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We investigate theoretically the simultaneous tunneling of two electrons from a superconductor into a normal metal at low temperatures and voltages. Such an emission process is shown to be equivalent to the Andreev reflection of an incident hole. We obtain a local tunneling Hamiltonian that permits to investigate transport through interfaces of arbitrary geometry and potential barrier shapes. We prove that the bilinear momentum dependence of the low-energy tunneling matrix element translates into a real space Hamiltonian involving the normal derivatives of the electron fields in each electrode. The angular distribution of the electron current as it is emitted into the normal metal is analyzed for various experimental setups. We show that, in a full three-dimensional problem, the neglect of the momentum dependence of tunneling causes a violation of unitarity and leads to the wrong thermodynamic (broad interface) limit. More importantly for current research on quantum information devices, in the case of an interface made of two narrow tunneling contacts separated by a distance $r$, the assumption of momentum-independent hopping yields a nonlocally entangled electron current that decays with a prefactor proportional to $r^{-2}$ instead of the correct $r^{-4}$.
We theoretically study transport properties of voltage-biased one-dimensional superconductor--normal metal--superconductor tunnel junctions with arbitrary junction transparency where the superconductors can have trivial or nontrivial topology. Motiva
We present the electron tunneling transport and its magnetic field modulation of a superconducting (SC) Josephson junction with a barrier of single ferromagnetic (FM) Kitaev layer. We find that at H = 0, the Josephson current IS displays two peaks at
A superconductor subject to electromagnetic irradiation in the terahertz range can show amplitude oscillations of its order parameter. However, coupling this so-called Higgs mode to the charge current is notoriously difficult. We propose to achieve s
We investigate electron cooling based on a clean normal-metal/spin-filter/superconductor junction. Due to the suppression of the Andreev reflection by the spin-filter effect, the cooling power of the system is found to be extremely higher than that f
We present measurements of current noise and cross-correlations in three-terminal Superconductor-Normal metal-Superconductor (S-N-S) nanostructures that are potential solid-state entanglers thanks to Andreev reflections at the N-S interfaces. The noi