Quantum Wells in Tilted Fields: Semiclassical Amplitudes and Phase Coherence Times

Abstract

Experiments on quantum wells in tilted fields have stimulated several groups to investigate semiclassical theories for the current fluctuations. As a result, there is now a sort of “Zoo” of different types of trajectories (Periodic Orbits, Normal Orbits, Central Closed Orbits, Ghost Periodic Orbits, Saddle Orbits, Minimal Orbits) which have all been used to analyse these experimental spectra. Here we review briefly the semiclassical descriptions for this system and discuss which types of trajectories are most appropriate in those regimes where one cannot use Periodic Orbits. We conclude that using either Saddle Orbits (SOs) or Minimal Orbits (MOs) yields excellent agreement with experiment and quantal calculations. We also investigate the damping of the amplitudes of POs (or other semiclassical trajectories). In these scaling systems, different experiments on wells of variable dimensions can correspond to the same classical dynamics and even the same effective ℏ. The trajectory associated with the experimental current oscillation is unchanged: the only significant alteration is a re-scaling of the period T of the PO, affecting only the amplitude damping factors τe^−T/τ due to incoherent processes in the experiment. By comparing measurements of the same period-doubling feature of the current in 85 nm and 120 nm wells we can probe the value of τ from the change in the PO (or SO/MO) amplitudes which are estimated from the experiment.