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According to the celebrated Onsagar-Lifshitz paradigm, the observation ofShubnikov de-Haas and de-Haas van Alphen (SdHvA) oscillations is an indicationof the presence of `closed' orbit Fermi surface in the bulk. We present areal-space based calculation of SdHvA oscillations in generalizedquasi-one-dimensional lattices by relaxing the quasi-classical approximationsembedded in this decades old Onsagar-Lifshitz paradigm. We find that sizablequantum oscillation can arise from `open' Fermi surfaces as long as cyclotronorbits can form in real-space with finite, but not necessarily equal, electronhopping along both x- and y-directions. Our results quantitatively explain thepuzzling emergence of SdHvA oscillation in various quasi-one-dimensionalmaterials, including the chain state of YBa2Cu3O6 cuprates, organic materials,various ladder compounds, weakly coupled linear chains, or quantum wires, andother related systems.

Quantum oscillations from `open' Fermi surface in quasi-one-dimensional  lattices: Application to YBa2Cu3O6 cuprates, organic salts, ladder compounds,  and related systems