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Zero modes arising from a planar Majorana equation in the presence of $N$ vortices require an $mathcal{N}$-dimensional state-space, where $mathcal{N} = 2^{N/2}$ for $N$ even and $mathcal{N} = 2^{(N + 1)/2}$ for $N$ odd. The mode operators form a restricted $mathcal{N}$-dimensional Clifford algebra.
We describe the occurrence and physical role of zero-energy modes in the Dirac equation with a topologically non-trivial background.
We provide a current perspective on the rapidly developing field of Majorana zero modes in solid state systems. We emphasize the theoretical prediction, experimental realization, and potential use of Majorana zero modes in future information processi
We introduce and study a class of anyon models that are a natural generalization of Ising anyons and Majorana fermion zero modes. These models combine an Ising anyon sector with a sector associated with $SO(m)_2$ Chern-Simons theory. We show how they
We investigate the decoherence patterns of topological qubits in contact with the environment by a novel way of deriving the open system dynamics other than the Feynman-Vernon. Each topological qubit is made of two Majorana modes of a 1D Kitaevs chai
We investigate the topological properties of spin polarized fermionic polar molecules loaded in a multi-layer structure with the electric dipole moment polarized to the normal direction. When polar molecules are paired by attractive inter-layer inter