Majorana zero-modes and topological phases of multi-flavored Jackiw-Rebbi model
Author(s)Ho, Shih-Hao; Lin, Feng-Li; Wen, Xiao-Gang
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Motivated by the recent Kitaev’s K-theory analysis of topological insulators and superconductors, we adopt the same framework to study the topological phase structure of Jackiw-Rebbi model in 3+1 dimensions. According to the K-theory analysis based on the properties of the charge conjugation and time reversal symmetries, we classify the topological phases of the model. In particular, we find that there exist Z Majorana zero-modes hosted by the hedgehogs/t’Hooft-Polyakov monopoles, if the model has a T [superscript 2] = 1 time reversal symmetry. Guided by the K-theory results, we then explicitly show that a single Majorana zero mode solution exists for the SU(2) doublet fermions in some co- dimensional one planes of the mass parameter space. It turns out we can see the existence of none or a single zero mode when the fermion doublet is only two. We then take a step further to consider four-fermion case and find there can be zero, one or two normalizable zero mode in some particular choices of mass matrices. Our results also indicate that a single normalizable Majorana zero mode can be compatible with the cancellation of SU(2) Witten anomaly.
DepartmentMassachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of Physics
Journal of High Energy Physics
Ho, Shih-Hao, Feng-Li Lin, and Xiao-Gang Wen. “Majorana Zero-Modes and Topological Phases of Multi-Flavored Jackiw-Rebbi Model.” J. High Energ. Phys. 2012, no. 12 (December 2012).