Inhomogeneity identification by measuring magnetic quantum oscillations

This study explores the identification of sample inhomogeneity via magnetic quantum oscillations analysis in semimetal NbSb$_2$. By doping Bi and Cr, we obtained a homogeneous Bi-doped sample and an inhomogeneous Cr-doped sample, whose homogeneity was confirmed by comparing the magnetic quantum oscillation before and after grinding the samples. The magnetic quantum oscillations in the inhomogeneous sample exhibited a distinct phase shift and unusual field-dependent amplitude, believed to result from a non-uniform Fermi energy. The analysis of the magnetic quantum oscillations demonstrated that the homogeneous Bi-doped sample can be interpreted by the symmetric and Lorentzian effective Fermi energy distribution, while the inhomogeneous Cr-doped sample exhibited an asymmetric distribution, illustrating an unconventional violation of the Lifshitz-Kosevich formula. This research provides a novel method for identifying material inhomogeneity and mitigating potential misinterpretations of magnetic quantum oscillations' unusual phase, commonly seen as a nontrivial Berry phase indicator in topological materials studies.