费米子倍增
费米子
迪拉克费米子
物理
马约拉纳
哈密顿量(控制论)
狄拉克方程
量子力学
数学物理
数学优化
数学
作者
C. W. J. Beenakker,A. Donís Vela,G. Lemut,M. J. Pacholski,J. Tworzydło
标识
DOI:10.1002/andp.202300081
摘要
Abstract Methods to discretize the Hamiltonian of a topological insulator or topological superconductor, without giving up on the topological protection of the massless excitations (respectively, Dirac fermions or Majorana fermions) are reviewed. The method of tangent fermions, pioneered by Richard Stacey, is singled out as being uniquely suited for this purpose. Tangent fermions propagate on a dimensional space‐time lattice with a tangent dispersion: in dimensionless units. They avoid the fermion doubling lattice artefact that will spoil the topological protection, while preserving the fundamental symmetries of the Dirac Hamiltonian. Although the discretized Hamiltonian is nonlocal, as required by the fermion‐doubling no‐go theorem, it is possible to transform the wave equation into a generalized eigenproblem that is local in space and time. Applications that are discussed include Klein tunneling of Dirac fermions through a potential barrier, the absence of localization by disorder, the anomalous quantum Hall effect in a magnetic field, and the thermal metal of Majorana fermions.
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