arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1206.0099cond-mat.mes-hall
收藏

四维空间中量子霍尔效应的金属相

Metallic phase of the quantum Hall effect in four-dimensional space

J. M. Edge, J. Tworzydło, C. W. J. Beenakker

摘要:

研究了量子霍尔效应在四维空间中的相图。与2D不同,在4D中存在金属相和绝缘相,这取决于无序强度。在时间反演对称性的存在下,量子Hall绝缘体-金属跃迁的发散局域化长度的临界指数$ν\approx 1.2$不同于4D Anderson跃迁的半经典值$ν=1$。我们的数值分析是基于一个映射的4D哈密顿到一个1D动力学系统,提供了一条通往实验实现的4D量子霍尔效应的路线。

英文摘要:

We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space. Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the disorder strength. The critical exponent $ν\approx 1.2$ of the diverging localization length at the quantum Hall insulator-to-metal transition differs from the semiclassical value $ν=1$ of 4D Anderson transitions in the presence of time-reversal symmetry. Our numerical analysis is based on a mapping of the 4D Hamiltonian onto a 1D dynamical system, providing a route towards the experimental realization of the 4D quantum Hall effect.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑