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Register a new userA quantitative model for IcR product in d-wave Josephson junctions
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We study theoretically the Josephson effect in d-wave superconductor / diffusive normal metal /insulator/ diffusive normal metal/ d-wave superconductor (D/DN/I/DN/D) junctions. This model is aimed to describe practical junctions in high-$T_C$ cuprate superconductors, in which the product of the critical Josephson current ($I_C$) and the normal state resistance ($R$) (the so-called $I_{rm C}R$ product) is very small compared to the prediction of the standard theory. We show that the $I_{rm C}R$ product in D/DN/I/DN/D junctions can be much smaller than that in d-wave superconductor / insulator / d-wave superconductor junctions and formulate the conditions necessary to achieve large $I_{rm C}R$ product in D/DN/I/DN/D junctions. The proposed theory describes the behavior of $I_{rm C}R$ products quantitatively in high-$T_{rm C}$ cuprate junctions.
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Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$pi$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evidence of the fractional ac Josephson effect, is enhanced significantly by the increase in the junction capacitance and IcRn product as well as the decrease in the microwave frequency even for the same portion of the 4$pi$-periodic supercurrent. Our study provides the optimal conditions for observing the fractional ac Josephson effect; furthermore, our new model can be used to precisely quantify the topological supercurrent from the experimental data of topological JJs.
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the normal region: We show how the interplay between the spin-momentum locking of the topological insulator and an in-plane magnetization parallel to the direction of phase bias leads to an asymmetry of the Andreev spectrum with respect to transverse momenta. If sufficiently large, this asymmetry induces a transition from a regime of gapless, counterpropagating Majorana modes to a regime with unprotected modes that are unidirectional at small transverse momenta. Intriguingly, the magnetization-induced asymmetry of the Andreev spectrum also gives rise to a Josephson Hall effect, that is, the appearance of a transverse Josephson current. The amplitude and current phase relation of the Josephson Hall current are studied in detail. In particular, we show how magnetic control and gating of the normal region can enable sizable Josephson Hall currents compared to the longitudinal Josephson current. Finally, we also propose in-plane magnetic fields as an alternative to the magnetization in the normal region and discuss how the planar Josephson Hall effect could be observed in experiments.
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