塞曼场中自旋轨道耦合冷原子和材料中量子无公度Skyrmion晶体和公度到无公度跃迁
Quantum incommensurate Skyrmion crystals and Commensurate to In-commensurate transitions in cold atoms and materials with spin orbit couplings in a Zeeman field
摘要：
本文研究了二维各向异性Rashba型自旋轨道耦合（SOC）和塞曼场作用下晶格中强相互作用的旋量原子。我们发现塞曼场和SOC之间的相互作用提供了一个新的平台，主机丰富和新颖类的量子公度和非公度相位，激发和相变。这些公度相分别包括低塞曼场和高塞曼场下的两个共线态和镜反射SOC参数下的两个共面倾斜态。最重要的是，存在由4个公度相包围的非共面的非公度Skyrmion（IC-SkX）晶体相。计算了所有5个相位以上的新激发谱，特别是IC-SKX相位。三个不同类别的量子相称的不相称的过渡从IC-SKX到其4个相邻的相称的阶段被确定。有限的温度行为和转变进行了讨论。所有相的临界温度可以通过简单地调整每个位点的原子数$ N $而提高到高于当前冷原子冷却技术所能达到的温度。鉴于最近在光晶格中产生冷原子的2d SOC方面取得的令人印象深刻的实验进展，这些新的多体现象可以在当前和不久的将来的冷原子实验中探索。给出了在MnSi、Fe $_{0.5}$ Co $_{0.5}$ Si等材料中的应用，特别是Li $_2$ IrO $_3$中的复杂无公度磁序.
英文摘要：
In this work, we study strongly interacting spinor atoms in a lattice subject to a 2 dimensional (2d) anisotropic Rashba type of spin orbital coupling (SOC) and an Zeeman field. We find the interplay between the Zeeman field and the SOC provides a new platform to host rich and novel classes of quantum commensurate and in-commensurate phases, excitations and phase transitions. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at Mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Skyrmion (IC-SkX) crystal phases surrounded by the 4 commensurate phases. New excitation spectra above all the 5 phases, especially on the IC-SKX phase are computed. Three different classes of quantum commensurate to in-commensurate transitions from the IC-SKX to its 4 neighboring commensurate phases are identified. Finite temperature behaviors and transitions are discussed. The critical temperatures of all the phases can be raised above that reachable by current cold atom cooling techniques simply by tuning the number of atoms $ N $ per site. In view of recent impressive experimental advances in generating 2d SOC for cold atoms in optical lattices, these new many-body phenomena can be explored in the current and near future cold atom experiments. Applications to various materials such as MnSi, Fe$_{0.5}$Co$_{0.5}$Si, especially the complex incommensurate magnetic ordering in Li$_2$IrO$_3$ are given.
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