本文探讨了在恒定电场中Wannier-Stark阶梯现象，即能量级$E_n$与电场强度的关系。这种阶梯状谱通常在弱耦合条件下导致隧道概率呈现特定电场间隔的峰值。研究发现，在出现标准的Wannier-Stark阶梯之前，存在其他级距的阶梯。文章进一步指出，标准和非标准的Wannier-Stark阶梯除了峰谷间距的差异外，还有其他显著区别，例如，标准阶梯的隧道概率随电压增加呈指数衰减，且峰谷比异常增大。此外，文章还基于首次推导出的近似精确表达式，讨论了扩展态、表面局域态和Wannier-Stark态在倾斜能带透过率谱中的特征。
摘要：
Predicted by Wannier in 1960 band states quantization in a constant electric field, $E_n$ = const $\pm n {\cal E}$, where $n =0$, 1, 2, ..., and ${\cal E}$ is proportional to the strength of electric field [this kind of spectrum is commonly referred as the Wannier-Stark ladder (WSL)], implies that the probability of tunneling through a tilted band should have ${\cal E}$ spaced peaks, at least, under the weak coupling of the band states to the source and drain electrodes. It has been shown, however, (Phys. Rev. B {\bf 63}, ..., 2001), that the appearance of the canonical WSL is preceded by WSLs with other level spacing, namely, ${\cal E}_{m'/m}/(1-2m'/m)$, where $m$ and $m'< m/2$ are positive integers specifying certain applied voltage. Here we show that canonical and noncanonical WSLs, in addition to different peak spacing in the transmission spectrum, have other pronouncedly distinctive features. As an example, for the former, the peak and valley tunneling probability decays exponentially with the increase of applied voltage. The corresponding exponents are given by the sum and difference of two Fowler-Nordheim-type exponents implying an anomalous increase of the peak-to-valley ratio. These and other signatures of extended states (es), surface localized states (sls), and Wannier-Stark (WS) states in the through tilted band transmission spectrum are discussed on the basis of (derived for the first time) nearly exact explicit expressions of es-, sls-, and WS states assisted tunneling probability.
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