Fractional ac Josephson effect in unconventional superconductors

Abstract

For certain orientations of Josephson junctions between two p_x-wave or two d-wave superconductors, the subgap Andreev bound states produce a 4pi-periodic relation between the Josephson current I and the phase difference phi: I ~ sin(phi/2). Consequently, the ac Josephson current has the fractional frequency eV/h, where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction.Comment: 8 pages, 3 figures, RevTEX 4; v2. - minor typos corrected in proof

Geometric dependence of Nb-Bi2Te3-Nb topological Josephson junction transport parameters

“…In contrast to a Fraunhofer pattern, it does not depend on the geometry of the junction, but on the current-phase relationship of the junction. A sum of different current-phase relationships [22][23][24][25][26][27] …”

Kitaev spin models from topological nanowire networks

“…To construct a nanowire array that would support such collective states, one needs to realize the two elementary building blocks: The p-wave nanowire [4] with Majorana end states and a Josephson junction of such wires [26]. Experiments on the first have already been carried out [9][10][11] and they give supporting evidence for the existence of Majorana end states.…”

“…where J = E √ T sin(δφ) with T being the transmission coefficient at k F between different wires, and δφ = φ 1 /2 − φ 2 /2 is half the difference of the superconducting phase in the two wires [26]. Referring to our convention of labeling the wire ends black and white, we can without loss of generality assume that the wire ends meeting at a junction always carry the same end label.…”

“…When the wires are in a topological phase with Majorana modes localized at their ends, tunneling of also single electrons is possible and one obtains a fractional Josephson junction where the tunneling amplitude now depends on half the relative superconducting phase difference [26].…”

“…In this work our focus is on a different setting that is directly relevant to the proposals for braiding the Majorana end states [8,17]. There the nanowires are placed in proximity to a common superconductor, which translates to an effective low-energy theory of free Majorana fermions subject to two distinct tunnelings: intrawire tunneling along the nanowires and a fractional Josephson tunneling between the nanowires [26]. Our main result is to show that the low-energy theories of various wire arrays realize parts of the phase diagrams of the class of spin-1/2 lattice models that we will collectively refer to as Kitaev spin models.…”