The modern scope of fermiology encompasses not just the classical geometry of Fermi surfaces but also the geometry of quantum wave functions over the Fermi surface. This enlarged scope is motivated by the advent of topological metals—metals whose Fermi surfaces are characterized by a robustly nontrivial Berry phase. We review the extent to which topological metals can be diagnosed from magnetic-field-induced quantum oscillations of transport and thermodynamic quantities. A holistic analysis of the oscillatory wave form is proposed, in which different characteristics of the wave form (e.g., phase offset, high-harmonic amplitudes, temperature-dependent frequency) encode different aspects of a topologically nontrivial Fermi surface. Which characteristic to focus on depends on ( a) the orientation of the magnetic field relative to certain crystallographic axes, ( b) the symmetry class of the topological metal, and ( c) the separation of Fermi-surface pockets in quasimomentum [Formula: see text] space. Closely proximate pockets arise when (1) spin–split pockets are nearly overlapping due to a weak spin–orbit force or when (2) two pockets touch at an isolated [Formula: see text] point, which can be a topological band-touching point or a saddlepoint in the energy-momentum dispersion. The emergence of a pseudospin degree of freedom (in case 1) and the implications of magnetic breakdown (in case 2) are reviewed, with emphasis on new aspects originating from the (nonabelian) Berry connection of the Fermi surface. Future extensions of topofermiology are suggested in the directions of interaction-induced Fermi-liquid instabilities and two-dimensional electron liquids.

中文翻译：

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拓扑金属的费米学


费米学的现代范围不仅包括费米表面的经典几何，还包括费米表面上的量子波函数的几何。这种扩大的范围是由拓扑金属的出现所推动的，拓扑金属的费米表面以稳健的非平凡 Berry 相为特征。我们回顾了从磁场诱导的传输量和热力学量的量子振荡中诊断拓扑金属的程度。提出了振荡波形的整体分析，其中波形的不同特性（例如，相位偏移、高谐波幅度、温度相关频率）编码拓扑非平凡费米表面的不同方面。关注哪个特性取决于 （ a） 磁场相对于某些晶体轴的方向，（ b） 拓扑金属的对称性类别，以及 （ c） 准动量 [公式：见正文] 空间中费米表面口袋的分离。当 （1） 由于较弱的自旋-轨道力而导致自旋分裂口袋几乎重叠时，或者当 （2） 两个口袋接触一个孤立的 [公式：见正文] 点时，就会出现非常接近的口袋，该点可以是拓扑带接触点或能量-动量色散中的鞍点。回顾了伪自旋自由度的出现（情况 1）和磁击穿的影响（情况 2），重点是源自费米表面的（非阿贝尔）Berry 连接的新方面。拓扑病学的未来扩展建议在相互作用诱导的费米液体不稳定性和二维电子液体的方向上。