Browsing by Author "Chen, Chun"

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    Topological Superconductivity And Superfluidity In Quasi-One-Dimensional Quantum Systems
    (2017-08) Chen, Chun
    Topological superconductors and superfluids are an exciting class of recently discovered materials. In one dimension, topological superconductors accommodate a novel kind of bound state, known as a Majorana zero mode, at their endpoints, and introducing strong correlations can lead to systems with related types of bound states known as parafermions. In this thesis, we systematically studied three correlated aspects of topological superconductivity and superfluidity in low-dimensional quantum systems. By using Bogoliubov--de Gennes (BdG) theory combined with proper topological-invariant calculation, we first predicted a new topological Fulde--Ferrell--Larkin--Ovchinnikov (\emph{topo}-FFLO) superfluid state in one-dimensional ($1$D) spin-orbit-coupled Fermi gases (with superfluid order stabilized by $3$D interactions). Specifically we demonstrate that Majorana zero modes can exist even if the superconducting/superfluid pairing is at nonzero momentum (i.e. of FFLO type), provided that the magnitude of the superconducting/superfluid gap is finite. $1$D topological superfluids are typically classified and understood through BdG mean-field Hamiltonians. This raises the question of whether they can exist in truly $1$D systems where particle number is conserved. We discuss a new mechanism by which Majorana zero modes can arise in a number-conserving Fermi ladder. This interaction-enabled topological phase is protected by a unitary $\mathbb{Z}_2$ symmetry that is not related to any microscopic fermion-parity symmetry. Generalizations of Majorana bound states can also occur by inducing superconductivity at the boundary states of certain types of fractional quantum Hall bilayers. Then how could we detect them experimentally? In this thesis, we discuss two answers---dynamical signatures and characterizing the finite-sized splitting of the otherwise degenerate ground-state Hilbert space associated with these bound states. Particularly, in the process we demonstrate how instanton methods can be applied to the general problem of ground-state energy splittings in these systems.