Symmetry-breaking orders can not only compete with each other, but also be intertwined, and the intertwined topological and symmetry-breaking orders make the situation more intriguing. This work examines the archetypal correlated flat band model on a checkerboard lattice at filling ν=2/3 and we find that the unique interplay between smectic charge order and topological order gives rise to two novel quantum states. As the interaction strength increases, the system first transitions from a Fermi liquid (FL) into FQAH smectic (FQAHS) state, where the topological order coexists cooperatively with smectic charge order with enlarged ground-state degeneracy and interestingly, the Hall conductivity is σxy=ν=2/3, different from the band-folding or doping scenarios. Further increasing the interaction strength, the system undergoes another quantum phase transition and evolves into a polar smectic metal (PSM) state. This emergent PSM is an anisotropic non-Fermi liquid, whose interstripe tunneling is irrelevant while it is metallic inside each stripe. Different from the FQAHS and conventional smectic orders, this PSM spontaneously breaks the two-fold rotational symmetry, resulting in a nonzero electric dipole moment and ferroelectric order. In addition to the exotic ground states, large-scale numerical simulations are also used to study low-energy excitations and thermodynamic characteristics. We find that the onset temperature of the incompressible FQAHS state, which also coincides with the onset of non-polar smectic order, is dictated by the magneto-roton modes. Above this onset temperature, the PSM state exists at an intermediate-temperature regime. Although the T = 0 quantum phase transition between PSM and FQAHS is first order, the thermal FQAHS-PSM transition could be continuous. We expect the features of the exotic states and thermal phase transitions could be accessed in future experiments.

中文翻译：

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从分数量子反常霍尔近晶到极性近晶金属：相关拓扑平带中电子液晶序与拓扑序之间的非平凡相互作用


对称破缺序不仅可以相互竞争，还可以相互交织，而拓扑和对称破缺序的交织使得情况更加耐人寻味。这项工作研究了填充 ν=2/3 时棋盘晶格上的原型相关平带模型，我们发现近晶电荷序和拓扑序之间的独特相互作用产生了两种新颖的量子态。随着相互作用强度的增加，系统首先从费米液体（FL）转变为FQAH近晶（FQAHS）态，其中拓扑序与近晶电荷序共存，基态简并度增大，有趣的是，霍尔电导率为 σxy= ν=2/3，与能带折叠或掺杂场景不同。进一步增加相互作用强度，系统经历另一个量子相变并演变成极性近晶金属（PSM）态。这种新兴的 PSM 是一种各向异性的非费米液体，其条带间隧道效应是无关的，而它在每个条带内部都是金属的。与FQAHS和传统近晶阶不同，这种PSM自发地打破了二次旋转对称性，从而产生非零电偶极矩和铁电阶。除了奇异的基态之外，大规模数值模拟还用于研究低能激发和热力学特性。我们发现不可压缩 FQAHS 态的起始温度（也与非极性近晶序的起始温度一致）由磁轮模式决定。高于该起始温度，PSM 状态存在于中间温度状态。 尽管 PSM 和 FQAHS 之间的 T = 0 量子相变是一阶的，但热 FQAHS-PSM 转变可以是连续的。我们期望在未来的实验中能够获得奇异态和热相变的特征。