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arXiv:1701.05206 · Physical review. B./Physical review. B

Sensing Floquet-Majorana fermions via heat transfer

Paolo Molignini, Evert van Nieuwenburg, R. Chitra

Published Sep 22, 2017• 37 citations
arXivHTMLPDF

Abstract

Time periodic modulations of the transverse field in the closed $XY$ spin-$\frac{1}{2}$ chain generate a very rich dynamical phase diagram, with a hierarchy of ${\mathbb{Z}}_{n}$ topological phases characterized by differing numbers of Floquet-Majorana modes. This rich phase diagram survives when the system is coupled to dissipative end reservoirs. Circumventing the obstacle of preparing and measuring quasienergy configurations endemic to Floquet-Majorana detection schemes, we show that stroboscopic heat transport and spin density are robust observables to detect both the dynamical phase transitions and Majorana modes in dissipative settings. We find that the heat current provides very clear signatures of these Floquet topological phase transitions. In particular, we observe that the derivative of the heat current, with respect to a control parameter, changes sign at the boundaries separating topological phases with differing nonzero numbers of Floquet-Majorana modes. We present a simple scheme to directly count the number of Floquet-Majorana modes in a phase from the Fourier transform of the local spin density profile. Our results are valid provided the anisotropies are not strong and can be easily implemented in quantum engineered systems.

DOI
10.1103/physrevb.96.125144

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We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad generator \hat{\mathcal{L}} ℒ ̂ of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes – localized eigenmodes of \hat{\mathcal{L}} ℒ ̂ . Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed system, which are now separated by intermediate regions where winding numbers are ill-defined and the bulk-boundary correspondence breaks down. Combining these techniques with the Floquet formalism reveals higher winding numbers and different types of edge modes under periodic driving. Finally, we link the presence of edge modes to a steady state current.
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Floquet Majorana fermions appear as steady states at the boundary of time-periodic topological phases of matter. In this work, we theoretically study the main features of these exotic topological phases in the periodically driven one-dimensional Kitaev model. By controlling the ac fields, we can predict topological phase transitions that should give rise to signatures of Majorana states in experiments. Moreover, the knowledge of the time dependence of these Majorana states allows one to manipulate them. Our work contains a complete analysis of the monochromatic driving in different frequency regimes.