AI 中文总结
本研究探究非磁性杂质对双节点多外尔半金属配对不稳定性的调控，通过投影杂质核与玻恩理论分析，揭示无序可驱动拓扑单极子配对向常规s波配对的交叉，并给出交叉判据与相关物理量的定量关系。
AI 中文摘要
我们研究了非磁性杂质散射如何影响双节点多外尔半金属中配对不稳定性的出现及其可能的共存。在一个明确指定的投影杂质核——谷对角且在每个费米口袋上动量无关——的框架下，在小口袋窗口$q^{\rm max}_{\rm intra}ξ_{\rm dis}\ll1\ll|2\mathbf Q|ξ_{\rm dis}$内，采用玻恩和阿布里科索夫-戈尔可夫理论领头阶处理的非磁性无序，将领头配对不稳定性从拓扑非平庸的单极子通道调控到常规（$s$波）通道，将我们此前的洁净系统分析拓展到了无序体系。随后在手性能带基下的玻恩自能计算给出：（i）能带各向同性的常规通道在节点内标量无序下受安德森保护（$η_s=1$），该保护在投影能带层面以唯象方式引入；对任意$η_s$求解竞争关系得到交叉判据$(1-η_s)/(1-η_m)<T_{c0}^{(s)}/T_{c0}^{(m)}$，表明该机制可承受常规通道保护的显著损耗；（ii）秩为一的单极子扇区将$f_m$确定为精确本征函数，且$η_m(J)=1/(J+2)$，在给定该核的条件下是精确的。$Γ_N/T_{c0}^{(m)}$中的交叉位置由$η_m(J)$、$η_s$以及$r=T_{c0}^{(s)}/T_{c0}^{(m)}$决定。从洁净的投影BdG哈密顿量来看，纯单极子节点携带贝里电荷$\pm J$，与有能隙的常规解不同；洁净节点的热力学性质与电荷相关，$N_{\rm SC}(E)\propto E^{2/J}$且$C\propto T^{1+2/J}$，且剩余态密度仅在$J=1$时存在阈值。该交叉处于中等金属性区域，对于图中使用的示例值$T_{c0}^{(m)}/μ=0.133$，$μ/Γ_N\simeq11$--$14$。
英文摘要
We study how non-magnetic impurity scattering affects the emergence and possible coexistence of pairing instabilities in a two-node multi-Weyl semimetal. Within an explicitly specified projected impurity kernel---valley diagonal and momentum independent across each Fermi pocket, the leading behaviour of non-magnetic disorder in the small-pocket window $q^{\max}_{\rm intra}ξ_{\rm dis}\ll1\ll|2\mathbf Q|ξ_{\rm dis}$, treated at leading order in Born and Abrikosov--Gor'kov theory---quenched disorder tunes the leading pairing instability from a topologically nontrivial monopole channel to a conventional ($s$-wave) one, extending our earlier clean-system analysis into the disordered regime. A Born self-energy calculation in the chiral band basis then gives: (i) a band-isotropic conventional channel that is Anderson protected against intra-node scalar disorder ($η_s=1$), introduced phenomenologically at the projected-band level; solving the competition for arbitrary $η_s$ yields the crossing criterion $(1-η_s)/(1-η_m)<T_{c0}^{(s)}/T_{c0}^{(m)}$, so the mechanism tolerates substantial loss of conventional-channel protection; and (ii) a rank-one monopole sector fixing $f_m$ as the exact eigenfunction with $η_m(J)=1/(J+2)$, exact given that kernel. The crossing location in $Γ_N/T_{c0}^{(m)}$ is set by $η_m(J)$, $η_s$, and $r=T_{c0}^{(s)}/T_{c0}^{(m)}$. From the clean projected BdG Hamiltonian the pure monopole nodes carry Berry charge $\pm J$, distinct from the gapped conventional solution; the clean nodal thermodynamics is charge-dependent, $N_{\rm SC}(E)\propto E^{2/J}$ and $C\propto T^{1+2/J}$, and the residual density of states shows a threshold only for $J=1$. The crossing lies in the moderately metallic regime, $μ/Γ_N\simeq11$--$14$ for the illustrative $T_{c0}^{(m)}/μ=0.133$ used in the figures.
Comments62 pages including appendices, 6 figures
