6 - Temperature decay of fluctuations

Summary

When the temperature is raised above absolute zero, the amplitudes of both the weaklocalization, universal conductance fluctuations and the Aharonov-Bohm oscillations are reduced below the nominal value e²/ħ. In fact, the amplitude of nearly all quantum phase interference phenomena is likewise weakened. There is a variety of reasons for this. One reason, perhaps the simplest to understand, is that the coherence length is reduced, but this can arise as a consequence of either a reduction in the coherence time or a reduction in the diffuson coefficient. In fact, both of these effects occur. In Chapter 2, we discussed the temperature dependence of the mobility in high-mobility modulation-doped GaAs/AlGaAs heterostructures. The decay of the mobility couples to an equivalent decay in the diffuson constant (discussed in Chapters 2 and 5), D = ε²_Fτ/d, where d is the dimensionality of the system, through both a small temperature dependence of the Fermi velocity and a much larger temperature dependence of the elastic scattering rate. The temperature dependence of the phase coherence time is less well understood but generally is thought to be limited by electron-electron scattering, particularly at low temperatures. At higher temperatures, of course, phonon scattering can introduce phase breaking.

Another interaction, though, is treated by the introduction of another characteristic length, the thermal diffuson length. The source for this lies in the thermal spreading of the energy levels or, more precisely, in thermal excitation and motion on the part of the carriers. At high temperatures, of course, the lattice interaction becomes important, and energy exchange with the phonon field will damp the phase coherence.