Vortex Spin Liquid with Fractional Quantum Spin Hall Effect in Moiré Chern Bands,Physical Review Letters

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Vortex Spin Liquid with Fractional Quantum Spin Hall Effect in Moiré Chern Bands
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-04 , DOI: 10.1103/physrevlett.133.106502
Ya-Hui Zhang ₁

Affiliation

Recently there is a report of the experimental signatures of a fractional quantum spin hall (FQSH) state at hole filling

n = 3

in a twisted

{MoTe}_{2}

bilayer. Previous theories of FQSH phases simply considered a decoupled pair of a fractional quantum Hall phase and its time reversal partner. Here, we show the first construction of an FQSH phase beyond the decoupling picture. We consider a pair of half-filled

C = \pm 1

Chern bands in the two valleys, similar to the well-studied quantum Hall bilayer, but now with opposite chiralities. Because of the strong intervalley repulsion, we expect a charge gap to open with low-energy physics dominated by the neutral intervalley excitons. However, the presence of an effective “flux” frustrates exciton condensation by proliferating vortices. Here, we construct a vortex liquid of excitons dubbed a vortex spin liquid, formed from exciton pairing of the composite fermions in the decoupled composite Fermi liquid phase. This insulator is a quantum spin liquid with gapless spin excitations carried by the flux of an emergent

U (1)

gauge field. Additionally, there exist neutral and spinless Fermi surfaces formed by fermionic vortices of a nearby intervalley-coherent order. Unlike a conventional Mott insulator, the vortex spin liquid phase also exhibits a quantized FQSH effect with gapless helical charge modes along the edge. Our work demonstrates the possibility of nontrivial FQSH phases and provides predictions to detect them in future experiments.

中文翻译：

莫尔陈能带中具有分数量子自旋霍尔效应的涡旋液体

最近有一份关于空穴填充时分数量子自旋霍尔（FQSH）态的实验特征的报告

n = 3

在扭曲的

{MoTe}_{2}

双层。先前的 FQSH 相理论只是简单地考虑了一对解耦的分数量子霍尔相及其时间反转伙伴。在这里，我们展示了解耦图片之外的 FQSH 阶段的第一个构造。我们考虑一对半满的

C = \pm 1

两个谷中的陈能带，类似于经过充分研究的量子霍尔双层，但现在具有相反的手性。由于强的层间排斥力，我们预计电荷能隙会在以中性层间激子为主的低能物理中打开。然而，有效“通量”的存在会通过扩散涡流来抑制激子凝聚。在这里，我们构建了一种激子涡旋液体，称为涡旋液体，由解耦复合费米液相中复合费米子的激子配对形成。该绝缘体是一种量子自旋液体，具有由涌现的通量携带的无间隙自旋激发