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Register a new userAnomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multi-level dots
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We study the combined effects of spin-orbit interaction, magnetic field, and Coulomb charging on the Josephson current-phase relation, I(varphi), for a multi-level quantum dot tunnel-contacted by two conventional s-wave superconductors with phase difference varphi. A general model is formulated and analyzed in the cotunneling regime (weak tunnel coupling) and in the deep subgap limit, fully taking into account interaction effects. We determine the conditions for observing a finite anomalous supercurrent I_a=I(varphi=0). For a two-level dot with spin-orbit coupling and arbitrarily weak Zeeman field B, we find the onset behavior I_apropto {rm sgn}(B) in the presence of interactions, suggesting the incipient spontaneous breakdown of time-reversal symmetry. We also provide conditions for realizing spatially separated (but topologically unprotected) Majorana bound states in this system, which have a clear signature in the 2pi-periodic current-phase relation.
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We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana states populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, thus far unexplored in the context of Majorana physics, allows to probe accurately the presence of Majorana bound states in the junction.
We investigate hybrid structures based on a bilayer quantum spin Hall system in proximity to an s-wave superconductor as a platform to mimic time-reversal symmetric topological superconductors. In this bilayer setup, the induced pairing can be of intra- or inter-layer type, and domain walls of those different types of pairing potentials host Kramers partners (time-reversal conjugate pairs) of Majorana bound states. Interestingly, we discover that such topological interfaces providing Majorana bound states can also be achieved in an otherwise homogeneous system by a spatially dependent inter-layer gate voltage. This gate voltage causes the relative electron densities of the two layers to vary accordingly which suppresses the inter-layer pairing in regions with strong gate voltage. We identify particular transport signatures (zero-bias anomalies) in a five-terminal setup that are uniquely related to the presence of Kramers pairs of Majorana bound states.
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.
As part of the intense effort towards identifying platforms in which Majorana bound states can be realized and manipulated to perform qubit operations, we propose a topological Josephson junction architecture that achieves these capabilities and which can be experimentally implemented. The platform uses conventional superconducting electrodes deposited on a topological insulator film to form networks of proximity-coupled lateral Josephson junctions. Magnetic fields threading the network of junction barriers create Josephson vortices that host Majorana bound states localized in the junction where the local phase difference is an odd multiple of $pi$, i.e. attached to the cores of the Josephson vortices. This enables us to manipulate the Majorana states by moving the Josephson vortices, achieving functionality exclusive to these systems in contrast to others, such as those composed of topological superconductor nanowires. We describe protocols for: 1) braiding localized Majorana states by exchange, 2) controlling the separation and hence the coupling of adjacent localized Majorana states to effect non-Abelian rotations via hybridization of the Majorana modes, and 3) reading out changes in the non-local parity correlations induced by such operations. These schemes make use of the application of current pulses and local magnetic field pulses to control the location of vortices, and measurements of the Josephson current-phase relation to reveal the presence of the Majorana bound states. We describe the architecture and schemes in the context of experiments currently underway.
The ac Josephson effect in a ferromagnetic Josephson junction, which is composed of two superconductors separated by a ferromagnetic metal (FM), is studied by a tunneling Hamiltonian and Greens function method. We obtain two types of superconducting phase dependent current, i.e., Josephson current and quasiparticle-pair-interference current (QPIC). These currents change their signs with thickness of the FM layer due to the 0-$pi$ transition characteristic to the ferromagnetic Josephson junction. As a function of applied voltage, the Josephson critical current shows a logarithmic divergence called the Riedel peak at the gap voltage, while the QPIC shows a discontinuous jump. The Riedel peak reverses due to the 0-$pi$ transition and disappears near the 0-$pi$ transition point. The discontinuous jump in the QPIC also represents similar behaviors to the Riedel peak. These results are in contrast to the conventional ones.
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