Motivated by the intriguing features of the insulating regime close to an SIT, I carry out a systematic study of magnetoresistance, elucidating a variety of approach that influence it. In Chapter 2 I introduce a model of hardcore bosons on a two dimensional honeycomb lattice in a magnetic field, as motivated by recent experiments on structured films [38, 39]. This aims at explaining several key features observed in the activated magnetotransport in those experiments. Taking into account long range Coulomb interactions among the bosons, I study the crossover from strong to weak localization of those excitations and how it is affected by a magnetic field. An effective mobility edge in the excitation spectrum of the insulating Bose glass is identified as the (intensive) energy scale at which excitations become nearly delocalized. Within the forward scattering approximation in the bosonic hopping I find the effective mobility edge to oscillate periodically with the magnetic flux per plaquette [51]. Furthermore, I contrast the magnetoresistance in bosonic and fermionic systems, and thus show convincingly that the magnetooscillations seen in experiments of SIT systems reflect the physics of localized electron pairs, i.e a Bose glass rather than a Fermi insulator. The bosonic magnetooscillations start with an increase of the mobility edge (and thus of resistance) with applied flux, as opposed to the equivalent fermionic problem. The amplitude of the oscillations is much more substantial in bosons than in fermions. Bosons exhibit a single hump per flux period, while fermion characteristics undergo two humps. Those are identical for noninteracting fermions, but Coulomb correlations are shown to lead to systematic deviations from this statistical period doubling. In this approach, only bosonic degrees of freedom are considered. It thus cannot cover the wide range of fields often explored in experiments, where fieldinduced pair breaking processes certainly take place and are relevant. Therefore, in Chapter 3 I introduce a microscopic model taking both bosonic and fermionic degrees of freedom into account. This model is then used to study the magnetic field driven crossover from pair to single electron regimes and the corresponding resistive transport. This study is motivated by the above mentioned experiments observing a strong magnetoresistance peak on the insulating side of the SIT which reflects that crossover. Assuming Mott variable range hopping transport, the pairtosingle crossover in transport is driven by the crossover in the characteristic temperature scale TM governing the stretched exponential growth of the resistance R(T) for pairs and single electrons. Within this work, I consider a system of electrons on a square lattice, subject to strong onsite disorder, a local pairing attraction, a magnetic field, and nearest neighbor hopping. The tuning parameter, the magnetic field, enters both by a (spatially) isotropic Zeeman depairing term and an anisotropic orbital effect proportional to the perpendicular component of the field incorporated via the complex phase of the hoppings. I found that the former leads to a strong effect on the density of state which causes and dominates the crossover, and thus the magnetoresistance peak. The orbital effect captures the effect of the quantum interference of different types of carriers. It further enhances the peak as the field orientation changes. I also discuss the effect of including Coulomb interactions into this theory. Having pointed out the peculiarity of two dimensional disordered systems which are marginal in terms of singleparticle localization, and in view of our finding of the effective mobility edge above, I address the question of whether Coulomb interactions can give rise to a genuine mobility edge in electronic systems in two dimensions. In Chapter 4 with Coulomb interactions being treated at a more quantum level (but still approximately) within a HartreeFock treatment, I carry out a numerical study aiming at addressing the possibility of an interactioninduced delocalization effect. This setting focuses on the multiplicity of electron species, or valley degeneracy, that Punnoose and Finkel'stein [11, 52] predicted to cause delocalization in two dimensional interacting electron system. As I will discuss, by looking at the densitydensity correlation function, the system with multiple species behaves differently from the system with single species. In the former, the twostage scaledependent behavior of the correlation function reflects the scaledependent resistance predicted in Punnoose and Finkel'stein's renormalization group equations.
Magnetotransport and localization in disordered systems with local superconductive attraction / Nguyen, Thi Thuong.  (2016 Oct 13).
Magnetotransport and localization in disordered systems with local superconductive attraction
Nguyen, Thi Thuong
20161013
Abstract
Motivated by the intriguing features of the insulating regime close to an SIT, I carry out a systematic study of magnetoresistance, elucidating a variety of approach that influence it. In Chapter 2 I introduce a model of hardcore bosons on a two dimensional honeycomb lattice in a magnetic field, as motivated by recent experiments on structured films [38, 39]. This aims at explaining several key features observed in the activated magnetotransport in those experiments. Taking into account long range Coulomb interactions among the bosons, I study the crossover from strong to weak localization of those excitations and how it is affected by a magnetic field. An effective mobility edge in the excitation spectrum of the insulating Bose glass is identified as the (intensive) energy scale at which excitations become nearly delocalized. Within the forward scattering approximation in the bosonic hopping I find the effective mobility edge to oscillate periodically with the magnetic flux per plaquette [51]. Furthermore, I contrast the magnetoresistance in bosonic and fermionic systems, and thus show convincingly that the magnetooscillations seen in experiments of SIT systems reflect the physics of localized electron pairs, i.e a Bose glass rather than a Fermi insulator. The bosonic magnetooscillations start with an increase of the mobility edge (and thus of resistance) with applied flux, as opposed to the equivalent fermionic problem. The amplitude of the oscillations is much more substantial in bosons than in fermions. Bosons exhibit a single hump per flux period, while fermion characteristics undergo two humps. Those are identical for noninteracting fermions, but Coulomb correlations are shown to lead to systematic deviations from this statistical period doubling. In this approach, only bosonic degrees of freedom are considered. It thus cannot cover the wide range of fields often explored in experiments, where fieldinduced pair breaking processes certainly take place and are relevant. Therefore, in Chapter 3 I introduce a microscopic model taking both bosonic and fermionic degrees of freedom into account. This model is then used to study the magnetic field driven crossover from pair to single electron regimes and the corresponding resistive transport. This study is motivated by the above mentioned experiments observing a strong magnetoresistance peak on the insulating side of the SIT which reflects that crossover. Assuming Mott variable range hopping transport, the pairtosingle crossover in transport is driven by the crossover in the characteristic temperature scale TM governing the stretched exponential growth of the resistance R(T) for pairs and single electrons. Within this work, I consider a system of electrons on a square lattice, subject to strong onsite disorder, a local pairing attraction, a magnetic field, and nearest neighbor hopping. The tuning parameter, the magnetic field, enters both by a (spatially) isotropic Zeeman depairing term and an anisotropic orbital effect proportional to the perpendicular component of the field incorporated via the complex phase of the hoppings. I found that the former leads to a strong effect on the density of state which causes and dominates the crossover, and thus the magnetoresistance peak. The orbital effect captures the effect of the quantum interference of different types of carriers. It further enhances the peak as the field orientation changes. I also discuss the effect of including Coulomb interactions into this theory. Having pointed out the peculiarity of two dimensional disordered systems which are marginal in terms of singleparticle localization, and in view of our finding of the effective mobility edge above, I address the question of whether Coulomb interactions can give rise to a genuine mobility edge in electronic systems in two dimensions. In Chapter 4 with Coulomb interactions being treated at a more quantum level (but still approximately) within a HartreeFock treatment, I carry out a numerical study aiming at addressing the possibility of an interactioninduced delocalization effect. This setting focuses on the multiplicity of electron species, or valley degeneracy, that Punnoose and Finkel'stein [11, 52] predicted to cause delocalization in two dimensional interacting electron system. As I will discuss, by looking at the densitydensity correlation function, the system with multiple species behaves differently from the system with single species. In the former, the twostage scaledependent behavior of the correlation function reflects the scaledependent resistance predicted in Punnoose and Finkel'stein's renormalization group equations.File  Dimensione  Formato  

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