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arXiv 0909.5267cond-mat.quant-gas
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超冷偶极费米子在晶格上的液晶相

Liquid crystal phases of ultracold dipolar fermions on a lattice

Chungwei Lin, Erhai Zhao, W. Vincent Liu

摘要:

受在超冷原子和分子气体中寻找量子液晶相的启发,我们研究了偶极费米子在二维正方晶格(在$x-y$平面)上的密度波和双极费米子的双极不稳定性,其中偶极指向$z$方向。我们确定的相图使用两个互补的方法,Hatree-Fock平均场论和压缩性的线性响应分析。两者都给出了一致的结果。除了交错的($π$,$π$)密度波,在有限的密度和跳跃参数范围内,该系统的基态首先成为双晶,然后近晶,当偶极相互作用强度增加。这两个阶段的特点是相同的破缺四重(C $_4$)旋转对称性。不同之处在于,双晶相具有封闭的费米面,而近晶相则没有。从双晶相到近晶相的转变与双晶序参量的跳跃有关。这种跳跃与范霍夫奇点密切相关。我们推导了正常各向同性相的集体激发的动力学方程,发现零声模是强朗道阻尼的,因此不是一个很好定义的激发。我们的研究结果的实验意义进行了讨论。

英文摘要:

Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x-y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complimentary methods, the Hatree-Fock mean field theory and the linear response analysis of compressibility. Both give consistent results. In addition to the staggered ($π$, $π$) density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken four-fold (C$_4$) rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well defined excitation. Experimental implications of our results are discussed.

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