Andreev reflection and Josephson effect in the $\alpha$-T3 lattice

TL;DR

This paper explores how the parameter alpha in the alpha-T3 lattice influences Andreev reflection and Josephson effects, revealing energy-dependent behaviors and perfect transmission conditions, with implications for superconducting transport.

Contribution

It provides a detailed analysis of Andreev reflection and Josephson effects in the alpha-T3 lattice, highlighting how these phenomena depend on alpha and incident energy, including conditions for perfect transmission.

Findings

Andreev reflection probability varies with alpha and incident energy.

Perfect transmission occurs at alpha=1 near the superconducting gap.

Josephson current increases with alpha, but critical current converges as junction length approaches zero.

Abstract

We investigate the Andreev reflection and Josephson effect in the $\alpha$-T3 lattice which falls between graphene ($\alpha = 0$) and the dice lattice ($\alpha = 1$) by adjusting the parameter $\alpha$. In the regime of specular Andreev reflection, when the incident energy of electron is small, the probability of Andreev reflection decreases as the parameter $\alpha$ increases. On the contrary, when the incident energy is large, the probability of Andreev reflection increases as the parameter $\alpha$ increases. Interestingly, when the incident energy approaches the superconducting energy-gap function, the Andreev reflection with approximate all-angle perfect transmission happens in the case of $\alpha = 1$. In the regime of Andreev retro-reflection, when the parameter $\alpha$ increases, the probability of Andreev reflection increases regardless of the value of incident energy. When the incident energy approaches the superconducting energy-gap function, the Andreev reflection with approximate all-angle perfect transmission happens regardless of the value of $\alpha$. We also give the differential conductance in these two regimes and find that the differential conductance increases as the parameter $\alpha$ increases generally. In addition, the $\alpha$-T3 lattice-based Josephson current increases as $\alpha$ increases. When the length of junction approaches zero, the critical Josephson currents in the different values of $\alpha$ approach the same value.