外场中的锯齿形和扶手椅形纳米管
Zigzag and armchair nanotubes in external fields
摘要：
我们考虑了在均匀磁场$\mB$和外部周期性电势中锯齿形和扶手椅形纳米管（紧束缚模型）上的薛定谔算符。磁场和电场平行于纳米管的轴。证明了该算子与Jacobi算子的有限正交和是酉等价的。我们描述所有谱带和所有本征值（具有无限多重性，即，平带）。此外，我们确定了小和大的潜力的光谱带的渐近性。我们将光谱描述为$|\mB|$的函数。例如，如果是$|\mB|\to {163}({\pi2}-{πkN}+πs)\tan {\pi2N}, k=1,2,..,N, s\in \Z$，则锯齿形纳米管的某些光谱带收缩成平坦带，并且确定了相应的渐近性。
英文摘要：
We consider the Schrödinger operator on the zigzag and armchair nanotubes (tight-binding models) in a uniform magnetic field $\mB$ and in an external periodic electric potential. The magnetic and electric fields are parallel to the axis of the nanotube. We show that this operator is unitarily equivalent to the finite orthogonal sum of Jacobi operators. We describe all spectral bands and all eigenvalues (with infinite multiplicity, i.e., flat bands). Moreover, we determine the asymptotics of the spectral bands both for small and large potentials. We describe the spectrum as a function of $|\mB|$. For example, if $|\mB|\to {163}({\pi2}-{πkN}+πs)\tan {\pi2N}, k=1,2,..,N, s\in \Z$, then some spectral band for zigzag nanotube shrinks into a flat band and the corresponding asymptotics are determined.
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