Browsing by Subject "Disorder effects"
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Item Disorder effects and non-equilibrium dynamics on the electronic orders of strongly correlated materials(2019-08) Cui, TianbaiStrongly correlated materials offer promising prospects for numerous applications, from superconductivity to quantum information processing. The exotic electronic properties arise from the collective behavior due to strong electron-electron correlation. This leads to the complex phase diagram of strongly correlated materials consists of multiple distinct yet intertwined electronic orders, for examples spin density-wave, charge density-wave, nematic order, and superconductivity. Most theoretical studies of this delicate balance between different electronic orders in strongly correlated systems assume disorder is absent and equilibrium is reached, which sometimes makes comparison with experiments challenging. In this thesis, I will surpass these assumptions to show how disorder dramatically changes the way electronic orders develop, and also demonstrate that non-equilibrium perturbations enable us to understand different dynamics in various timescales and to search for new physical behaviors which are absent in equilibrium. In particular, I will discuss the rare region effect in inhomogeneous systems and show how it changes the critical behaviors of nematic and magnetic quantum phase transitions. I will propose a self-consistent perturbative approach to study the dynamics of the superconducting gap at the picosecond time scales after driven out of equilibrium. Using this approach, I will show that the dynamics of the multi-band superconductor is distinct from the single-band conventional superconductors. I will also elaborate on the damping and relaxation effects on the gap dynamics within the electronic system at picosecond time scales.Item Disorder effects in the Kitaev spin liquid(2024-09) Kao, Wen-HanOne of the long-standing open questions in condensed matter physics, which has recently garnered significant attention, is how a quantum spin liquid (QSL) state responds to the various forms of structural disorder that are inevitable in real materials. Despite numerous theoretical proposals and candidate materials for QSLs over the past half-century, the existence of this exotic magnetic phase remains contentious due to two primary challenges in experimental identification. First, the absence of long-range magnetic order in QSLs results in a featureless ground state, making its characterization largely dependent on the excitation spectrum and dynamical probes. Second, the unavoidable presence of structural disorder in real materials can significantly affect the spin-liquid phase or even lead to its destruction. This underscores the urgent need for a deeper understanding of the effects of disorder in quantum spin liquids. The Kitaev honeycomb model, discovered in 2006, is an exactly solvable model that hosts quantum spin liquid phases and holds the potential for realization in transition-metal compounds with strong spin-orbit coupling. The spin fractionalization into locally conserved fluxes and itinerant Majorana fermions underpins the model's exact solvability, even in real-space representation. This characteristic makes the Kitaev model an ideal testbed for studying disorder effects in quantum spin liquids, allowing us to address the aforementioned challenges by enabling the calculation of the energy spectrum and dynamical response without relying on translational invariance. In this dissertation, various aspects of disorder within the Kitaev spin liquid model have been explored, including disorder-induced flux binding, localization of Majorana modes, power-law divergence in the density of states, signatures of Majorana zero modes in the local dynamical correlation function, and strong-disorder criticality in the quasi-one-dimensional Kitaev model. These studies provide not only a deeper understanding of the role of disorder in the Kitaev spin liquid, but also propose potentially observable consequences in thermal conductivity, specific heat, and inelastic tunneling conductance.Item Disorder effects on electron transport in nanocrystal assemblies and topological insulators(2014-08) Chen, TianranThe 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 n-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.