有限周期系统相干共振隧穿时间和速度的严格推导
Rigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems
摘要：
用两种方法解析计算了有限周期结构中共振隧穿电子的速度$v_{res}$。第一种方法是基于这样一个事实，即统一的传输导致所有仍然竞争的隧道时间定义的重合。因此，具有无可争议的共振隧穿时间$τ_{res},$，我们应用自然定义$v_{res}=L/τ_{res}$来计算速度。对于第二种方法，我们结合Bloch定理和传递矩阵方法将波函数分解成两个Bloch波。然后计算速度的期望值。这两种不同的方法导致相同的结果，表明它们的物理等效性。所获得的共振隧穿速度$v_{res}$小于或等于群速度乘以单位晶胞的复透射振幅的大小。只有在周期性结构的晶胞具有单位透射率的能量下，$v_{res}$才等于群速度。对GaAs/AlGaAs超晶格进行了数值计算。对于典型参数，共振速度低于群速度的三分之一。
英文摘要：
The velocity $v_{res}$ of resonant tunneling electrons in finite periodic structures is analytically calculated in two ways. The first method is based on the fact that a transmission of unity leads to a coincidence of all still competing tunneling time definitions. Thus, having an indisputable resonant tunneling time $τ_{res},$ we apply the natural definition $v_{res}=L/τ_{res}$ to calculate the velocity. For the second method we combine Bloch's theorem with the transfer matrix approach to decompose the wave function into two Bloch waves. Then the expectation value of the velocity is calculated. Both different approaches lead to the same result, showing their physical equivalence. The obtained resonant tunneling velocity $v_{res}$ is smaller or equal to the group velocity times the magnitude of the complex transmission amplitude of the unit cell. Only at energies where the unit cell of the periodic structure has a transmission of unity $v_{res}$ equals the group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are performed. For typical parameters the resonant velocity is below one third of the group velocity.
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