Semiclassical theory of Landau levels and magnetic breakdown in topological metals
Semiclassical theory of Landau levels and magnetic breakdown in topological metals
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DOI：
10.1103/physrevb.97.144422
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发表时间：
2018-04-26
影响因子：
3.7
通讯作者：
Glazman, Leonid
中科院分区：
文献类型：
--
作者：
Alexandradinata, A.;Glazman, Leonid
玻尔-索末菲量子化规则是磁场中布洛赫电子的半经典理论的核心。这一规则预示着常规金属的朗道能级和de Haas-van Alphen振荡，以及最近在能带理论、晶体对称性和拓扑学之间的交流中出现的许多拓扑金属。任何量子化规则的基本成分都是连接公式，这些公式在强量子涨落区域与半经典（WKB）波函数相匹配。在这里，我们提出了（a）一个多分量WKB波函数，描述简并带子空间内的传输，和（B）鞍点和II型狄拉克点，其中隧道分别发生在同一个频带内，和不同的频带之间的必要的连接公式。(a)以及（B）通过结合场幂次领先的相位校正来扩展之前的工作;这些校正包括几何Berry相位，并解释了轨道磁矩和塞曼耦合。一个全面的对称性分析进行这样的相位修正发生在封闭的轨道，这是适用于固体在任何（磁性）空间群。我们进一步制定了半经典轨道的图论描述。这使我们能够系统化建设的量子化规则的一大类封闭轨道（有或没有隧道），以及制定的概念，拓扑不变的半经典磁输运作为一个数量是不变的连续变形下的图形。存在隧穿的朗道能级一般是准随机的，即，无序的最近邻水平间距的规模，但有较长的范围内的相关性，我们开发了一个微扰理论，以确定朗道水平在这样的quasirandom光谱。
The Bohr-Sommerfeld quantization rule lies at the heart of the semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and de Haas-van Alphen oscillations for conventional metals, as well as for a host of topological metals which have emerged in the recent intercourse between band theory, crystalline symmetries, and topology. The essential ingredients in any quantization rule are connection formulas that match the semiclassical (WKB) wave function across regions of strong quantum fluctuations. Here, we propose (a) a multicomponent WKB wave function that describes transport within degenerate-band subspaces, and (b) the requisite connection formulas for saddle points and type-II Dirac points, where tunneling respectively occurs within the same band, and between distinct bands. (a) and (b) extend previous works by incorporating phase corrections that are subleading in powers of the field; these corrections include the geometric Berry phase, and account for the orbital magnetic moment and the Zeeman coupling. A comprehensive symmetry analysis is performed for such phase corrections occurring in closed orbits, which is applicable to solids in any (magnetic) space group. We have further formulated a graph-theoretic description of semiclassical orbits. This allows us to systematize the construction of quantization rules for a large class of closed orbits (with or without tunneling), as well as to formulate the notion of a topological invariant in semiclassical magnetotransport-as a quantity that is invariant under continuous deformations of the graph. Landau levels in the presence of tunneling are generically quasirandom, i.e., disordered on the scale of nearest-neighbor level spacings but having longer-ranged correlations; we develop a perturbative theory to determine Landau levels in such quasirandom spectra.