Pseudospin pairing and transport in atomic Fermi gases and bilayer systems

In this Thesis we consider the behavior of the drag conductivity close to exciton condensation in bilayer systems and close to the superfluid transition in cold Fermi gases. In chapter 2 we calculate the transition temperature for exciton condensation in double-layer graphene, showing that the remote bands can play a supporting role in this transition. In chapter 3 we consider a topological insulator thin film and calculate the behavior of the drag resistivity close to the transition temperature. We find a strong enhancement which can be used as a precursor for the transition. In chapter 4 we discuss an ultracold Fermi gas close to the superconducting transition and compare two different methods to obtain the drag resistivity, each taking into account a different phenomenon which affects the drag resistivity close to the transition. Finally, in chapter 5, we present a uniform theoretical framework to determine the drag resistivity in all experimental systems considered in this Thesis

Unified Boltzmann-transport theory for the drag resistivity close to an interlayer-interaction-driven second-order phase transition

We present a unified Boltzmann transport theory for the drag resistivity ρD in two-component systems close to a second-order phase transition. We find general expressions for ρD in two and three spatial dimensions, for arbitrary population and mass imbalance, for particle- and holelike bands, and show how to incorporate, at the Gaussian level, the effect of fluctuations close to a phase transition. We find that the proximity to the phase transition enhances the drag resistivity upon approaching the critical temperature from above, and we qualitatively derive the temperature dependence of this enhancement for various cases. In addition, we present numerical results for two concrete experimental systems: (i) three-dimensional cold atomic Fermi gases close to a Stoner transition and (ii) two-dimensional spatially separated electron and hole systems in semiconductor double quantum wells

Unified Boltzmann-transport theory for the drag resistivity close to an interlayer-interaction-driven second-order phase transition

We present a unified Boltzmann transport theory for the drag resistivity ρD in two-component systems close to a second-order phase transition. We find general expressions for ρD in two and three spatial dimensions, for arbitrary population and mass imbalance, for particle- and holelike bands, and show how to incorporate, at the Gaussian level, the effect of fluctuations close to a phase transition. We find that the proximity to the phase transition enhances the drag resistivity upon approaching the critical temperature from above, and we qualitatively derive the temperature dependence of this enhancement for various cases. In addition, we present numerical results for two concrete experimental systems: (i) three-dimensional cold atomic Fermi gases close to a Stoner transition and (ii) two-dimensional spatially separated electron and hole systems in semiconductor double quantum wells

Influence of remote bands on exciton condensation in double-layer graphene

We examine the influence of remote bands on the tendency toward exciton condensation in a system consisting of two parallel graphene layers with negligible interlayer tunneling. We find that the remote bands can play a crucial supporting role, especially at low carrier densities, and comment on some challenges that arise in attempting quantitative estimates of condensation temperatures

Probing the topological exciton condensate via Coulomb drag

The onset of exciton condensation in a topological insulator thin film was recently predicted. We calculate the critical temperature for this transition, taking into account screening effects. Furthermore, we show that the proximity to this transition can be probed by measuring the Coulomb drag resistivity between the surfaces of the thin film as a function of temperature. This resistivity shows an upturn upon approaching the exciton-condensed state

Spin Transport in a Unitarity Fermi Gas Close to the BCS Transition

We consider spin transport in a two-component ultracold Fermi gas with attractive interspecies interactions close to the BCS pairing transition. In particular, we consider the spin-transport relaxation rate and the spin-diffusion constant. Upon approaching the transition, the scattering amplitude is enhanced by pairing fluctuations. However, as the system approaches the transition, the spectral weight for excitations close to the Fermi level is decreased by the formation of a pseudogap. To study the consequence of these two competing effects, we determine the spin-transport relaxation rate and the spin-diffusion constant using both a Boltzmann approach and a diagrammatic approach. The former ignores pseudogap physics and finite lifetime effects. In the latter, we incorporate the full pseudogap physics and lifetime effects, but we ignore vertex corrections, so that we effectively calculate single-particle relaxation rates instead of transport relaxation rates. We find that there is qualitative agreement between these two approaches, although the results for the transport coefficients differ quantitatively

Spin Transport in a Unitarity Fermi Gas Close to the BCS Transition

We consider spin transport in a two-component ultracold Fermi gas with attractive interspecies interactions close to the BCS pairing transition. In particular, we consider the spin-transport relaxation rate and the spin-diffusion constant. Upon approaching the transition, the scattering amplitude is enhanced by pairing fluctuations. However, as the system approaches the transition, the spectral weight for excitations close to the Fermi level is decreased by the formation of a pseudogap. To study the consequence of these two competing effects, we determine the spin-transport relaxation rate and the spin-diffusion constant using both a Boltzmann approach and a diagrammatic approach. The former ignores pseudogap physics and finite lifetime effects. In the latter, we incorporate the full pseudogap physics and lifetime effects, but we ignore vertex corrections, so that we effectively calculate single-particle relaxation rates instead of transport relaxation rates. We find that there is qualitative agreement between these two approaches, although the results for the transport coefficients differ quantitatively

Field of inserted charges during Scanning Electron Microscopy of non-conducting samples

Three different approaches to calculating the electric potential in an inhomogeneous dielectric next to vacuum due to a charge distribution built up by the electron beam are investigated. An analytical solution for the electric potential cannot be found by means of the image charge method or Fourier analysis, both of which do work for a homogenous dielectric with a planar interface to vacuum. A Born approximation gives a good approach to the real electric potential in a homogenous dielectric up to a relative dielectric constant of 5. With this knowledge the electric potential of an inhomogenous dielectric is calculated. Also the electric field is calculated by means of a particle-mesh method. Some inhomogeneous dielectric configurations are calculated and their bound charges are studied. Such a method can yield accurate calculations of the electric potential and can give quantitative insight in the charging process. A capacitor model is described to estimate the potential due to the charge build up. It describes the potential build up in the first microseconds of the charging. Thereafter, it seems that more processes have to be taken into account to describe the potential well. This potential can further be used in a macroscopic approach to the collective motion of the electrons described by the Boltzmann transport equations or a derived density model, which can be a feasible alternative approximation to the more commonly used Monte-Carlo simulation of individual trajectorie