UC San Diego

Superfluidity and superconductivity are similar and can be considered as the counterpart of each other in various systems. In this dissertation, I will examine my works on both superfluidity and superconductivity, which are two subjects that I mainly studied. The platform of bosonic systems that I worked on is indirect exciton, and as for superconductivity I mainly focused on the unconventional $p-$wave one.

Indirect excitons, or interlayer excitons are bound states of electrons and holes, where electrons and holes live in separate layers. Indirect excitons can interact with photon at infrared and visible wavelength. We first study the transport properties of one layer of exctions going through a single quantum point contact, and discuss the conductance behavior of such bosonic quasiparticles, where we neglect the interaction between excitons. Then we include the interacting effect by the Gross-Pitaevskii equation, and study the non-linear diffraction and interference of interacting condensates, transporting through nanoconstrictions. Using the classical inverse scattering method, we can map the interference problem to a one dimensional scattering problem to solve the the interference pattern. Instead of the properties of one layer of excitons, we also study the properties of two layers of excitons, electron-hole quadrilayers. If two electron-hole bilayer is well separated, we can treat this quadrilayer system as two layers of excitons, that have dipolar interaction between each other. We calculate ground state energies, static structural factors, and collective modes (sound excitations) for various of densities of these two exciton layers. If the densities of excitons in two layers are equal (balanced), the system may evolve into a biexciton phase, where exciton pairs up with another exciton in another layer, when the density is dilute enough. In the limit of strong imbalance, we can treat the exciton in the dilute layer as a polaron interacting with sound modes of the other layer.

The $p-$wave superconducting pairing can be of two types, that are the counterparts of $^3${\rm{He}}-A and $^3${\rm{He}}-B phases. In a $^3${\rm{He}}-A type superconductor, which is also referred as $p_x+ip_y$ (or simply $p+ip$) superconductor, the pairing is quasi two dimensional. We study a junction between a conventional $s-$wave superconductor and a $p+ip$ superconductor. Using Ginzburg-Landau free energy analysis, we can determine the symmetry breaking patterns of superconducting orders. In addition, we find that the symmetry breaking pattern at junction implies the existence of a magnetoelectric effect, and a finite spin polarization at the edge of the junction. If the $^3${\rm{He}}-B type pairing and $s-$wave superconducting pairing coexist, they may prefer to have a $\pi/2$ phase difference, and it is called $p+is$ superconductor. We perform a systematic study of the electrodynamics in $p+is$ superconductors, where we calculate the effective action for the external fields, which proves to be similar to the axion action. We will show how to define the axion angle in a $p+is$ superconductor, and we point out some differences between our effective action and the axion action, which corresponds to the relativistic case.