CRITICAL-BEHAVIOR OF DISORDERED DEGENERATE SEMICONDUCTORS .1. MODELS, SYMMETRIES, AND FORMALISM
CRITICAL-BEHAVIOR OF DISORDERED DEGENERATE SEMICONDUCTORS .1. MODELS, SYMMETRIES, AND FORMALISM
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DOI：
10.1103/physrevb.33.3257
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发表时间：
1986-03-01
影响因子：
3.7
通讯作者：
FRADKIN, E
中科院分区：
文献类型：
--
作者：
FRADKIN, E
提出了一种描述具有有限数量简并点的无序简并半导体的电子态定性特性的模型。我引入了与随机分布场耦合的狄拉克算子形式的有效哈密顿量。结果表明，半金属相和金属相之间存在相变，随后发生局域化转变。与此跃迁相关的对称性破缺与空间群的非对称性有关。态密度起到阶次参数的作用，弹性平均自由程是相关长度。引入路径积分表示并用于表征此转换的普遍性类别。下临界维数为 2。提出了二维情况到一维自相互作用费米系统的映射。讨论了零间隙半导体和其他系统的应用。
A model that describes the qualitative properties of the electronic states of a disordered degenerate semiconductor with a finite number of degeneracy points is proposed. I introduce an effective Hamiltonian of the form of a Dirac operator coupled to randomly distributed fields. It is shown that there is a phase transition between the semimetal and metallic phases followed by a localization transition. The symmetry breaking associated with this transition is related to the nonsymmorphic character of the space group. The density of states plays the role of the order parameter and the elastic mean free path is the correlation length. A path-integral representation is introduced and used to characterize the universality class of this transition. The lower critical dimension is 2. A mapping of the two-dimensional case to one-dimensional self-interacting Fermi systems is presented. Applications to zero-gap semiconductors and other systems are discussed.