AI 中文总结
该研究探究合成费米子梯子的霍尔响应，分析粒子密度对其的影响，结合能带结构的 Lifshitz 转变解释相关行为，并探讨其与 Meissner-涡旋转变的关联。
AI 中文摘要
我们表征了存在人工磁通量时无相互作用费米子M腿梯子的霍尔响应，该体系可通过一维光晶格结合合成维度实现。我们聚焦于霍尔不平衡，其可在超冷费米子原子实验中直接测量。在相对大的合成磁通量下，我们发现霍尔不平衡对密度的依赖关系与此前报道的密度无关行为形成鲜明对比。特别地，在粒子（或空穴）密度极小的极限下，霍尔不平衡可被显著增强，或在特定通量下消失并改变符号——我们在腿间耦合很大的 regime 中解析得到了这些特定通量。该行为可通过能带结构的 Lifshitz 转变解释，其中费米点的数量随通量和密度变化。最后，我们通过计算位点分辨的腿电流与 rung 电流，探讨了这些转变与费米子梯子所谓 Meissner-涡旋转变的关联，并讨论了其与玻色子对应体系的异同。
英文摘要
We characterize the Hall response of non-interacting fermionic $M$-leg ladders in the presence of an artificial magnetic flux, that can be realized in one-dimensional optical lattices supplemented with a synthetic dimension. We focus on the Hall imbalance, which can be directly measured in experiments with ultracold fermionic atoms. At relatively large synthetic flux we find a dependence of the density that contrasts with previously reported density-independent behavior. In particular, the Hall imbalance can be significantly enhanced in the limit of small density of particles (or holes), or it can vanish and change sign at specific fluxes, which we obtain analytically in the large inter-leg coupling regime. This behavior is explained in terms of Lifshitz transitions of the band structure, where the number of Fermi points changes as a function of the flux and density. Finally, we explore the connection between these transitions and the so-called Meissner-vortex transition for fermionic ladders by computing the site-resolved leg and rung currents and discussing the similarities and differences with the bosonic counterpart.
Comments14 pages, 6 figures
