二维倾斜Dirac锥系统中的带电Andreev模
Electrically charged Andreev modes in two-dimensional tilted Dirac cone systems
摘要：
在基于石墨烯的约瑟夫森结中，Andreev反射可以变成镜面反射，这引起传播Andreev模式。这些传播的Andreev模式基本上是电荷中性的，因此它们传递能量但不传递电荷。这项工作的一个主要结果是，当石墨烯的狄拉克理论变形为倾斜的狄拉克锥时，狄拉克方程的电荷共轭对称性的破坏使所得的Andreev模式带电。我们计算了一个否则零电荷电导所产生的倾斜参数$\vecζ=(ζ_x,ζ_y)$。这种形式的电荷输运与由正常电子引起的电荷输运的区别特征在于它们依赖于两个超导体的相位差$ϕ$，该相位差可以通过采用通量偏置来实验地提取。另一个结果涉及约瑟夫森电流的增强，而不是传播Andreev模式，局部Andreev能级形成的制度。在这个制度中，我们发现增强的数量级的约瑟夫森电流时，倾斜参数带来的接近和接近$ζ=1$限制。我们阐明，增强是由于两种效果的组合：（i）通过在倾斜到$ζ\approx 1$时平坦化频带来增强传输信道的数量，以及（ii）对倾斜矢量$\vecζ$的角度$θ$的非平凡依赖性。
英文摘要：
In a graphene-based Josephson junction, the Andreev reflection can become specular which gives rise to propagating Andreev modes. These propagating Andreev modes are essentially charge neutral and therefore they transfer energy but not electric charge. One main result of this work is that when the Dirac theory of graphene is deformed into a tilted Dirac cone, the breaking of charge conjugation symmetry of the Dirac equation renders the resulting Andreev modes electrically charged. We calculate an otherwise zero charge conductance arising solely from the tilt parameters $\vecζ=(ζ_x,ζ_y)$. The distinguishing feature of such a form of charge transport from the charge transport caused by normal electrons is their dependence on the phase difference $ϕ$ of the two superconductors which can be experimentally extracted by employing a flux bias. Another result concerns the enhancement of Josephson current in a regime where instead of propagating Andreev modes, localized Andreev levels are formed. In this regime, we find enhancement by orders of magnitude of the Josephson current when the tilt parameter is brought closer and closer to $ζ=1$ limit. We elucidate that, the enhancement is due to a combination of two effects: (i) enhancement of number of transmission channels by flattening of the band upon tilting to $ζ\approx 1$, and (ii) a non-trivial dependence on the angle $θ$ of the the tilt vector $\vecζ$.
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