论文标题

掺杂手性自旋液体 - 拓扑超导体还是手性金属?

Doping the chiral spin liquid -- topological superconductor or chiral metal?

论文作者

Song, Xue-Yang, Vishwanath, Ashvin, Zhang, Ya-Hui

论文摘要

我们指出,三角形晶格上有两种不同的手性自旋液态,并讨论了掺杂它们的导电状态。这些标记为CS1和CS2的状态与两个不同边缘状态的不同拓扑顺序相关,尽管它们都自发地打破了时间逆转对称性并表现出相同的量化自旋霍尔电导。尽管CSL1与Kalmeyer-Laughlin州有关,但CSL2是Kitaev的16倍方法分类的$ν= 4 $成员。两种状态都在旋转的Abrikosov fermion表示中描述,并且可以通过引入带电的果实来访问掺杂的效果。在掺杂CSL2上,带电的圆环的冷凝导致拓扑D+ID超导体。然而,在掺杂CSL1的掺杂时,可能会出现两种不同的情况:首先,如果Holons凝结,则获得了具有双重单元和有限霍尔电导率的手性金属。然而,在第二个新颖的情况下,内部磁通量通过掺杂和圆顶形成骨器整数量子厅(BIQH)状态。值得注意的是,后一个阶段与$ D+ID $超导体相同。在这种情况下,莫特绝缘体到超导体过渡与霍隆的整数量子霍尔高原过渡的骨变体有关。我们将上述两种情况连接到三角晶格上掺杂的手性旋转液体的两项最近数值研究。我们的工作阐明了拓扑超导体,手性旋转液体和量子关键性之间的复杂关系。

We point out that there are two different chiral spin liquid states on the triangular lattice and discuss the conducting states that are expected on doping them. These states labeled CS1 and CS2 are associated with two distinct topological orders with different edge states, although they both spontaneously break time reversal symmetry and exhibit the same quantized spin Hall conductance. While CSL1 is related to the Kalmeyer-Laughlin state, CSL2 is the $ν=4$ member of Kitaev's 16 fold way classification. Both states are described within the Abrikosov fermion representation of spins, and the effect of doping can be accessed by introducing charged holons. On doping CSL2, condensation of charged holons leads to a topological d+id superconductor. However on doping CSL1 , in sharp contrast , two different scenarios can arise: first, if holons condense, a chiral metal with doubled unit cell and finite Hall conductivity is obtained. However, in a second novel scenario, the internal magnetic flux adjusts with doping and holons form a bosonic integer quantum Hall (BIQH) state. Remarkably, the latter phase is identical to a $d+id$ superconductor. In this case the Mott insulator to superconductor transition is associated with a bosonic variant of the integer quantum Hall plateau transition for the holon. We connect the above two scenarios to two recent numerical studies of doped chiral spin liquids on triangular lattice. Our work clarifies the complex relation between topological superconductors, chiral spin liquids and quantum criticality .

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