Temporal Propagation of Electron Wave in a Periodic Structure with Finite Length

Abstract

Performance of quanta having a finite coherence length ℓ c in a periodic structure is studied. Classification between wave and particle properties depends strongly on the magnitude of coupling constant K, determined by the quantum mass, periodic potential depth and wavenumber. It is found that if K increases in a periodic structure with a fixed length, then a transmitted quantum is inclined to show wave properties even if ℓ c is short. As ℓ c becomes short, more quanta transmit through the structure even in the stop band. Coherence and medium lengths play an equivalent role in transmission. Namely, transmittance is nearly identical even if medium and coherence lengths are exchanged. Many oscillations due to the wave properties appearing in the transmission temporal wave can be explained by the effective mode mismatch among many eigenmodes. The oscillation period is controllable by changing the periodic potential depth or the effective mass.