Conductance fluctuations in GaAs nanowires and graphene nanoribbons

In mesoscopic physics, conductance fluctuations are a quantum interference phenomenon that comes from the phase interference of electron wave functions scattered by the impurity disorder. During the past few decades, conductance fluctuations have been studied in various materials including metals, semiconductors and graphene. Since the patterns of conductance fluctuations is related to the distributions and configurations of the impurity scatterers, each sample has its unique pattern of fluctuations, which is considered as a sample fingerprint. Thus, research on conductance fluctuations attracts attention worldwide for its importance in both fundamental physics and potential technical applications. Since early experimental measurements of conductance fluctuations showed that the amplitudes of the fluctuations are on order of a universal value (e2/h), theorists proposed the hypothesis of ergodicity, e.g. the amplitudes of the conductance fluctuations by varying impurity configurations is the same as that from varying the Fermi energy or varying the magnetic field. They also proposed the principle of universality; e.g., that the observed fluctuations would appear the same in all materials. Recently, transport experiments in graphene reveal a deviation of fluctuation amplitudes from those expected from ergodicity.

Thus, in my thesis work, I have carried out numerical research on the conductance fluctuations in GaAs nanowires and graphene nanoribbons in order to examine whether or not the theoretical principles of universality and ergodicity hold. Finite difference methods are employed to study the conductance fluctuations in GaAs nanowires, but an atomic basis tight-binding model is used in calculations of graphene nanoribbons. Both short-range disorder and long-range disorder are considered in the simulations of graphene. A stabilized recursive scattering matrix technique is used to calculate the conductance. In particular, the dependence of the observed fluctuations on the amplitude of the disorder has been investigated. Finally, the root-mean-square values of the amplitude of conductance fluctuations are calculated as a basis with which to draw the appropriate conclusions. The results for Fermi energy sweeps and magnetic field sweeps are compared and effects of magnetic fields on the conductance fluctuations of Fermi energy sweeps are discussed for both GaAs nanowires and graphene nanoribbons.