AI 中文总结
本研究开发了可描述六角晶格等体系非常规键密度波、电流密度波等调制相的框架，推导了朗道自由能，通过随机相位近似从电子相互作用中得到三角晶格上的相关序的基态，为这类体系研究提供了系统方法。
AI 中文摘要
电荷密度波（CDW）序通常被描述为在有序波矢Q处的格点电荷调制，与对称性相关的波矢通常构成多分量序参量流形。近期的研究将这一现象学显著拓展至键密度波与环流密度波，这类波除了在Q处的空间调制外，还在原胞内具有非平凡、可能破缺对称性的结构。这类结构源于具有非零角动量的粒子-空穴凝聚体，与非常规超导体类似，其对称性由小群G_Q描述。本研究开发了一套描述非常规CDW相的框架，该框架同时纳入小群描述的局域对称性，以及多个与对称性相关的有序波矢（即星）的存在。由此得到的多分量序参量在完整空间群的表示下变换，该表示由G_Q的不可约表示诱导而来。我们将该框架应用于具有六重对称性的二维晶格，以及沿高对称线的有序波矢，并推导了对应的朗道自由能。作为微观实例，我们在随机相位近似框架下，从三角晶格上的电子相互作用出发，展示了非常规键序与环流序的涌现，并通过微观评估自由能中的相关系数确定了它们的基态。本框架为描述非常规调制相提供了系统途径，且可便捷拓展至更复杂的晶格。
英文摘要
Charge-density wave (CDW) orders are conventionally described as modulations of on-site charge at an ordering wave vector $\boldsymbol{Q}$ with symmetry-related wave vectors typically forming a multicomponent order-parameter manifold. Recent developments significantly broadened this phenomenology to bond and loop-current density waves, which possess nontrivial, potentially symmetry-breaking textures within the unit cell in addition to their spatial modulation at $\boldsymbol{Q}$. Such textures arise from particle-hole condensates with nonzero angular momentum, analogous to unconventional superconductivity, and their symmetries are described by the little group $G_{\boldsymbol{Q}}$. In this work, we develop a framework for unconventional CDW phases that simultaneously incorporates the local symmetries described by little group and the presence of multiple symmetry-related ordering wave vectors, also known as the star. The resulting multicomponent order parameter transforms under representations of the full space group induced from irreducible representations of $G_{\boldsymbol{Q}}$. We apply this framework to two-dimensional lattices with sixfold symmetry and ordering wave vectors along high-symmetry lines, and derive the corresponding Landau free energies. As a microscopic example, we demonstrate the emergence of unconventional bond and loop-current orders from electronic interactions on the triangular lattice within the random phase approximation, and determine their ground states by microscopically evaluating the relevant coefficients in the free energy. Our framework provides a systematic route to describing unconventional modulated phases and can be readily extended to more complex lattices.
Comments12 pages, 6 figures
