Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu$_3$Zn(OH)$_6$FBr
Yuan Wei1,2, Xiaoyan Ma1,2, Zili Feng1,3, Yongchao Zhang1,2, Lu Zhang1,2, Huaixin Yang1,2,4, Yang Qi5, Zi Yang Meng1,6, Yan-Cheng Wang7*, Youguo Shi1,8*, and Shiliang Li1,2,8*
1Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China 3Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan 4Yangtze River Delta Physics Research Center Co., Ltd., Liyang 213300, China 5State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, China 6Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China 7School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China 8Songshan Lake Materials Laboratory, Dongguan 523808, China
Abstract：We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu$_{3}$Zn(OH)$_6$FBr. The specific heat exhibits a $T^{1.7}$ dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of $Z_2$ quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size $d$, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard's coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.
Feng Z, Li Z, Meng X, Yi W, Wei Y, Zhang J, Wang Y C, Jiang W, Liu Z, Li S, Liu F, Luo J, Li S, Zheng G Q, Meng Z Y, Mei J W, and Shi Y 2017 Chin. Phys. Lett.34 077502
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Wei Y, Feng Z, Hu D H, Lohstroh W, dela C C, Yi W, Ding Z F, Zhang J, Tan C, Shu L, Wang Y C, Wu H Q, Luo J, Mei J W, Meng Z Y, Shi Y, and Li S 2019 arXiv:1710.02991 [cond-mat.str-el]
2021, Vol. 38 
