Switching from Crossed Andreev Reflection to Electron Teleportation via Quantum dot

Abstract

We study electron transport through a normal lead-quantum dot-topological superconductor-quantum dot-normal lead (N-QD-TS-QD-N) junction. Due to the non-local nature of Majorana fermions (MFs) in the topological superconductor, there are two types of single electron transport processes in the junction: crossed Andreev reflection (CAR) and electron teleportation (ET). When the coupling energy of MFs is much larger than the coupling between MFs and QDs, electron can tunnel through topological superconductor either via CAR or ET depending on the energy levels of QDs. For instance, when both energies of QDs (labeled as $\epsilon_1$ and $\epsilon_2$) are equal to the coupling energy of MFs (denoted as $E_M$), the electron in the left lead can teleport to the right lead via MFs while when $\epsilon_1=-\epsilon_2=E_M$ is satisfied, the electron in the left lead can combine one electron in the right lead to form a cooper pair and tunnel into the topological superconductor via MFs. Since both electron teleportation and crossed Andreev reflection manifest the non-local properties of MFs, they can be used to examine the nature of MFs.