Floquet generation of Majorana end modes and topological invariants

By Manisha Thakurathi, Aavishkar A. Patel, D. Sen, Amit Kumar Dutta. 2013

178 citations recorded by the source corpus.

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, 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 which are always equal to +/- 1 for time-reversal symmetric systems. 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. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to +1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/6a8b78ca7475ed388e0d48d92172d4aaddecb0e5

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields (2014, background): “This strategy has been generalized for superfluids, where “Floquet Majorana fermions” could be created by driving superconducting systems [47–51].”
Floquet topological transitions in a driven one-dimensional topological insulator (2015, background): “Although previous works have addressed driven one-dimensional systems in a variety of contexts [11,24,31,44], the above question still remains.”
Periodic table for Floquet topological insulators (2016, background): “Notably, previous work has considered dynamical topological phases in 1D chains with emergent Majorana fermions [31, 33], 2D systems without symmetries [32] and driven analogues of the 2D time-reversal invariant topological insulators [37].”
Classification of Interacting Topological Floquet Phases in One Dimension (2016, background): “[10] Manisha Thakurathi, Aavishkar A Patel, Diptiman Sen, and Amit Dutta, “Floquet generation of majorana end modes and topological invariants,” Phys.”