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首页> 外文期刊>Physical review >Two-dimensional Bloch electrons in perpendicular magnetic fields: An exact calculation of the Hofstadter butterfly spectrum
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Two-dimensional Bloch electrons in perpendicular magnetic fields: An exact calculation of the Hofstadter butterfly spectrum

机译：垂直磁场中的二维Bloch电子：霍夫施塔特蝴蝶光谱的精确计算

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摘要

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here, we report calculations of the full spectrum of the single-particle Schrodinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential.
机译：二维的，独立的电子受到周期性电势和均匀垂直磁场的影响，揭示了令人惊讶的丰富物理学，正如被称为霍夫施塔特蝴蝶的分形能谱所体现的那样。迄今为止，已经使用了各种基于强势或强场限制情况的近似方法来解决该问题。在这里，我们报告了单粒子薛定inger方程全谱的计算，而没有进一步的近似。对于势能和均匀场强的任何组合，我们的方法都是精确的，达到数值精度。我们首先研究与强势极限相对应的情况，然后将精确结果与类似Hofstadter模型的预测进行比较。然后，我们通过调整调制电势的幅度，分析了分形谱从类似Landau的近自由电子系统到Hofstadter紧束缚极限的过程。

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  • 来源
    《Physical review》 |2013年第23期|235429.1-235429.7|共7页
  • 作者

    S. Janecek; M. Aichinger; E. R. Hernandez;

  • 作者单位

    Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Campus de Cantoblanco, 28049 Madrid, Spain,Institut de Ciencia de Materials de Barcelona (ICMAB-CSIC), Campus de Bellaterra, 08193 Barcelona, Spain,Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences,Altenberger Strasse 69, A-4040 Linz, Austria,MathConsult GmbH, Altenberger Strasse 69, A-4040 Linz, Austria;

    Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences,Altenberger Strasse 69, A-4040 Linz, Austria,Uni Software Plus GmbH, Kreuzstrasse 15a, A-4040 Linz, Austria;

    Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Campus de Cantoblanco, 28049 Madrid, Spain,Institut de Ciencia de Materials de Barcelona (ICMAB-CSIC), Campus de Bellaterra, 08193 Barcelona, Spain;

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  • 关键词

    galvanomagnetic and other magnetotransport effects (including thermomagnetic effects); collective excitations; magnetotransport phenomena; materials for magnetotransport;

    机译：电磁和其他磁传输效应（包括热磁效应）;集体激励;磁传输现象;磁运输材料;

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