Fermi-surface topology of the iron pnictide LaFe$_2$P$_2$

We report on a comprehensive de Haas--van Alphen (dHvA) study of the iron pnictide LaFe$_2$P$_2$. Our extensive density-functional band-structure calculations can well explain the measured angular-dependent dHvA frequencies. As salient feature, we observe only one quasi-two-dimensional Fermi-surface sheet, i.e., a hole-like Fermi-surface cylinder around $Gamma$, essential for $s_pm$ pairing, is missing. In spite of considerable mass enhancements due to many-body effects, LaFe$_2$P$_2$ shows no superconductivity. This is likely caused by the absence of any nesting between electron and hole bands.