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We study all the possible different two terminal configurations of Josephson junctions containing wires of time-reversal invariant topological superconductors (TRITOPS) and ordinary superconductors, including combinations with an interacting quantum dot between both wires in the junction. We introduce simple effective Hamiltonians which explain the different qualitative behaviors obtained. We analyze a wide range of phenomena, including occurrence and quenching of the so called $0-pi$ transition, anomalous periodicity and jumps of the Josephson current as a function of the phase difference, and finite Josephson current in the absence of magnetic flux.
Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with $4pi$ periodicity in the superconducting phase difference. We explore the TRITOPS fr
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 consider a model proposed before for a time-reversal-invariant topological superconductor (TRITOPS) which contains a hopping term $t$, a chemical potential $mu$, an extended $s$-wave pairing $Delta$ and spin-orbit coupling $lambda$. We show that f
We study the emergent band topology of subgap Andreev bound states in the three-terminal Josephson junctions. We scrutinize the symmetry constraints of the scattering matrix in the normal region connecting superconducting leads that enable the topolo
We study the ground state and low-energy subgap excitations of a finite wire of a time-reversal-invariant topological superconductor (TRITOPS) with spin-orbit coupling. We solve the problem analytically for a long chain of a specific one-dimensional