AI 中文总结
该研究在调谐至拓扑相变的自旋轨道耦合李伯格模型中，揭示了拓扑带隙闭合附近量子几何增强可通过减小库仑矩阵元增大激子半径，为激子态工程提供了新途径。
AI 中文摘要
激子工程传统上聚焦于修改半经典材料性质，如有效质量与介电屏蔽，却很大程度上忽略了底层电子和空穴布洛赫态的量子几何。这种近似对许多材料适用，但在拓扑带隙闭合附近会失效，此处带隙极值附近的量子度量会大幅增强。该区域中，不同动量的布洛赫态相似性降低，使投影电子-空穴库仑矩阵元减小，进而削弱激子结合能。我们在调谐至拓扑相变的自旋轨道耦合李伯格模型中验证了该机制，被抑制的库仑矩阵元使激子波函数在动量空间变窄，导致实空间中激子半径增大，激子尺寸的这种增大可产生实验可观测的弱场抗磁响应增强。我们的结果表明，量子几何可在拓扑相变附近从根本上重塑激子性质，为激子态工程开辟了此前未被充分探索的途径。
英文摘要
Exciton engineering traditionally focuses on modifying semiclassical material properties, such as the effective mass and dielectric screening, while largely overlooking the quantum geometry of the underlying electron and hole Bloch states. This approximation is adequate for many materials but breaks down near a topological band-gap closing, where the quantum metric around the band extrema becomes strongly enhanced. In this regime, Bloch states at different momenta become less similar, reducing the projected electron--hole Coulomb matrix elements and consequently weakening exciton binding. We demonstrate this mechanism in a spin--orbit-coupled Lieb-lattice model tuned toward a topological phase transition. The suppressed Coulomb matrix elements narrow the exciton wavefunction in momentum space, leading to an enlarged exciton radius in real space. This increase in exciton size produces an experimentally accessible enhancement of the weak-field diamagnetic response. Our results show that quantum geometry can fundamentally reshape exciton properties near a topological phase transition, revealing a previously underexplored route for engineering excitonic states.
