Andreev reflection and Josephson effect in the $α$-T3 lattice

Abstract

We investigate the Andreev reflection and Josephson effect in the α−T3 lattice which falls between graphene (α = 0) and the dice lattice (α = 1) by adjusting the parameter α. In the regime of specular Andreev reflection, when the incident energy of electron is small, the probability of Andreev reflection decreases as the parameter α increases. On the contrary, when the incident energy is large, the probability of Andreev reflection increases as the parameter α 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 α = 1. In the regime of Andreev retro-reflection, when the parameter α 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 α. We also give the differential conductance in these two regimes and find that the differential conductance increases as the parameter α increases generally. In addition, the α − T3 lattice-based Josephson current increases as α increases. When the length of junction approaches zero, the critical Josephson currents in the different values of α approach the same value.

Adjustable propagating plasmons in $α-\mathcal{T}_3$ lattice-based armchair nanoribbons

“…Recently, Dirac semifinals also demonstrates some interesting electronic phenomena 47,48 close but not completely similar to α − T 3 . The unique electron bandstructure of α − T 3 model leads to its unusual electronic, optical, collective, magnetic and topological properties [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] which has been rigorously investigated over the last several years.…”