DOI: 10.5061/dryad.qfttdz0pj
title: Emergent symmetry in lithium molybdate (LMO)

description: 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.
description: 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 &lt; T &lt;
 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 contain the corresponding MR
 results, namely the (inverse square root of the) coefficients of the
 low-field H^2 MR at each temperature (obtained from the raw data files
 shown in the Supplementary Material). Panel G of Fig. 3 is the theoretical
 prediction, while panel H shows the MR coefficients, similarly plotted,
 for field and current along different crystallographic axes. Panel A of
 Fig. 4 shows Hall effect R_H(T) data in LMO at two different field
 strengths, whle panel B compares the T-dependence of R_H(T) with the
 Lorenz ratio whose data were reported in a different
 publication.  In the Supplementary Material, there are 8
 figures containing experimental data (Figs. S1-S8). Figures S1 to S7 all
 show essentially the same thing, namely a zero-field resistivity curve of
 a particular sample (panel A) and MR field sweeps of the corresponding
 sampe at different temperatures (plotted in various ways in panels B-D).
 Figure S8 shows the zero-field resistivity (panel A) and Hall effect data
 (panel B) for two LMO crystals, one superconducting, the other
 non-superconducting. Finally, Figures S9-S11 are results from theoretical
 modelling, as described in the text.