AI 中文总结
研究拓扑平带中反常朗道能级在里夫希茨 - 科瑟维奇框架内的行为及热阻尼能否揭示量子几何信息。通过最小模型推导理论并分析振荡，发现其有效质量有限且依赖磁场，热阻尼可测量子度规，使量子振荡成探测平带量子几何的工具。
AI 中文摘要
在传统金属中，量子振荡源于费米面回旋轨道的朗道量子化，其动力学由里夫希茨 - 科瑟维奇（LK）理论中的费米速度和回旋有效质量支配。相比之下，完美平带的群速度为零，这会天真地暗示无限的回旋质量和量子振荡的完全热抑制。然而，拓扑平带可支持反常朗道能级（LLs），其有限场间距由量子几何而非能带曲率产生，使量子振荡得以持续。本文研究此类反常平带 LLs 在 LK 框架内的行为，以及它们的热阻尼是否能揭示量子几何信息。利用具有精确平拓扑带的最小模型，我们推导了这些反常 LLs 的 LK 理论并分析固定密度磁化振荡。结果振荡呈现出有限的 LK 有效质量，其远大于正常能带值且具有强磁场依赖性。在弱场极限下，这种反常质量反映了 LL 间距的量子几何起源，并与磁场和量子度规的迹成反比。因此，平带量子振荡的热阻尼直接测量量子度规，确立了量子振荡作为平带量子几何探测器的地位。
英文摘要
In conventional metals, quantum oscillations arise from Landau quantization of Fermi-surface cyclotron orbits, whose dynamics are governed by the Fermi velocity and cyclotron effective mass within Lifshitz-Kosevich (LK) theory. A perfectly flat band, by contrast, has vanishing group velocity, which would naively imply an infinite cyclotron mass and complete thermal suppression of quantum oscillations. Yet topological flat bands can support anomalous Landau levels (LLs) whose finite-field spacing is generated by quantum geometry rather than band curvature, allowing quantum oscillations to persist. This work addresses how such anomalous flat-band LLs behave within the LK framework and whether their thermal damping can reveal quantum geometric information. Using a minimal model with exactly flat topological bands, we derive an LK theory for these anomalous LLs and analyze fixed-density magnetization oscillations. The resulting oscillations exhibit a finite LK effective mass that is substantially larger than the normal-band value and possesses a strong magnetic-field dependence. In the weak-field limit, this anomalous mass reflects the quantum geometric origin of the LL spacing and scales inversely with both the magnetic field and the trace of the quantum metric. Thus, thermal damping of flat-band quantum oscillations directly measures the quantum metric, establishing quantum oscillations as a probe to flat-band quantum geometry.
Comments5 pages, 4 figures
