We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are described by a two-dimensional (2D) Gross–Pitaevskii (GP) equation with a periodic potential and Lee–Huang–Yang (LHY) term. The LQDs are divided in two types: onsite-centered and offsite-centered LQDs, the centers of which are located at the minimum and the maximum of the potential, respectively. The stability areas of these two types of LQDs with different number of sites for zero-vorticity and vorticity with S = 1 are given. We found that the μ–N relationship of the stable LQDs with a fixed number of sites can violate the Vakhitov–Kolokolov (VK) criterion, which is a necessary stability condition for nonlinear modes with an attractive interaction. Moreover, the μ–N relationship shows that two types of vortex LQDs with the same number of sites are degenerated, while the zero-vorticity LQDs are not degenerated. It is worth mentioning that the offsite-centered LQDs with zero-vorticity and vortex LQDs with S = 1 are heterogeneous.

我们研究零涡度和涡旋晶格量子液滴（LQDs）的稳定性，这些液滴由具有周期性势和Lee-Huang-Yang（LHY）项的二维（2D）Gross-Pitaevskii（GP）方程描述。LQD分为两种：以现场为中心的LQD和以场外为中心的LQD，其中心分别位于电位的最小值和最大值。给出了两种类型的LQD的稳定区域，其中零涡旋和S = 1的涡旋具有不同的站点数。我们发现，具有固定位置数的稳定LQD的μ– N关系可能违反Vakhitov–Kolokolov（VK）准则，这是具有吸引作用的非线性模式的必要稳定性条件。此外，μ– N这种关系表明，具有相同位点数量的两种涡旋LQD都退化了，而零涡度LQD却没有退化。值得一提的是，具有零涡度的偏心LQD和具有S = 1的涡旋LQD是异质的。