Manisha Thakurathi, Aavishkar A. Patel, Diptiman Sen, Amit Dutta
We show how Majorana end modes can be generated in a one-dimensional system by varying one of the parameters in the Hamiltonian periodically in time. The specific model we consider is a wire containing spinless electrons with a p-wave superconducting term and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the z direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number while the second invariant has not appeared in the literature before. We show that the second invariant correctly predicts the numbers of end modes with Floquet eigenvalues equal to +1 and -1.
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http://arxiv.org/abs/1303.2300
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