Shubnikov–de Haas effect in the Falicov–Kimball model: strong correlation meets quantum oscillation

Abstract

We present a comprehensive investigation of quantum oscillations (QOs) in the strongly-correlated Falicov-Kimball model (FKM). The FKM is a particularly suitable platform for probing the non-Fermi liquid (NFL) state devoid of quasiparticles, affording exact Monte Carlo simulation across all parameter spaces. In the high-correlation regime, we report the presence of prominent QOs in magnetoresistance and electron density at low temperatures within the phase separation state. The frequency behavior of these oscillations uncovers a transition in the Fermi surface as electron density diminishes, switching from hole-like to electron-like. Both types of Fermi surfaces are found to conform to the Onsager relation, establishing a connection between QOs frequency and Fermi surface area. Upon exploring the temperature dependence of QOs amplitude, we discern a strong alignment with the Lifshitz-Kosevich (LK) theory, provided the effective mass is suitably renormalized. Notwithstanding, the substantial enhancement of the overall effective mass results in a notable suppression of the QOs amplitude within the examined temperature scope, a finding inconsistent with Fermi liquid predictions. For the most part, the effective mass diminishes as the temperature increases, but an unusual increase is observed at the proximity of the second-order phase transition instigated by thermal effects. As the transition ensues, the regular QOs disappear, replaced by irregular ones in the NFL state under a high magnetic field. We also uncover significant QOs in the insulating charge density wave state under weak interactions ( $0 \lt U \lt 1$ ), a phenomenon we elucidate through analytical calculations. Our findings shed light on the critical role of quasiparticles in the manifestation of QOs, enabling further understanding of their function in this context.

Keywords

• quantum oscillation
• exactly solvable model
• doped Mott insulator