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Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations

机译:揭示来自磁量子振荡的FERMI表面波函数的拓扑

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The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase ( λ ) that is subleading in powers of the field; λ is measurable in the phase offset of the de Haas–van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, λ / π are robustly integer valued, owing to the symmetry of the extremal orbit; i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which λ is a topological invariant, as well as the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalcogenides, 3D Weyl and Dirac metals, and crystalline and Z 2 topological insulators. In particular, we point out that a π phase offset in the fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac metal.
机译:磁场中的Bloch电子的现代半导体理论现在包括轨道磁矩和几何相位。这两个概念在BoHR-Sommerfeld量化条件中被编码为作为磁场的电源的相位(λ); λ可在DE HAAS-VAN ALPHEN振荡的相位偏移中测量,以及隧道光谱中的差分电导的固定偏置振荡。在一些固体上并且对于某些场取向,由于极值轨道的对称性,λ/π是强大的整数的重量;即,它们是MagnetOcransport的拓扑不变性。我们的全面对称分析识别任何(磁性)空间组中的固体,其中λ是拓扑不变量,以及Landau水平的对称性退化。通过对封闭,费米表面轨道的十个(且仅为十种)对称类的配方简化了分析。将案例研究用于石墨烯,过渡金属二甲基甲基化物,3D Weyl和Dirac金属,以及结晶和Z 2拓扑绝缘体。特别是,我们指出,基本振荡中的π相位偏移不应被视为用于3D Dirac金属的吸烟枪。

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