Sample preparation and fabrication

WTe₂ single-crystal films were prepared by a standard mechanical exfoliation technique from bulk WTe₂ crystals (HQ Graphene) onto substrates. The typical film dimension is about 300 μm, greater than the beam size under an infrared microscope. The film thickness was determined by a Bruker Dimension Edge AFM system (probe model RTESP-300, tapping mode). Here, all the films we investigated have thickness of above 50 nm, in which the possible surface oxidation has a negligible effect on the spectrum measurement⁴⁷. Actually, no degradation of plasmonic devices was found during the nanofabrication and measurement process. Two types of substrates were used in this work. One is Si/SiO₂ substrate with SiO₂ thickness of 300 nm. The other is polycrystalline diamond grown by chemical vapor deposition (CVD) method with thickness of 300 μm, in which no polar phonon exists in our range of interest. Using the latter substrate, one can eliminate the hybridization effect of surface-polar phonons with plasmon, and hence measure the intrinsic plasmon dispersion. Disk/rectangle/ribbon arrays were fabricated from the exfoliated films by electron-beam lithography and subsequent reactive ion etching. Sulfur hexafluoride (SF₆) was used as the reaction gas. For the rectangle (ribbon) arrays, the gaps between adjacent rectangles along a and b axes (ribbons) are kept larger than half of L_a and L_b (ribbon width), so that the rectangles (ribbons) can be approximately regarded as isolated resonance cavities. Because of the inevitable lateral etching, the dimensions listed in Fig. 3a are nominal values, with real length of about 10% uncertainty and the corresponding aspect ratio of 2 ± 0.15 (see Supplementary Table ¹). The film thickness d_film is normalized to 100 nm with the wave vector q multiplied by d_film/100 in Figs. 4a and ​and5b,5b, given that the sheet conductivity σ is proportional to the thickness.