The Dissipative Flow in Topological Superconductors and Solid ⁴He

Using two piezoelectric transducers, one measures the stress tensor response from the strain field generated by the second transducer. The ratio between the stress response and strain velocity determines the dissipative response. In the first part, we show that the dissipative stress response can be used for studying excitations in a topological superconductor. We investigate a topological superconductor for the case when an Abrikosov vortex lattice is formed. In this case, the Majorana fermions are dispersive, a fact that is used to compute the dissipative stress response. In the second part, we analyse the dissipative superfluid flow through solid 4He discoused recently. We identify low energy, an excitation which plays the role of the Majorana mode which is free to move in a direction perpendicular to the two dimensional plane spaces of the dislocations.

Fractional Topological Insulators—A Bosonization Approach

A metallic disk with strong spin orbit interaction is investigated. The finite disk geometry introduces a confining potential. Due to the strong spin-orbit interaction and confining potential the metal disk is described by an effective one-dimensional model with a harmonic potential. The harmonic potential gives rise to classical turning points. As a result, open boundary conditions must be used. We bosonize the model and obtain chiral Bosons for each spin on the edge of the disk. When the filling fraction is reduced to the electron-electron interactions are studied by using the Jordan Wigner phase for composite fermions which give rise to a Luttinger liquid. When the metallic disk is in the proximity with a superconductor, a Fractional Topological Insulator is obtained. An experimental realization is proposed. We show that by tunning the chemical potential we control the classical turning points for which a Fractional Topological Insulator is realized.