The continuing development of new energy technologies for electronic devices and medical applications necessitates the search for advanced nanomaterials. Among the more promising candidates are two novel materials: nanocrystal (NC) assemblies and three-dimensional (3D) topological insulators (TIs). The former have great promise for optoelectronic and photovoltaic devices, while the latter can be applied in spintronics and quantum computing. Thus far, however, the development of NC- and TI-based devices have been slowed by a lack of a solid theoretical understanding of many of their electronic properties, in particular, the influence of the presence of disorder on charge transport. In this thesis we propose to help address this need by performing a detailed, theoretical analysis of the disorder effects on electronic transport properties of NC arrays and TIs.NC assemblies can be made from different materials. Specifically, we consider three types of systems: semiconductor NCs, metallic NCs and superconducting grains. As-grown semiconductor NCs are insulators, and in order for them to be useful in photovoltaic devices, their electrical conductivity must be tuned by doping. Recent experiments have shown that the resistivity of a dense crystalline array of semiconductor NCs depends in a sensitive way on the level of doping as well as on the NC size and spacing. We show that in sufficiently small NCs, the fluctuations in donor number from one NC to another provide disorder that helps to determine the conduction mechanism in the array. Using this model, we explain how the different regimes of resistivity observed in experiment arise based on the interplay between the charging spectrum of NCs, the long-ranged Coulomb interactions between charged NCs, and the discrete quantum energy levels of confined electrons. We supplement our theory with a computer simulation, which we use to calculate the single particle density of states (DOS) and the resistivity. Compared to semiconductor NCs, the quantum gaps in metallic NCs become negligible and disorder is provided by donors and acceptors that are randomly situated in the interstitial spaces between grains. These changes may lead to different results for electron energy distribution and charge transport. Using a computer simulation we calculate the DOS and the conductivity in 2D and 3D arrays of metallic NCs. While the Coulomb gap in the DOS is a universal consequence of electron-electron interaction in disordered systems with localized electron states, we show that for granular metals there is not one but three identical adjacent Coulomb gaps, which together form a structure that we call a ``Coulomb gap triptych." Furthermore, unlike in the conventional Coulomb glass models, in metallic NC arrays the DOS has a fixed width in the limit of large disorder.The third type of NC assemblies we consider are granular superconductors in the strongly insulating regime, in which the array as a whole is insulating while individual grains may still contain Cooper pairs. In such cases, coherent tunneling is absent. Instead, electronic states are localized and electron conduction proceeds primarily by hopping of electrons between grains through the insulating gaps which separate them. In principle, electronic conduction can occur either through tunneling of single electrons or through simultaneous tunneling of an electron pair (or both). Using a simple computer simulation, we numerically calculate the DOS and conductivity, and study the evolution of conduction mechanism as a function of temperature, charging energy and superconducting gap. The implications of our results for magnetoresistance and tunneling experiments are also discussed.The rest of the thesis discusses another type of disorder system: 3D TI. The 3D TI has gapless surface states that are expected to exhibit a range of interesting quantum phenomena. However, as-grown TIs are typically heavily-doped <italic>n</italic>-type crystals. Compensation by acceptors is used to move the Fermi level to the middle of the band gap, but even then TIs have a frustratingly small bulk resistivity. We show that this small resistivity is the result of band bending by poorly screened fluctuations in the random Coulomb potential. Using numerical simulations of a completely compensated TI, we find that the bulk resistivity has an activation energy of just 0.15 times the band gap, in good agreement with experimental data. At lower temperatures activated transport crosses over to variable range hopping with a relatively large localization length. We also extend our theory to the more practical case of strongly compensated semiconductors, as in experiments the exact condition of complete compensation is difficult to meet. We calculate the DOS, conductivity and activation energy of a strongly compensated TI as a function of compensation degree. Historically known as good thermoelectric materials, the thermopower properties of compensated TIs are also discussed.
University of Minnesota Ph.D. dissertation. August 2014. Major: Physics. Advisor: Boris Shklovskii. 1 computer file (PDF); viii, 114 pages.
Disorder effects on electron transport in nanocrystal assemblies and topological insulators.
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