A quantum hall effect without landau levels in a quasi one dimensional system

[摘要] ENGLISH ABSTRACT: The experimental observation of the quantum Hall effect in a two-dimensional electron gas posedan intriguing question to theorists: Why is the quantization of conductance so precise, given theimperfections of the measured samples? The question was answered a few years later, when aconnection was uncovered between the quantum Hall effect and topological quantities associatedwith the band structure of the material in which it is observed. The Hall conductance was revealedto be an integer topological invariant, implying its robustness to certain perturbations.The topological theory went further than explaining only the usual integer quantum Hall effectin a perpendicular magnetic field. Soon it was realized that it also applies to certain systems inwhich the total magnetic flux is zero. Thus it is possible to have a quantized Hall effect withoutLandau levels.We study a carbon nanotube in a magnetic field perpendicular to its axial direction. Recentstudies suggest that the application of an electric field parallel to the magnetic field would inducea gap in the electronic spectrum of a previously metallic carbon nanotube. Despite the quasi onedimensionalnature of the carbon nanotube, the gapped state supports a quantum Hall effect andis associated with a non zero topological invariant. This result is revealed when an additionalmagnetic field is applied parallel to the axis of the carbon nanotube. If the flux due to thismagnetic field is varied by one flux quantum, exactly one electron is transported between theends of the carbon nanotube.

[发布机构] Stellenbosch University