Floquet Majorana fermions are steady states of equal superposition of electrons and holes in a periodically driven superconductor. We study the experimental signatures of Floquet Majorana fermions in transport measurements and show, both analytically and numerically, that their presence is signaled by a quantized conductance sum rule over discrete values of lead bias differing by multiple absorption or emission energies at drive frequency. We also study the effects of static disorder and find that the quantized sum rule is robust against weak disorder. Thus, we offer a unique way to identify the topological signatures of Floquet Majorana fermions.
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e., metallic bulk transport with conductivity of order e^{2}/h, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.
We study the combined effects of spin-orbit interaction, magnetic field, and Coulomb charging on the Josephson current-phase relation, I(ϕ), for a multi-level quantum dot tunnel-contacted by two conventional s-wave superconductors with phase difference ϕ. A general model is formulated and analyzed in the cotunneling regime (weak tunnel coupling) and in the deep subgap limit, fully taking into account interaction effects. We determine the conditions for observing a finite anomalous supercurrent Ia = I(ϕ = 0). For a two-level dot with spin-orbit coupling and arbitrarily weak Zeeman field B, we find the onset behavior Ia ∝ sgn(B) in the presence of interactions, suggesting the incipient spontaneous breakdown of time-reversal symmetry. We also provide conditions for realizing spatially separated (but topologically unprotected) Majorana bound states in a double dot variant of this system. Here Majoranas are predicted to leave a clear signature in the 2π-periodic current-phase relation.
We present a theoretical study of electron-phonon scattering effects in thin
films made of a strong topological insulator. Phonons are modelled by isotropic
elastic continuum theory with stress-free boundary conditions, and the
interaction with the helical surface Dirac fermions is mediated by the
deformation potential. We determine the temperature-dependent electrical
resistivity $\rho(T)$ and the quasiparticle decay rate $\Gamma(T)$ observable
in photoemission. The low- and high-temperature power laws for both quantities
are obtained analytically. Detailed estimates covering the full temperature
range are provided for Bi$_2$Se$_3$.Comment: 11 pages, 6 figure
Valley degrees of freedom offer a potential resource for quantum information processing if they can be effectively controlled. We discuss an optical approach to this problem in which intense light breaks electronic symmetries of a two-dimensional Dirac material. The resulting quasienergy structures may then differ for different valleys, so that the Floquet physics of the system can be exploited to produce highly polarized valley currents. This physics can be utilized to realize a valley valve whose behavior is determined optically. We propose a concrete way to achieve such valleytronics in graphene as well as in a simple model of an inversion-symmetry broken Dirac material. We study the effect numerically and demonstrate its robustness against moderate disorder and small deviations in optical parameters.
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