Jiang Hong-Chen, Li Zi-Xiang, Seidel Alexander, Lee Dung-Hai
Stanford Institute for Materials and Energy Science, SLAC and Stanford University, Menlo Park, CA 94025, USA.
Department of Physics, University of California, Berkeley, CA 94720, USA.
Sci Bull (Beijing). 2018 Jun 30;63(12):753-758. doi: 10.1016/j.scib.2018.05.010. Epub 2018 May 17.
We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singlet d in the non-trivial phase and triplet S=0 in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.
我们表明，具有反铁磁链内和铁磁链间耦合的掺杂自旋-1/2梯子是一种对称性保护的拓扑非平凡卢廷格液体。开启大的易平面自旋各向异性会驱使系统进入拓扑平凡的卢廷格液体。这两个相都有完全的自旋能隙，并表现出幂律超导对关联。在非平凡相中，库珀对对称性是单重态d，在平凡相中是三重态S = 0。拓扑非平凡的卢廷格液体在存在边界时表现出无隙自旋激发，并且即使在电荷部分的涨落相位被固定时，它也没有非相互作用或平均场理论的类似物。作为自旋各向异性强度的函数，存在一个拓扑相变，在该相变处自旋能隙关闭。我们推测这些卢廷格液体与金属化整数自旋梯子或链中的超导性有关。
