两种具有Kitaev自旋液体胶的超导配对模型：微观核与奇数重键星上的宇称交替
Two superconducting pairing models with a Kitaev spin-liquid glue: microscopic kernel and parity alternation on odd-fold bond stars
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中文总结 AI 辅助
本文在掺杂Kitaev蜂窝上构建两种超导配对模型，推导出微观核，揭示键星几何决定宇称-手性关联，并证明奇数重键星上宇称交替定理，给出Chern数等拓扑响应。
中文摘要 AI 辅助
我们在掺杂的Kitaev蜂窝晶格上构建了两种超导配对模型，其微观核是推导出来的而非假设的。两者均由一种键局域胶驱动，该胶在偶宇称和奇宇称配对通道之间保持中性；手性-宇称关联由键星几何决定，而非由微观胶决定。(i) 模型1（奇宇称扇区）：核遵循纯模型的通量扇区选择规则，固定了其分量对角、最近邻可分离、每键秩一的形式，其中$w_\alpha=J_K^2\chi_\alpha\propto r_\alpha m_\alpha$，$m_\alpha$由Hellmann-Feynman定理得出，$r_\alpha\simeq0.24$为数值计算。自旋顶点态为具有键锁定各向异性$\mathbf d$矢量的幺正三重态；其能隙为键正弦的Gram和，因此节点方向由几何固定。(ii) 模型2（偶宇称）：核由区域角手性声子的$C_3$小群选择规则固定，并辅以我们明确陈述其动量约束的Cooper通道扩展。电荷顶点配对为$d+id$单态：宇称分解$f_\pm=g_\pm+p_\pm$投影到$g_\pm$上，因此手性受声子极化支配，$C=\pm4$且$\kappa_{xy}/T=2\kappa_0$。反转泵浦螺旋度会反转Chern数、Kerr旋转和热Hall符号。(iii) 一般定理：在奇数重键星上，单星手性形状因子的角动量阶梯在宇称上交替。由这种键局域形状因子选择的每个手性态都是几何强制的单态-三重态复合体，具有普适振幅比（$n=3$：$d\oplus p$；$n=5$：$g\oplus p$或$d\oplus f$）；相干的加倍星组合可以恢复宇称纯度。混合态的Chern数在拓扑边界上遵循主导的壳上分量。自旋胶驱动$C=\pm2$；电荷核$C=\pm4$。
英文摘要
We construct two superconducting pairing models on doped Kitaev honeycomb, whose microscopic kernels are derived rather than assumed. Both are driven by a bond-local glue neutral between the even- and odd-parity pairing channels; the chirality--parity linkage is set by bond-star geometry, not by the microscopic glue. (i) Model~1(odd-parity sector): the kernel follows from the flux-sector selection rule of the pure model, fixing its component-diagonal, nearest-neighbor separable, rank-one-per-bond form, with $w_α=J_K^2χ_α\propto r_αm_α$, where $m_α$ follows from the Hellmann--Feynman theorem and $r_α\simeq0.24$ is computed numerically. The spin-vertex state is a unitary triplet with a bond-locked anisotropic $\mathbf d$ vector; its gap is a Gram sum of bond sines, so nodal directions are fixed by geometry. (ii) Model~2(even): the kernel is fixed by the $C_3$ little-group selection rule of a zone-corner chiral phonon, up to a Cooper-channel extension whose momentum constraint we state explicitly. The charge-vertex pairing is a $d+id$ singlet: the parity decomposition $f_\pm=g_\pm+p_\pm$ projects onto $g_\pm$, so chirality is slaved to the phonon polarization, with $C=\pm4$ and $κ_{xy}/T=2κ_0$. Reversing the pump helicity reverses the Chern number, Kerr rotation, and thermal Hall sign. (iii) General theorem: on odd-fold bond stars, the angular-momentum ladder of a single-star chiral form factor alternates in parity. Every chiral state selected by such a bond-local form factor is a geometrically enforced singlet--triplet composite with universal amplitude ratios ($n=3$: $d\oplus p$; $n=5$: $g\oplus p$ or $d\oplus f$); coherent doubled-star combinations can restore parity purity. The Chern number of the mixed state follows the dominant on-shell component across a topological boundary. The spin glue drives $C=\pm2$; the charge kernel $C=\pm4$.
发表机构
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）
机构由 AI 辅助整理，请以论文原文为准。
