Curved graphene: A possible answer to the problem of graphene's diverging magnetic susceptibility

A study of curved graphene in the presence and absence of a real magnetic field is conducted to determine the magnetization and magnetic susceptibility. Utilizing a Dirac model, the Landau-level energy corrections are found. These results are compared with those obtained from a tight-binding model analysis, showing good agreement with the Dirac model. The obtained spectra are then used to calculate the free energy, magnetization, and magnetic susceptibility as functions of the external magnetic field and curvature. The resulting de Haas--van Alphen effect exhibits distinctive signatures due to the curvature of graphene, including a resonance effect when the pseudomagnetic and the real magnetic fields are equal. Considering that curvature induces effective pseudomagnetic fields, a mechanical effect stemming from an electronic contribution is found, resulting in a pseudo de Haas--van Alphen effect without needing an external magnetic field. This effect is associated with oscillating (electronic) forces opposing deformations. These forces, divergent in flat graphene, suggest that graphene (without a substrate) attains mechanical equilibrium through local corrugations. These mechanical deformations prevent the theoretically calculated pristine graphene's diamagnetic divergence at low temperatures, indicating that corrugations produce a finite, experimentally measurable magnetic susceptibility. The divergent susceptibility becomes apparent only when such corrugations are removed using various strategies.