发表机构
University of Florida; University of Utah（佛罗里达大学; 犹他大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对零磁场下无费米面的平带，利用量子几何推导了磁场诱导的能带位移与轨道响应公式，修正了德哈斯-范阿尔芬效应的 Lifshitz-Kosevich 公式，并通过 Chern 晶格模型数值验证了结论。
AI 中文摘要
零磁场下完全平带的速度为零、有效质量发散且无费米面，因此标准轨道磁性理论不适用。我们证明磁场会产生有效色散。在非对运动量的莫伊尔代数展开中，能带能量获得一阶位移 $B\\,\mathcal{M}(\mathbf k)$（由布洛赫态的轨道矩决定）和二阶位移 $\tfrac12\mathcal{X}(\mathbf k)B^{2}$，我们得到了该二阶位移的规范不变系数的闭式表达式。这两个函数与贝里曲率 $\Omega$ 共同决定了整个轨道响应。磁化率完全由几何决定，对于一般的孤立平带，它重现了已确立的规范不变响应公式。当化学势固定在平带上时，$\mathcal{M}=0$ 的等值线成为涌现费米面，对其附近的激发进行玻色化处理可得到修正的 Lifshitz-Kosevich 公式，其能级间距与 $B$ 的平方成正比。振荡的相移由涌现费米面周围的贝里相位和 $\mathcal{X}$ 共同决定。当能带是窄带而非完全平带时，振荡频率以无参数的形式从零场费米面面积过渡到 $\mathcal{M}=0$ 等值线的面积。我们通过精确对角化平化的 Chern 晶格模型，数值验证了这些分析结果。
英文摘要
A band that is exactly flat at zero magnetic field has zero velocity, a divergent effective mass, and no Fermi surface, so the standard theory of orbital magnetism does not apply. We show that the magnetic field generates an effective dispersion. In the expansion organized by the Moyal algebra of the noncommutative kinetic momenta, the band energy acquires a first-order shift $B\,\mathcal{M}(\mathbf k)$, set by the orbital moment of the Bloch state, and a second-order shift $\tfrac12\mathcal{X}(\mathbf k)B^{2}$, whose gauge-invariant coefficient we obtain in closed form. These two functions, together with the Berry curvature $Ω$, fix the entire orbital response. The susceptibility is purely geometric, and for a generic isolated flat band it reproduces the established gauge-invariant response formula. With the chemical potential pinned to the flat band, the $\mathcal{M}=0$ contour becomes an emergent Fermi surface, and bosonizing excitations in its vicinity yields a modified Lifshitz--Kosevich formula with level spacing quadratic in $B$. The phase shift of the oscillations is given jointly by the Berry phase around the emergent Fermi surface and $\mathcal{X}$. When the band is narrow rather than exactly flat, the oscillation frequency crosses over, with a parameter-free profile, from the zero-field Fermi-surface area to the area of the $\mathcal{M}=0$ contour. We verify our analytical findings numerically by exactly diagonalizing a flattened Chern lattice model.
