Many-particle Majorana bound states. Derivation and signatures in superconducting double quantum dots

We consider two interacting quantum dots coupled by standard s-wave superconductors. We derive an effective Hamiltonian, and show that over a wide parameter range a degenerate ground state can be obtained. An exotic form of Majorana bound states is supported at these degeneracies, and the system can be adiabatically tuned to a limit in which it is equivalent to the one-dimensional wire model of Kitaev. We give the form of a Majorana bound state in this system in the strong interaction limit in the many-particle picture. We also study the Josephson current in this system, and demonstrate that a double slit-like pattern emerges in the presence of an extra magnetic field. This pattern is shown to disappear with increasing interaction strength, which is due to the current being carried by chargeless Majorana bound states. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)