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Register a new userDissipation-enabled fractional Josephson effect
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Added by
Doru Cristian Sticlet
Publication date
2018
fields
Physics
and research's language is
English
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The anomalous $4pi$-periodic ac Josephson effect, a hallmark of topological Josephson junctions, was experimentally observed in a quantum spin Hall insulator. This finding is unexpected due to time-reversal symmetry preventing the backscattering of the helical edge states and therefore suppressing the $4pi$-periodic component of the Josephson current. Here we analyze the two-particle inelastic scattering as a possible explanation for this experimental finding. We show that a sufficiently strong inelastic scattering restores the $4pi$-periodic component of the current beyond the short Josephson junction regime. Its signature is an observable peak in the power spectrum of the junction at half the Josephson frequency. We propose to use the exponential dependence of the peak width on the applied bias and the magnitude of the dc current as means of verifying that the inelastic scattering is indeed the mechanism responsible for the $4pi$-periodic signal.
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Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBSs) among a continuum of conventional Andreev bound states. The distinct feature of these MBSs lies in the $4pi$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_2$Se$_3$ exhibit a fractional ac Josephson effect acting on the first Shapiro step only. With a modified resistively shunted junction model, we demonstrate that the resilience of higher order odd Shapiro steps can be accounted for by thermal poisoning driven by Joule overheating. Furthermore, we uncover a residual supercurrent at the nodes between Shapiro lobes, which provides a direct and novel signature of the current carried by the MBS. Our findings showcase the crucial role of thermal effects in topological Josephson junctions and lend support to the Majorana origin of the partial suppression of odd Shapiro steps.
Topological superconductors which support Majorana fermions are thought to be realized in one-dimensional semiconducting wires coupled to a superconductor. Such excitations are expected to exhibit non-Abelian statistics and can be used to realize quantum gates that are topologically protected from local sources of decoherence. Here we report the observation of the fractional a.c. Josephson effect in a hybrid semiconductor/superconductor InSb/Nb nanowire junction, a hallmark of topological matter. When the junction is irradiated with a radio-frequency f in the absence of an external magnetic field, quantized voltage steps (Shapiro steps) with a height hf/2e are observed, as is expected for conventional superconductor junctions, where the supercurrent is carried by charge-2e Cooper pairs. At high magnetic fields the height of the first Shapiro step is doubled to hf/e, suggesting that the supercurrent is carried by charge-e quasiparticles. This is a unique signature of Majorana fermions, elusive particles predicted ca. 80 years ago.
We theoretically study the stability of more than one Majorana Fermion appearing in a $p$-wave superconductor/dirty normal metal/$p$-wave superconductor junction in two-dimension by using chiral symmetry of Hamiltonian. At the phase difference across the junction $varphi$ being $pi$, we will show that all of the Majorana bound states in the normal metal belong to the same chirality. Due to this pure chiral feature, the Majorana bound states retain their high degree of degeneracy at the zero energy even in the presence of random potential. As a consequence, the resonant transmission of a Cooper pair via the degenerate MBSs carries the Josephson current at $varphi=pi-0^+$, which explains the fractional current-phase relationship discussed in a number of previous papers.
A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle-hole symmetry. Tunneling of Majorana quasi-particle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with $4pi$-periodicity.
In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current-voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.
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