Employing the Keldysh Nonequilibrium Green’s function method, we investigate time-dependent transport through a topological superconductor with Majorana bound states in the presence of a high frequency microwave field. It is found that Majorana bound states driven by photon-assisted tunneling can absorb(emit) photons and the resulting photon-assisted tunneling side band peaks can split the Majorana bound state that then appears at non-zero bias. This splitting breaks from the current opinion that Majorana bound states appear only at zero bias and thus provides a new experimental method for detecting Majorana bound states in the Non-zero-energy mode. We not only demonstrate that the photon-assisted tunneling side band peaks are due to Non-zero-energy Majorana bound states, but also that the height of the photon-assisted tunneling side band peaks is related to the intensity of the microwave field. It is further shown that the time-varying conductance induced by the Majorana bound states shows negative values for a certain period of time, which corresponds to a manifestation of the phase coherent time-varying behavior in mesoscopic systems.

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We propose a model to study the spin transport properties of a regular polygonal quantum ring with two leads, which is subjected to Rashba spin-orbit coupling (SOC). The transmission coefficient has been derived analytically using a standard quantum network method. It is found that in the absence of Rashba SOC, there are two conditions for which zero conductances arise when the leads are asymmetrically located, and in this case, the transmitted electron is unpolarized. In the presence of SOC, however, one kind of conductance zero can be lifted by the Rashba SOC, while the other persists. We also study the conductance of spin-polarized carriers. It is found that Rashba SOC can be used as an effective mean for inducing spin flip. In addition, based on our calculations, the device considered may demonstrate the properties of a spin filter.

In the presence of an elastic barrier at both interfaces of a mesoscopic d-wave superconductor-normalmetal-d-wave superconductor ͑DND junction͒, the Josephson current at zero temperature is studied by using a simple matrix method. As a limiting case, the tunneling between two d-wave superconductors coupled by a insulator barrier ͑DID structure͒ is particularly addressed. The effects of sign change and anisotropic gap structure of the d x 2 Ϫy 2 superconductor are carefully considered in the Andreev reflection. The coupling of forward-moving quasiparticles and backward-moving quasiparticles with different pair potentials leads to contrasting Andreev spectra in different motion angle regions, which is specific to our model. Unlike conventional superconducting point-contact junctions, the conduction crossing the Fermi surface plays an important role in determining the critical current. Our theoritical results suggest that the dependence of the critical current on the grain boundary tilt angle provides a clue to identify the pairing symmetry of high-T c superconductors.

We have investigated the superconducting phase difference dependence of Andreev levels and Josephson current through a mesoscopic normal-metal layer in contact with two superconducting electrodes with s-wave and d-wave pairing symmetry (S s NS d junction͒. It is shown that, regardless of the junction length, due to the sign change of the d-wave order parameter under suitable arrangements, the zero-energy point of Andreev levels for the negative process appears at ϭ0. In particular, at zero temperature, the amplitude of the total Josephson current through the point contact S s NS d junction could be enhanced by the sign change of the d-wave order parameter. However, for an S s NS d junction of special length, the amplitude of Josephson current may be suppressed by this sign change. Moreover, as a special case, the midgap surface states discovered by Hu ͓Phys. Rev. Lett. 72, 1526 ͑1994͔͒ are recovered naturally. ͓S0163-1829͑96͒06933-0͔