QUANTUM TRANSPORT AND CHAOS IN SEMICONDUCTOR MICROSTRUCTURES

It is shown that classical chaotic scattering has experimentally measurable consequences for the quantum conductance of semiconductor microstructures. These include the existence of conductance fluctuations -a sensitivity of the conductance to either Fermi energy or magnetic field- and weak-localization -a change in the average conductance upon applying a magnetic field. We use semiclassical theory, random S-matrix theory, and numerical results to describe these interference effects for microstructures modeled by billiards attached to leads. The semiclassical theory predicts that the difference between chaotic and regular classical scattering produces a qualitative difference in the fluctuation spectrum and weak-localization lineshape of chaotic versus non-chaotic structures. The random S-matrix theory yields results for the magnitude of these interference effects. The conductance fluctuation and weak-localization magnitudes are universal if the number of incoming modes, N, is large: they are independent of the size and shape of the cavity. Of more relevance experimentally, in the limit of small N the full distribution of the conductance shows a striking dependence on N and magnetic field.