. This discovery not only confirms TaAs as a 3D TWS, but also provides an ideal platform for realizing exotic physical phenomena (for example, negative magnetoresistance, chiral magnetic e ects and the quantum anomalous Hall e ect) which may also lead to novel future applications.

We found that the high-pressure-synthesized material LiOsO 3 (see Supplementary Information) shows a structural transition at a temperature T s = 140 K. The room-temperature crystal structure of LiOsO 3 was initially examined using powder X-ray diffraction (XRD). The Goldschmidt diagram predicts that LiOsO 3 crystallizes into a LiNbO 3 -type structure 3,10 , and a preliminary refinement of the structure was carried out in the R-3c space group with Os at the 6b site 0,0,0 and O at the 18e siteTo investigate the position of the Li ion we turned to neutron diffraction, which is much more sensitive to Li than XRD. The neutron diffraction patterns collected above T s could be successfully described in the R-3c space group, in agreement with the XRD refinement, with the Li ion at the 6a position 0,0,1/4. Atomic absorption spectrometry (see Supplementary Information) indicated that the average Li mass was 2.77%, which corresponds to the composition Li 0.98 OsO 3 . We have used the stoichiometric composition throughout the structural analysis. The refinement indicated highly anisotropic thermal displacements of the Li ions with considerable extension along the c-axis (Table 1 and Fig. 1), which might indicate that the Li ions are distributed equally among equivalent 12c sites 0,0,z and 0,0,1/2-z either side of the oxygen layer at z = 1/4, as reported for LiNbO 3 and LiTaO 3 (refs 3, 11).The thermal variation of the structure of LiOsO 3 was studied by neutron diffraction for temperatures between 10 and 300 K. Figure 1a-d shows structural data obtained from refinements in the R-3c space group. The lattice parameters ( Fig. 1a) decrease uniformly from 300 K until T s = 140 K, below which the parameter c increases and a decreases with only a small variation in the unit-cell volume. Just below T s , the non-symmetry-breaking strain components e xx + e yy and e zz vary almost linearly (Fig. 1b). These 4 results show that the phase transition is continuous and the strain components behave like a secondary order parameter coupled to a primary one via a linear-quadratic free energy invariant 12 . The primary order parameter must necessarily be symmetry-breaking according to Landau's theory of second-order phase transitions 12 . Furthermore, the anisotropic thermal parameter  33 , which describes Li displacements along the c-axis, increases markedly below T s (Fig. 1c). This indicates that the primary structural instability involves the position of the Li ions along the c-axis (Fig. 1d).Given that the phase transition involves a change in symmetry, we find from representation theory 13 that there are three isotropy subgroups, R-3, R32 and R3c, which maintain the translational invariance of the R-3c space group and allow the transition to be continuous. These space groups were tested by refinement against the neutron diffraction data at 10 K. Note that R-3 and R32 should generate additional reflections below T s which were not observed in the experiment. The refinement in the non-centrosymmetric R3c space group gave the best de...

Two-dimensional materials provide extraordinary opportunities for exploring phenomena arising in atomically thin crystals. Beginning with the first isolation of graphene, mechanical exfoliation has been a key to provide high-quality two-dimensional materials, but despite improvements it is still limited in yield, lateral size and contamination. Here we introduce a contamination-free, one-step and universal Au-assisted mechanical exfoliation method and demonstrate its effectiveness by isolating 40 types of single-crystalline monolayers, including elemental two-dimensional crystals, metal-dichalcogenides, magnets and superconductors. Most of them are of millimeter-size and high-quality, as shown by transfer-free measurements of electron microscopy, photo spectroscopies and electrical transport. Large suspended two-dimensional crystals and heterojunctions were also prepared with high-yield. Enhanced adhesion between the crystals and the substrates enables such efficient exfoliation, for which we identify a gold-assisted exfoliation method that underpins a universal route for producing large-area monolayers and thus supports studies of fundamental properties and potential application of two-dimensional materials.

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