Condensed Matter Theory Group, Paul Scherrer Institute, Villigen PSI, Switzerland.
Phys Rev Lett. 2011 Jun 10;106(23):236804. doi: 10.1103/PhysRevLett.106.236804. Epub 2011 Jun 6.
We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest-neighbor hoppings in the Haldane model and, similarly, in the chiral-π-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.
我们提出了一个简单的方法来使具有非零陈数的局域化布洛赫能带变平。我们首先展示了通过调节近邻和次近邻跳跃的比例，在哈尔丹模型中和类似的手性π通量正方晶格模型中，可以实现对具有非零陈数的能带进行近似平坦化。然后我们表明，通过进一步的指数衰减距离的范围跳跃，可以实现完全平坦化。最后，我们在模型中添加相互作用，并给出了在 1/3 填充的小系统中的精确对角化结果，这些结果支持（i）存在能隙，（ii）基态是拓扑态，以及（iii）霍尔电导率是量子化的。
