Text S1 MT-measured electrical conductivity beneath the Hengshan Mountains, north China In the initial report by Wei et al. , the upper limit of the electrical conductivity was ~0.25 S/m. However, a careful re-examination of the “resistivity profile model by MT” provided by them yields an upper boundary of ~0.15 S/m. In our calculation we used a value of ~0.2 S/m as approximation. References: Wei, W. B., et al. (2008), Geoelectric structure of lithosphere beneath eastern North China: features of a thinned lithosphere from magnetotelluric soundings, paper presented at The 19th International Workshop on Electromagnetic Induction in the Earth, Beijing, China. Figure S1 Sample assembly for the electrical conductivity measurement of single crystal. The Pt-capsule was used to seal the sample and also as a shielding layer to minimize the influence of leakage current through the assembly. Dimensions of the sample are ~0.70×0.95 mm for the cross section and ~0.15 mm for the thickness. Figure S2 Profile analysis of FeO content across the boundary between Pt-electrode foil and sample. The relative loss of Fe to the electrode was not significant, and only the outmost ~1-2 m lost ~25% Fe and the adjacent ~2-9 m lost ~12-20% Fe. Figure S3 The complex impedance spectra of a single crystal mantle clinopyroxene determined with the same assembly, from 400 to 1000 °C, as in the measurements of polycrystalline lower crustal clinopyroxene. Inset is the spectrum at 900 °C but on a different scale. The composition of this sample is dramatically different from that of the lower crust clinopyroxene, and the purpose of these measurements on this crystal was only to address the shape of the spectra, as well as its shifting with increasing temperatures. The general shapes of the spectra of this crystal, and also the shifting to higher frequency with increasing temperature, are almost the same as those on the polycrystalline lower crustal clinopyroxene, with the same assembly, and as those on the lower crustal clinopyroxene crystal, with the assembly in Figure 1. Note that grain size of clinopyroxene derived from the lower crust is usually up to ~1 mm, which cannot be used for the assembly of the powdered samples, e.g. ~3.0 mm in diameter and ~2.0 mm in length. Obtained data on the mantle clinopyroxene will be published elsewhere. Figure S4 Representative (a) Complex and (b) Bode diagram of impedance spectra in the frequency range of 0.01 to 106 Hz. These spectra are from the mixture of lower crustal clinopyroxene with 190 ppm H2O and <0.1% NaCl at 400 ºC. |Z| and Theta are the modulus of Z’ and Z’’ and phase angle, respectively. No essential changes in the spectra shapes are observed from 1 to 0.03 Hz. Figure S5 Impedance spectra obtained from the background (dense ceramic Al2O3) measurements in the range of 106 to 0.1 Hz (from left to right along the Z’-axis). 1 0.1 (S/m) 0.01 1E-3 1E-4 1E-5 1E-6 6 8 10 12 14 16 18 -1 10000/T (K ) Figure S6 Comparison of activation enthalpies between a failed and a normal experiment. Data in black color are from the sample with ~375 ppm H2O; data in red color are from a failed experiment in which the water content changed from ~190 ppm to ~350 ppm after the run. Figure S7 Lower crustal granulite with typical layering. The starting material used in our experiments was separated from this sample (Hannuoba, north China). The mineral assemblages present in this sample are clinopyroxene (cpx), orthopyroxene (opx) and plagioclase (plag), without other phases in visible amount (e.g. <1%).