Talk Title: CPT symmetry, supersymmetry, and Majorana fermion in a
generalized Fu-Kane system The prediction and discovery of Weyl fermions on the surface
of topological insulators are one of the most intriguing accomplishments from
condensed matter physics community in the past five years. Via the proximity-induced
superconductivity, two copies of Weyl fermions, electrons and holes, turn out
to be coupled and their dynamics is governed by the Dirac equation. It has been shown that a blizzard quantum state, Majorana fermion, which is the antiparticle of itself, can exist within an isolated superconducting vortex. In fact, the existence of such state is related to the underlying chiral, time-reversal, and particle-hole symmetries associated with the Dirac equation, in which zero chemical potential and magnetic field is considered. I would demonstrate that there exists a generalized Jackiw-Rossi-Dirac Hamiltonian which considers both the effects of finite chemical potential and magnetic field but only preserves the particle-hole symmetry. In addition, the considered mass-gap can also possess the momentum-dependence as in the unconventional superconductivity on surface. Another interesting aspect of the Dirac equation is the hidden supersymmetry, which also suggests the presence of the zero-mode, according to G. Volovik. One can also re-express the Dirac matrices in terms of a set of fermion operators, which leaves the original Clifford algebra intact. By doing so and assuming a very large core for the isolated vortex, a set of boson operators appears due to the linear momenta and coordinates operators, and an ensuing supersymmetric Hamiltonian for the entire vortex bound states is emergent. I would demonstrate the underlying accidental degeneracy associated with the spectrum in terms of a set of SU(2) angular momentum and a set of supersymmetric Lenz operators.
Ref.1 I.F. Herbut and C.-K. Lu, PRB 82 125402 2010 Ref.2 C.-K. Lu and I.F. Herbut, PRB 82 144505 2010 Ref.3 I.F. Herbut and C.-K. Lu, PRB 83 125412 2011 Ref.4 C.-K. Lu and I.F. Herbut, arXiv:1102.5163 Click to download: Presentation File |