Emergent symmetry in lithium molybdate (LMO)

Upon cooling, condensed matter systems typically transition into states of lower symmetry. While the converse, i.e. the emergence of higher symmetry at lower temperatures, has been hypothesized, it is extremely rare. Here, we show how an unusually isotropic 25 magnetoresistance in the highly anisotropic, one-dimensional conductor Li0.9Mo6O17 (LMO), and its temperature dependence, can be interpreted as a renormalization group (RG) flow towards a so-called separatrix. This approach is equivalent to an emergent symmetry in the system. The existence of two distinct ground states – Mott insulator and superconductor – can then be traced back to two opposing RG trajectories. By establishing a direct link between quantum field theory 30 and an experimentally measurable quantity, we uncover a path through which emergent symmetry might be identified in other candidate materials., Hall effect and magnetoresistance (MR) measurements were carried out using a standard ac lockin detection technique in three different magnet cryostat systems: an 8 T Cryogen Free Measurement System from CryogenicTM, a 16 T superconducting magnet from Oxford InstrumentsTM and a 35 T Bitter magnet from the High Field Magnet Laboratory at Radboud University, Nijmegen. For all measurements, field sweeps were performed in both polarities. For the thermal conductivity measurements, we used a zero-field set-up housed in a He-4 flow cryostat that covers the temperature range 10K < T < 300K. We employed a modified steady-state method in which a temperature gradient, measured using a differential thermocouple, is set up across the sample through a pair of calibrated heat-links attached to each end.
In the main manuscript, only Figures 3 and 4 contain data. Panels A/C/E of Fig. 3 contain zero-field resistivity data of LMO with the current applied along the chain. Panels B/D/F of Fig. 3 cont..., ,

凝聚态系统在降温过程中通常会转变为对称性更低的物态。反之，即在更低温度下出现更高对称性的情况虽已被假说提出，但极为罕见。本文中，我们展示了在高度各向异性的一维导体Li₀.₉Mo₆O₁₇（LMO）中，异常各向同性的磁阻（对应第25行）及其温度依赖性，可被解释为朝着所谓分离线的重整化群（renormalization group, RG）流。该过程等价于系统中涌现出的对称性。两种截然不同的基态——莫特绝缘体（Mott insulator）与超导体（superconductor）——的存在，可追溯至两条相反的RG轨迹。通过建立量子场论（对应第30行）与实验可测量量之间的直接联系，我们揭示了一条可在其他候选材料中识别涌现对称性的路径。
霍尔效应与磁阻（magnetoresistance, MR）测量采用标准交流锁相检测技术，在三套不同的磁低温系统中完成：分别是CryogenicTM公司的8 T无液氦测量系统、Oxford InstrumentsTM公司的16 T超导磁体，以及奈梅亨拉德堡德大学高场磁体实验室的35 T比特磁体。所有测量均在磁场正负两种极性下完成扫场。热导率测量则采用置于He-4流动低温恒温器中的零场装置，测量温度范围为10 K < T < 300 K。我们使用了改进的稳态法：通过连接样品两端的一对标定热链接，在样品两侧建立温度梯度，并使用差分热电偶对该梯度进行测量。
在主稿件中，仅图3与图4包含相关数据。图3的A/C/E面板展示了电流沿链方向时LMO的零场电阻率数据。图3的B/D/F面板则……