Extended Data Table 1 Numerical validation of the static BECs sum rule

From: Born effective charges and vibrational spectra in superconducting and bad conducting metals

  1. Numerical values of the terms appearing in equation (6) are reported for H3S and Al as computed by the DFPT calculation described in Supplementary Section V. We introduce the following shorthand notation in the table: V stands for \(-{n}_{{\varepsilon }_{F}}{\sum }_{s}{\langle \frac{\partial {\bar{V}}_{s\beta }^{\Gamma }}{i\partial {q}_{\alpha }}\rangle }_{F}\) and T for \( {n}_{{\varepsilon }_{F}}{\langle {v}_{\bf k}^{\alpha }{p}_{\bf k}^{\beta }\rangle }_{F}\). As a comparison, we provide numerical results for the dynamical BECs sumrule in the dynamic limit, equation (S3), at equal convergence parameters. The values of the individual atomic contributions to the sum rule of H3S are listed in the Supplementary Table 3. The largest errors are observed in the dynamic sum rule for H3S and are due to the finite imaginary constant of the i0+ regularization in \({\bar{Z}}_{s,\alpha \beta }^{{{{\rm{Dyn}}}}}(i{0}^{+})\) (see Sec. V). A finite i0+ constant should be used only in the dynamical case and in presence of low-energy vertical interband transitions, that occur in the H3S band-structure, but not in the Al one.
  2. Source data
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