Bloch Oscillations in Superlattices
Semiconductor superlattices (SL) have recently gained much attention as a model system for the investigation of the electronic states in a periodic potential (Bloch states) . As an example, the Wannier-Stark ladder (WSL)  has been observed by cw optical techniques in semiconductor SL several years ago [3,4]: The extended Bloch states become localized due to the field F, which transforms the continuous energy miniband into evenly spaced ladder states with energies En=E0+nΔE, where ΔE=eFd (d: lattice constant) . This WSL behavior is, albeit with some qualitative changes, also observed when the excitonic correlation of photo-excited eh pairs is considered . There is only one condition due to the excitonic behavior imposed to the miniband width: the bandwidth needs to be larger than the exciton binding energy (5–10 meV) . Recently, the interest has focussed [8,9,10] on the time-domain equivalent of the WSL, the periodic motion of Bloch electrons in an homogeneous electric field (Bloch oscillations, BO ). A simple semiclassical description is frequently given in literature : Without scattering, electrons will accelerate in the electric field till they reach the upper edge of the band at the end of the Brillouin zone. There, they will be reflected and return to the initial state. These oscillations in the Brillouin zone have a period τB=h/eFd. More recently, several groups [5,13,14,15] have modeled the BO in a fully quantum-mechanical picture and shown that the essential features of the simple picture outlined above are preserved, e.g., the field-dependence of the oscillation frequency. Recent numerical calculations for realistic initial superposition of WSL states  predict the existence of an oscillating dipole moment, which is a prerequisite for the observation of strong THz emission.
KeywordsReverse Bias Energy Splitting Quantum Beat Electromagnetic Transient Bloch Electron
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