子之间发生轨道（$\hat{O}$）或频率（$\hat{T}$）交换时，并不会简单地仅改变符号后保持自身不变，这与此前未经验证就被使用的普遍假设相矛盾。这一现象源于配对相互作用在$\hat{O}$或$\hat{T}$操作下不具有不变性，且被证实对正确解读和理解多带超导态至关重要。我们新发现的对称性规则所蕴含的独特性质之一，是线性化能隙方程中可能出现复本征值，其对应的能隙函数$Δ$在实频率下的实部和虚部始终均不为零，从而内禀地破坏时间反演对称性。我们的数值结果表明，这种独特配对在实际材料Sr$_2$RuO$_4$中存在可能性，且该材料的洪特特性在其中发挥着关键作用。修正后的对称性规则不仅让我们对已知超导态有了更全面的理解，还为探索新奇独特的超导态开辟了新的可能。
英文摘要
We investigate the basic symmetry rule for the particle permutation in superconducting (SC) pairing states by examining the numerical solution of the linearized Eliashberg equation for Sr$_2$RuO$_4$. We find that the general multi-band, frequency-dependent SC gap function does not simply transform to itself up to the minus sign with either orbital ($\hat{O}$) or frequency ($\hat{T}$) exchange between two pairing electrons, contradicting the common assumption which has been used without verification. It originates from the fact that paring interactions are not invariant under the $\hat{O}$ or $\hat{T}$ operation, and is demonstrated to be essential to correctly interpret and understand multi-band SC states. One of unique properties implied by our newly found symmetry rule is the possibility of the complex eigenvalue in the linearized gap equation where the corresponding gap functions $Δ$ always have real and imaginary components both non-zero in real frequencies, inherently breaking the time-reversal symmetry. Our numerical results suggest the possibility of this unique pairing in a real material, Sr$_2$RuO$_4$, for which the Hundness of the material is found to play a key role. The revised symmetry rule not only leads us to more comprehensive understanding of the known SC states, but also opens new possibilities into exotic and unique states.
Comments14 pages, 2 figures in single column, a supplementary file
