In this thesis I present the theoretical work on Fermionic surface states, and bulk Bosonic collective excitations in topological superfluids and superconductors. Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. For the B-phase of superfluid 3He, which is a 3D time-reversal invariant (TRI) topological superfluid with an isotropic energy gap, ∆, we report calculations of the surface spectrum, spinand mass current densities originating from the Andreev surface states . The surface states are Majorana Fermions with their spins polarized transverse to their direction of propagation along the surface, pk. The negative energy states give rise to a ground-state helical spin current confined on the surface. Superfluid flow through a channel of confined 3He-B is characterized by the flow field, ps = 2h¯ ∇ϕ, which breaks SO(2)Lz+Sz rotational symmetry and time reversal (T) symmetry. However, the Bogoliubov-Nambu Hamiltonian remains invariant under the combined symmetry, Uz(π)× T, where Uz(π) is a π rotation about the surface normal. As a result the B-phase in the presence of a superflow remains a topological phase with a gapless spectrum of Majorana modes on the surface. These negative energy states do not contribute to the T = 0 mass current. Thermal excitation of the Doppler shifted Majorana branches leads to a power law suppression of the superfluid mass current for 0 < T . 0.5Tc, providing a direct signature of the Majorana branches of surface excitations in the fully gapped 3D topological superfluid, 3He-B. In the case of 3He-A, the edge Fermionic spectrum consists of a branch of chiral edge states (Weyl Fermions). The negative energy states are related to the ground-state edge current, J = (n/4)h¯, where n is the number density of 3He atoms. The power law suppression of the edge current, J(T) ' (n/4)h¯ (1−βT2) for 0 Tc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the branch of Weyl Fermions. We discuss the effects of wave function overlap, and hybridization between edge states bound to opposing edges, on the mass current and ground-state order parameter. Under increasing lateral confinement, the chiral A phase undergoes a sequence of quantum phase transitions, first to a periodic domain wall (PDW) phase with broken translational symmetry at Dc2 ≈ 13ξ0. The PDW phase is a periodic array of chiral domains with alternating chirality, separated by domain walls. The PDW phase exhibits a complex mass current distribution resulting from the combination of low-energy Fermionic excitations bound to the domain walls, and the Fermions bound to the confining edges. Under stronger confinement, a second-order transition occurs to the non-chiral “polar state” at Dc1 ≈ 9ξ0, with a single orbital component aligned along the channel. Unconventional superconductors and superfluid 3He share a common property that the ground state breaks a subset of space-time symmetries in addition to the U(1)N gauge symmetry of conventional superconductors. Bosonic collective modes in unconventional superconductors and superfluid 3He provide signatures to the broken symmetry phase. We report the effects of gap anisotropy on the Bosonic modes’ masses, lifetimes, and their coupling to transverse electromagnetic (EM) waves in two-dimensional chiral superconductors. We show that the two Bosonic modes with opposite chirality relative to the ground state couple to the transverse waves Under strong tetragonal anisotropy, the higher mass Bosonic mode is heavily damped while the lower mass Bosonic mode is weakly damped. We also obtain selection rules for the couplings of the modes to the transverse field. The resulting current response originating from the Bosonic modes depends on the polarization of the vector field ~A. This leads to distinct power absorption spectra as a function of the EM polarization. Finally, we report results for the collective modes spectrum and power absorption in the presence of impurity scattering. The mode spectra are very sensitive to the impurities. For weak impurity scattering, in which the electron-impurity mean free path is long compared to the size of the Coper pairs (limp ), the power absorption dependends on the EM polarization due to the selective coupling of collective modes to the transverse field.

Last modified

• 02/27/2018

Creator

• Hao Wu

DOI

• https://doi.org/10.21985/N2XT39

Subject

• Physics

Keyword

• Physics
• Topological Superfluids

Date created

• 2017-01-01

Resource type

• Dissertation

Rights statement

• In Copyright