Department of Physics, Bilkent University, 06800 Ankara, Turkey.
J Phys Condens Matter. 2012 Aug 29;24(34):345501. doi: 10.1088/0953-8984/24/34/345501. Epub 2012 Jul 31.
The electronic properties of a square lattice under an applied perpendicular magnetic field in the presence of impurities or vacancies are investigated by the tight-binding method including up to second nearest neighbor interactions. These imperfections result in new gaps and bands in the Hofstadter butterfly even when the second order interactions break the bipartite symmetry. In addition, the whole spectrum of the Hall conduction is obtained by the Kubo formula for the corresponding cases. The results are in accordance with the Thouless-Kohmoto-Nightingale-den Nijs integers when the Fermi energy lies in an energy gap. We find that the states due to the vacancies or impurities with small hopping constants are highly localized and do not contribute to the Hall conduction. However, the impurities with high hopping constants result in new Hall plateaus with constant conduction of σ(xy) =± e(2)/h, since high hopping constants increase the probability of an electron contributing to the conduction.
通过紧束缚方法研究了在存在杂质或空位的情况下施加垂直磁场时正方形晶格的电子性质，其中包括最多二阶近邻相互作用。这些不完美会导致 Hofstadter 蝴蝶中出现新的间隙和能带，即使二阶相互作用破坏了二部对称性。此外，对于相应的情况，通过 Kubo 公式获得了整个 Hall 传导谱。当费米能级位于能隙中时，结果与 Thouless-Kohmoto-Nightingale-den Nijs 整数相符。我们发现，由于跳跃常数较小的空位或杂质引起的状态高度局域化，并且不会对 Hall 传导做出贡献。然而，具有高跳跃常数的杂质会导致新的 Hall 平台，其 σ(xy)的传导恒定为±e(2)/h，因为高跳跃常数增加了电子对传导做出贡献的可能性。
