Department of Physics, The University of Texas at Austin, Austin, TX 78712;
Department of Physics, The University of Texas at Austin, Austin, TX 78712.
Proc Natl Acad Sci U S A. 2017 Jul 11;114(28):7295-7300. doi: 10.1073/pnas.1702595114. Epub 2017 Jun 27.
We present a fresh perspective on the Landau level quantization rule; that is, by successively including zero-field magnetic response functions at zero temperature, such as zero-field magnetization and susceptibility, the Onsager's rule can be corrected order by order. Such a perspective is further reinterpreted as a quantization of the semiclassical electron density in solids. Our theory not only reproduces Onsager's rule at zeroth order and the Berry phase and magnetic moment correction at first order but also explains the nature of higher-order corrections in a universal way. In applications, those higher-order corrections are expected to curve the linear relation between the level index and the inverse of the magnetic field, as already observed in experiments. Our theory then provides a way to extract the correct value of Berry phase as well as the magnetic susceptibility at zero temperature from Landau level fan diagrams in experiments. Moreover, it can be used theoretically to calculate Landau levels up to second-order accuracy for realistic models.
我们提出了朗道能级量子化规则的新视角；也就是说，通过依次包含零场温度下的磁响应函数，如零场磁化率和磁化率，我们可以对昂萨格（Onsager）规则进行逐阶修正。这种视角可以进一步重新解释为固体中半经典电子密度的量子化。我们的理论不仅在零阶重现了昂萨格（Onsager）规则以及一阶的贝里（Berry）相位和磁矩修正，而且还以通用的方式解释了高阶修正的本质。在应用中，这些高阶修正有望使能级指数与磁场的倒数之间的线性关系发生弯曲，这已经在实验中观察到了。因此，我们的理论为从实验中的朗道能级扇形图中提取正确的贝里相位和零温磁化率提供了一种方法。此外，它可以在理论上用于计算二阶精度的现实模型的朗道能级。
