Extracting a More Realistic Pseudopotential for Aluminum, Lead, Niobium and Tantalum from Superconductor Electron Tunnelling Spectroscopy Data

Comparison of Heine–Abarenkov and alternative pseudopotentials for electron–phonon interaction in aluminium, lead, lithium and calcium

“…We transform Eqs. (6) and (7) into a programmable version [19]. To this end we have to transform summation over q in Eq.…”

“…We assume the Coulomb force between atoms depends only on the interatomic distance (central force model) and calibrate the force constants with neutron scattering data (Born-von Karman theory). The task is relatively straightforward for aluminium when, for sufficiently accurate dispersion, we are able to cut the interatomic force off beyond the 6th spherical shell formed by other atoms surrounding a given atom, see [19] for further details. For lead we have to calibrate the interatomic force over 20 atomic shells, see FIG.…”

“…This may lead to a spectacular longitudinal peak of the phonon density of states if we simply differentiate the dispersion curve numerically. We devised a method to avoid this difficulty, see [19] for further details.…”

“…We can adjust the values of δV and r 1 in Eq. (10) to minimise the difference between theoretical and experimental data of tunnelling conductance [19], that is we are seeking the potential via a procedure of inversion with no physics other than what is implied by Eqs. (6) and (7).…”

“…(6) and (7). For completeness we note that in a previous publication [19] we found V (r) in aluminium in the superconducting state via a slightly different inversion procedure: we sought V (q) in reciprocal space, free to vary over the range 0 ≤ q ≤ 2k F , and then converted it via Eq. (4) into a potential well in real space, with a maximum depth slightly deeper than 1 in Fermi energy, compared with the current depth ∼1.13 in Fermi energy.…”