AI 中文总结
该研究探究自旋轨道耦合BCS-BEC渡越中配对关联与量子几何的相互作用，推导对尺寸张量并分解为带内与量子几何带间贡献，分析库珀对尺寸和相干长度的演化及量子几何贡献，揭示其与费米面拓扑的关联。
AI 中文摘要
我们研究自旋轨道耦合BCS-BEC渡越中配对关联与量子几何之间的相互作用。在螺旋度基下，我们推导了两体束缚态的精确对尺寸张量，并表明它可分为带内贡献和由量子度量决定的量子几何带间贡献。我们将这种分解扩展到零温度下的两个不同多体长度尺度：从平均场BCS理论得到的库珀对尺寸，以及从高斯涨落理论得到的相干长度。尽管这些量在BCS区几乎重合，但在远离BCS区时它们描述不同的物理性质：对尺寸表征对的内部范围，而相干长度表征序参量的长波长响应。我们针对三维Rashba、三维Weyl和二维Rashba自旋轨道耦合模型计算了这两个量。我们发现，随着自旋轨道耦合增强，对尺寸随对的局域化而单调减小，而相干长度在渡越区呈现明显的极小值，之后在BEC区随着复合玻色子变得弱相互作用而再次增大。该极小值与无相互作用费米面坍缩到螺旋度带极小值的环或球上有关。量子几何贡献可达对尺寸的近三分之一、相干长度的约40%，并跟踪底层螺旋度费米面拓扑的相同变化。
英文摘要
We investigate the interplay between pairing correlations and quantum geometry in the spin-orbit-coupled BCS-BEC crossover. Working in the helicity basis, we derive the exact pair-size tensor for the two-body bound states and show that it separates into intraband and quantum-geometric interband contributions, with the latter determined by the quantum metric. We extend this decomposition to two distinct many-body length scales at zero temperature: the Cooper-pair size, obtained from mean-field BCS theory, and the coherence length, obtained from the Gaussian fluctuation theory. Although these quantities almost coincide in the BCS regime, they describe distinct physical properties away from it, with the pair size characterizing the internal extent of a pair and the coherence length characterizing the long-wavelength response of the order parameter. We evaluate both quantities for three-dimensional Rashba, three-dimensional Weyl, and two-dimensional Rashba spin-orbit coupling models. We find that the pair size decreases monotonically with increasing spin-orbit coupling as the pair localizes, whereas the coherence length develops a pronounced minimum in the crossover regime before growing again in the BEC regime as the composite bosons become weakly interacting. This minimum is tied to the collapse of the noninteracting Fermi surface onto the ring or sphere of helicity-band minima. The quantum-geometric contributions reach up to nearly one third of the pair size and about 40\% of the coherence length, tracking these same changes in the underlying helicity Fermi-surface topology.
Comments14 pages with 3 figures
