  Recent experimental work has brought the twin issues of the origin of
non-Lifshitz-Kosevich scaling in de Haas van Alphen (dHvA) and its precise
relation to anomalously broad non-quasiparticle spectral features in "strange"
metals, to the forefront. Here, we revisit these issues in the specific context
of a "local" quantum critical phase in an extended periodic Anderson model
(EPAM). In contrast to the famed Kondo-RKKY scenarios for local quantum
criticality, strong local valence fluctuations cause Kondo destruction in the
EPAM. We uncover a common underlying element, namely, the
Kondo-destruction-driven infra-red continuum branch-cut behavior in the
one-electron propagator, as the relevant feature that governs both
non-Lifshitz-Kosevich scaling in dHvA and anomalously broad non-quasiparticle
spectral responses in such a "strange" metal. Employing a non-perturbative
scheme to treat effects of non-magnetic disorder in this version of a local
strange metal, we propose a modified Dingle scaling that can also be used to
test "local" criticality scenarios. Thus, our findings potentially afford an
internally consistent description of novel fermiology expected to manifest in
strange metals arising as a result of Kondo-destruction coming from an
underlying orbital-selective Mott transition.
