We show that attractive two-dimensional spinor Bose-Einstein condensates with helicoidal spatially periodic spin-orbit coupling (SOC) support a rich variety of stable fundamental solitons and bound soliton complexes. Such states exist with chemical potentials belonging to the semi-infinite gap in the band spectrum created by the periodically modulated SOC. All these states exist above a certain threshold value of the norm. The chemical potential of fundamental solitons attains the bottom of the lowest band, whose locus is a ring in the space of Bloch momenta, and the radius of the ring is a non-monotonous function of the SOC strength. The chemical potential of soliton complexes does not attain the band edge. The complexes are bound states of several out-of-phase fundamental solitons whose centers are placed at local maxima of the SOC-modulation phase. In this sense, the impact of the helicoidal SOC landscape on the solitons is similar to that of a periodic two-dimensional potential. In particular, it can compensate repulsive forces between out-of-phase solitons, making their bound states stable. Extended stability domains are found for complexes built of two and four solitons (dipoles and quadrupoles, respectively). They are typically stable below a critical value of the chemical potential.

中文翻译：

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具有螺旋自旋轨道耦合的玻色-爱因斯坦凝聚中的稳定二维孤子配合物

我们展示了具有螺旋空间周期性自旋轨道耦合 (SOC) 的有吸引力的二维旋量玻色-爱因斯坦凝聚物支持丰富多样的稳定基本孤子和束缚孤子配合物。这种状态与属于由周期性调制的 SOC 产生的带谱中的半无限间隙的化学势一起存在。所有这些状态都存在于规范的某个阈值之上。基本孤子的化学势达到最低带的底部，其轨迹是布洛赫动量空间中的一个环，环的半径是SOC强度的非单调函数。孤子配合物的化学势不能达到能带边缘。复合物是几个异相基本孤子的束缚态，其中心位于 SOC 调制相位的局部最大值处。从这个意义上说，螺旋状 SOC 景观对孤子的影响类似于周期性二维势的影响。特别是，它可以补偿异相孤子之间的排斥力，使它们的束缚态稳定。对于由两个和四个孤子（分别为偶极子和四极子）构建的复合物，发现了扩展稳定性域。它们通常在化学势的临界值以下是稳定的。对于由两个和四个孤子（分别为偶极子和四极子）构建的复合物，发现了扩展稳定性域。它们通常在化学势的临界值以下是稳定的。对于由两个和四个孤子（分别为偶极子和四极子）构建的复合物，发现了扩展稳定性域。它们通常在化学势的临界值以下是稳定的。