Fractional ac Josephson effect in p- and d-wave superconductors

Abstract

For certain orientations of Josephson junctions between two px-wave or two d-wave superconductors, the subgap Andreev bound states produce a 4π-periodic relation between the Josephson current I and the phase difference φ: I ∝ sin(φ/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. We also study junctions between singlet s-wave and triplet px-wave, as well as between chiral px ± ipy-wave superconductors.

Microwave transitions as a signature of coherent parity mixing effects in the Majorana-transmon qubit

“…The operators satisfy g y i ¼ g i and {g i ,g j } ¼ d ij . The properties of the device are determined by the interplay of the Josephson coupling E J , the charging energy E C , the coupling E M between the Majorana excitations and the superconducting phase difference j 18,20,[35][36][37][38][39][40] . The Hamiltonian for the hybrid junction is…”

“…When the nanowire bridges a Josephson junction, the presence of Majorana zero modes was predicted to lead to several observable effects [18][19][20][21][22][23][24] , of which first experimental signatures were recently observed 25 and explained theoretically 26 . Even more intriguing is the case of an isolated mesoscopic Josephson junction, which in the absence of the nanowire is known as a Cooper-Pair-Box (CPB), embedded within an optical cavity.…”

Majorana Fermion Surface Code for Universal Quantum Computation

“…Majorana fermions in topological superconductors are of great interest as they are predicted to produce exotic quantum phenomena such as the fractional Josephson effect [15][16][17] and electron teleportation [18]. Most remarkably, vortices or defects that carry Majorana fermions are predicted to exhibit non-Abelian statistics [19][20][21], which have yet to be observed in nature.…”

Quantum information sharing between topologically distinct platforms

“…[30,31] Here m 0 (x) is the bare coupling strength along the domain in the absence of the phase difference. As threading a magnetic field through the domain wall effectively changes the phase difference ∆φ(x)/2, it effectively tune the coupling strength m(x).…”

“…Intuitively, such a transfer should lead to decoherence of quantum information as the domain wall separating the two droplets hosts co-propagating gapless chiral edge states [30,31], these states cannot be gapped and hence even the notion of adiabaticity is not applicable to such a transfer process. However, as we shall see, these gapless edge states can actually be used as intermediate agents facilitating quantum information transfer [32].…”