Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions

  title={Coulomb stability of the 4$\pi$-periodic Josephson effect of Majorana fermions},
  author={Bernard van Heck and Fabian Hassler and A. Akhmerov and C. W. J. Beenakker},
  journal={Physical Review B},
The Josephson energy of two superconducting islands containing Majorana fermions is a 4\pi-periodic function of the superconducting phase difference. If the islands have a small capacitance, their ground state energy is governed by the competition of Josephson and charging energies. We calculate this ground state energy in a ring geometry, as a function of the flux -\Phi- enclosed by the ring, and show that the dependence on the Aharonov-Bohm phase 2e\Phi/\hbar remains 4\pi-periodic regardless… 

Figures from this paper

Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are
Spectral response of Josephson junctions with low-energy quasiparticles
We study nanowire-based Josephson junctions shunted by a capacitor and take into account the presence of low-energy quasiparticle excitations. These are treated by extending conventional models used
Transport properties of the Coulomb-Majorana junction
We provide a comprehensive theoretical description of low-energy quantum transport for a Coulomb-Majorana junction, where several helical Luttinger liquid nanowires are coupled to a joint mesoscopic
Signatures of topological phase transitions in mesoscopic superconducting rings
We investigate Josephson currents in mesoscopic rings with a weak link which are in or near a topological superconducting phase. As a paradigmatic example, we consider the Kitaev model of a spinless
Strong-coupling topological Josephson effect in quantum wires.
  • F. Nogueira, I. Eremin
  • Physics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2012
The Josephson current shows the characteristic 4π periodicity expected for a topological Josephson effect and discusses the additional features of the current associated with a closure of the energy gap between the energy levels.
Kondo physics in the Josephon junction with DIII-class topological and s-wave superconductors
We discuss the Kondo effect in the Josephson junction formed by the indirect coupling between a one-dimensional DIII -class topological and s -wave superconductors via a quantum dot. By performing
Hysteresis from nonlinear dynamics of Majorana modes in topological Josephson junctions
We reveal that topological Josephson junctions provide a natural platform for the interplay between the Josephson effect and the Landau-Zener effect through a two-level system formed by coupled


Observing Majorana bound states of Josephson vortices in topological superconductors
The equations governing the dynamics of phase solitons (fluxons) in a Josephson junction in a topological superconductor are studied and it is shown that the fluxon will bind a localized zero energy Majorana mode and will consequently behave as a non-Abelian anyon.
Anyonic interferometry without anyons: how a flux qubit can read out a topological qubit
Proposals to measure non-Abelian anyons in a superconductor by quantum interference of vortices suffer from the predominantly classical dynamics of the normal core of an Abrikosov vortex. We show how
Measurement of the effect of quantum phase slips in a Josephson junction chain
Coulomb interactions can cause a rapid change in the phase of the wavefunction along a very narrow superconducting system. Such a phase slip is now measured in a chain of Josephson junctions.
Search for Majorana fermions nearing success at last?
Experimental groups around the world are racing to spot a never-beforeseen type of particle, known as a Majorana fermion, and it looks as if some groups are closing in fast or may even have bagged Majoranas already.
One can distinguish the two currents by their size dependence: While I N decays as 1/R or faster, I J has the R independence of a supercurrent
    The flux induced by the supercurrent I J due to the nonzero inductance L μ 0 R of the ring may be neglected relative to the applied flux if LI J h/e. The magnitude of the supercurrent can be