Abstract
We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field the quasi-one-dimensional region between the two superconductors can support a topological superconducting phase hosting Majorana bound states at its ends. We study the phase diagram of the system as a function of the Zeeman field and the phase difference between the two superconductors (treated as an externally controlled parameter). Remarkably, at a phase difference of $\pi$, the topological phase is obtained for almost any value of the Zeeman field and chemical potential. In a setup where the phase is not controlled externally, we find that the system undergoes a first-order topological phase transition when the Zeeman field is varied. At the transition, the phase difference in the ground state changes abruptly from a value close to zero, at which the system is trivial, to a value close to $\pi$, at which the system is topological. The critical current through the junction exhibits a sharp minimum at the critical Zeeman field, and is therefore a natural diagnostic of the transition. We point out that in presence of a symmetry under a modified mirror reflection followed by time reversal, the system belongs to a higher symmetry class and the phase diagram as a function of the phase difference and the Zeeman field becomes richer.
Highlights
Since the realization of two-dimensional topological insulators a decade ago, a plethora of new phases of matter with nontrivial topology in one, two, and three dimensions have been discovered in experiment
We show the derivation of the phase diagram for the system as a function of the phase difference and the Zeeman field, and we discuss the magnitude of the topological gap and the appearance of Majorana end modes in Sec
We have shown that one-dimensional topological superconductivity can be realized in a Josephson junction across a 2DEG with Rashba spin-orbit coupling and in-plane magnetic field
Summary
Since the realization of two-dimensional topological insulators a decade ago, a plethora of new phases of matter with nontrivial topology in one, two, and three dimensions have been discovered in experiment. The system can self-tune into a topological phase when the magnetic field is varied and realizes a first-order topological phase transition without a gap closing This transition is accompanied by a minimum of the critical current. The critical current vanishes at the magnetic field of the underlying zero-temperature topological transition This insight suggests that the experimental results presented by. The paper is followed by four appendixes that cover several technical details
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