Are there quantum oscillations in an incommensurate charge density wave?

Abstract

Because a material with an incommensurate charge density wave (ICDW) is only quasi-periodic, Bloch's theorem does not apply and there is no sharply defined Fermi surface. We will show that, as a consequence, there are no quantum oscillations which are truly periodic functions of $1/B$ (where $B$ is the magnitude of an applied magnetic field). For a weak ICDW, there exist broad ranges of $1/B$ in which approximately periodic variations occur, but with frequencies that vary inexorably in an unending cascade with increasing $1/B$. For a strong ICDW, e.g. in a quasi-crystal, no quantum oscillations survive at all. Rational and irrational numbers really are different.

arXiv comment14 pages, 17 figures

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• Semiclassical Dynamics, Berry Curvature and Spiral Holonomy in Optical Quasicrystals
• Quantum oscillations in a bilayer with broken mirror symmetry: a minimal model for YBa${}_2$Cu${}_3$O${}_{6+\delta }$
• Low-frequency Quantum Oscillations from Interactions in Layered Metals
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• Anomalous magnetic transport and extra quantum oscillation in semi-metallic photon-like fermion gas
• Emergent channel over a pair of pockets in strong density waves
• Density-wave tendency from a topological nodal-line perspective