Andreev reflection and Josephson effect in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> lattice
Xingfei Zhou
Abstract
We investigate the Andreev reflection and the Josephson effect in the $\ensuremath{\alpha}\ensuremath{-}{T}_{3}$ lattice, which falls between graphene ($\ensuremath{\alpha}=0$) and the dice lattice ($\ensuremath{\alpha}=1$), by adjusting the parameter $\ensuremath{\alpha}$. In the regime of the specular Andreev reflection, when the incident energy of the electron is small, the probability of Andreev reflection decreases as the parameter $\ensuremath{\alpha}$ increases. On the contrary, when the incident energy is large, the probability of Andreev reflection increases as the parameter $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}=1$. In the regime of Andreev retroreflection, when the parameter $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$. We also give the differential conductance in these two regimes and find that it increases as the parameter $\ensuremath{\alpha}$ increases generally. In addition, the $\ensuremath{\alpha}\ensuremath{-}{T}_{3}$ lattice-based Josephson current increases as $\ensuremath{\alpha}$ increases. When the length of the junction approaches zero, the critical Josephson currents in the different values of $\ensuremath{\alpha}$ approach the same value.