摘要:
1937年,Majorana发现Dirac所提出的相对论性协变的电子波动方程,在另一个表象下所得到解可以描述不带电荷的费米子,具有与Dirac费米子不同的性质.在基本粒子领域,对这种Majorana费米子的寻找至今一直在进行中;而在凝聚态物理领域,对拓扑超导体和分数量子霍尔态的研究,人们已经发现了与Majorana费米子有相同行为的准粒子.特别是在二维拓扑超导体系中出现的涡旋元激发包含了零能量的Majorana准粒子,它们在交换操作下表现出非阿贝尔的统计性质,因而有望借以实现拓扑量子计算.文章系统地介绍了凝聚态物质系统中获得Majorana费米子的理论模型和物理实现,并进一步介绍了与之相关的拓扑量子计算的实现方法.
Abstract:
In 1937, Majorana noticed that in a different representation the relativistic wave equation for electrons proposed by Dirac has a solution describing chargeless neutral fermi-ons, which have completely different properties from Dirac fermions. In particle physics, the search for such Majorana fermions is still being pursued, while in condensed matter physics it has already been found that certain kinds of quasiparticles in the low-energy excitations of topological superconductors and fractional quantum Hall effects share a similar behavior to Majorana fermi-ons. In particular, the vortex excitations in two-dimensional topological superconductors include zero-energy Majorana fermion modes, which exhibit non-abelian anyonic statistical properties un-der exchange operations, leading to the possibility of topological quantum computation. In this ar-ticle we will review the physical models and realization of Majorana fermions, and then discuss the corresponding implementation of topological quantum computation.
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