As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry $C_4$ broken down to $C_2$. Here, we report an observation of a three-state (${\mathbb{Z}}_3$) quantum nematic order, dubbed “Potts-nematicity”, in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an $s{p}^2$-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.

中文翻译：

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六角形sp2光学晶格中Potts向列超流动的证据

由于在向液相和向液相之间存在向列型液晶，该向列型液晶在保持平移对称性的同时破坏了旋转，因此存在一个向列型超流相将超流体和超固体桥接起来。向列级数也出现在相互作用的电子中，并且在高温超导性中已与多轨道相关性很大程度上交织，其中伊辛向列性是由四重旋转对称性引起的$C_4$ 分解为 $C_2$。在这里，我们报告对三态（${\mathbb{ž}}_3$）被称为“ Potts-nematicity”的量子向列级，在冷原子系统中，冷原子装载在由六方晶格描述的六角形光学晶格的激发带中 $s{p}^2$轨道杂交模型。该Potts向列量子态自发地打破了晶格的三重旋转对称性，从质上不同于伊辛向列性。我们的场论分析表明，通过六方晶格中存在的强烈的轨道间混合，复杂的重归一化效应使Potts向列级稳定。这一发现为研究多轨道原子超流体中的量子残留阶数铺平了道路。