Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions

Abstract

We show how the superconducting phase difference in a Josephson junction may be used to split the Kramers degeneracy of its energy levels and to remove all the properties associated with time-reversal symmetry. The superconducting phase difference is known to be ineffective in two-terminal short Josephson junctions, where irrespective of the junction structure the induced Kramers degeneracy splitting is suppressed and the ground state fermion parity must stay even, so that a protected zero-energy Andreev level crossing may never appear. Our main result is that these limitations can be completely avoided by using multiterminal Josephson junctions. There the Kramers degeneracy breaking becomes comparable to the superconducting gap, and applying phase differences may cause the change of the ground state fermion parity from even to odd. We prove that the necessary condition for the appearance of a fermion parity switch is the presence of a "discrete vortex" in the junction: the situation when the phases of the superconducting leads wind by 2π . Our approach offers strategies for creation of Majorana bound states as well as spin manipulation. Our proposal can be implemented using any low density, high spin-orbit material such as InAs quantum wells, and can be detected using standard tools.

Coherent transport properties of a three-terminal hybrid superconducting interferometer

“…However, the periodicity and the presence of nodes at precise values of L,R / 0 are well reproduced by Eq. (16). This fact corroborates the idea that these features are robust in a topological sense and connected to the nontrivial geometry of the three-terminal JJ.…”

“…It is composed of a T-shaped N nanowire proximized by two S loops, encircling two independent magnetic fluxes. The ω-SQUIPT represent a useful tool to explore the nontrivial physics accessible in multiterminal Josephson junctions (JJs), in which the Andreev bound states can cross the Fermi level (zero-energy) [10] to tailor exotic quantum states [11][12][13][14][15], to simulate topological materials able to support Majorana bound states in the case of quasiballistic junctions with strong spin-orbit coupling [12,16], or to implement different kinds of Q-bits [17] or switchers [18]. The first ω-SQUIPT was realized [19] very recently with a diffusive three-terminal JJ.…”

Random-matrix theory of Majorana fermions and topological superconductors

“…31 we illustrate the latter system, studied in Van Heck, Mi, and Akhmerov (2014). A minimum of two independent fluxes Φ 1 , Φ 2 is needed to produce a discrete vortex, so the minimal configuration consists of a quantum dot connected to three superconducting leads (panel a).…”

Singularities in the Andreev spectrum of a multiterminal Josephson junction

“…In the case of two-terminal junction, the Andreev levels touch zero energy only when the transmission coefficient of the normal region is unity and the phase difference is ϕ = ±π. For the multi-terminal junctions, the Andreev levels can reach zero energy at some isolated points in N − 1 dimensional space of phase differences [15][16][17] . Such points are topologically protected being the Weyl singularities studied theoretically in 3D solids 19 .…”

“…There is a recent interest in multi-terminal Josephson junctions [15][16][17] . Such junctions have been realized, for instance, with crossed InSb/As nanowires 18 , where SO interaction is strong.…”