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Register a new userJosephson junction dynamics in the presence of $2pi$- and $4pi$-periodic supercurrents
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We investigate theoretically the dynamics of a Josephson junction in the framework of the RSJ model. We consider a junction that hosts two supercurrrent contributions: a $2pi$- and a $4pi$-periodic in phase, with intensities $I_{2pi}$ and $I_{4pi}$ respectively. We study the size of the Shapiro steps as a function of the ratio of the intensity of the mentioned contributions, i.e. $I_{4pi}/I_{2pi}$. We provide detailed explanations where to expect clear signatures of the presence of the $4pi$-periodic contribution as a function of the external parameters: the intensity AC-bias $I_text{ac}$ and frequency $omega_text{ac}$. On the one hand, in the low AC-intensity regime (where $I_text{ac}$ is much smaller than the critical current, $I_text{c}$), we find that the non-linear dynamics of the junction allows the observation of only even Shapiro steps even in the unfavorable situation where $I_{4pi}/I_{2pi}ll 1$. On the other hand, in the opposite limit ($I_text{ac}gg I_text{c}$), even and odd Shapiro steps are present. Nevertheless, even in this regime, we find signatures of the $4pi$-supercurrent in the beating pattern of the even step sizes as a function of $I_text{ac}$.
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We propose a tunable topological Josephson junction in silicene where electrostatic gates could switch between a trivial and a topological junction. These aspects are a consequence of a tunable phase transition of the topologically confined valley-chiral states from a spin-degenerate to a spin-helical regime. We calculate the Andreev bound states in such a junction analytically using a low-energy approximation to the tight-binding model of silicene in proximity to s-wave superconductors as well as numerically in the short- and long-junction regime and in the presence of intervalley scattering. Combining topologically trivial and non-trivial regions, we show how intervalley scattering can be effectively switched on and off within the Josephson junction. This constitutes a topological Josephson junction with an electrically tunable quasiparticle poisoning source.
The Josephson energy of two superconducting islands containing Majorana fermions is a 4pi-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 2ePhi/hbar remains 4pi-periodic regardless of the ratio of charging and Josephson energies - provided that the entire ring is in a topologically nontrivial state. If part of the ring is topologically trivial, then the charging energy induces quantum phase slips that restore the usual 2pi-periodicity.
The $4pi$-periodic Josephson effect is an indicator of Majorana zero modes and a ground-state degeneracy which are central to topological quantum computation. However, the observability of a $4pi$-periodic Josephson current-phase relation (CPR) is hindered by the necessity to fix the fermionic parity. As an alternative to a $4pi$-periodic CPR, this paper proposes a chiral CPR for the $4pi$-periodic Josephson effect. This is a CPR of the form $J(phi) propto C , |sin(phi/2)|$, describing a unidirectional supercurrent with the chirality $C= pm 1$. Its non-analytic dependence on the Josephson phase difference $phi$ translates into the $4pi$-periodic CPR $J(phi) propto sin(phi/2)$. The proposal requires a spin-polarized topological Josephson junction which is modeled here as a short link between spin-split superconducting channels at the edge of a two-dimensional topological insulator. In this case, $C$ coincides with the Chern number of the occupied spin band of the topological insulator. The paper details three scenarios of achieving a chiral CPR: By only Zeeman-like splitting, by Zeeman splitting combined with bias currents, and by an external out-of-plane magnetic field.
Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity in a short Josephson junction at an edge of a 2D topological insulator subject to a perpendicular magnetic field. The magnetic field effect is entirely orbital, coming from a gradient of the order parameter phase at the edge, which results in a soliton defect at the junction with a pair of gapless Andreev bound states. The latter are reducible to Majorana zero modes by a unitary rotation and protected by a chiral symmetry. Furthermore, both ground state and excitations are quasiperiodic in the magnetic flux enclosed in the junction, with the period equal to the double flux quantum $2Phi_0 = h/e$. This behaviour follows from the gauge invariance of the $4pi$ - phase periodicity of the Majorana states and manifests itself as $2Phi_0$ - spaced magnetic oscillations of the critical current. Another proposed observable is a persistent current occurring in the absence of an external phase bias. Beside the oscillations, it shows a sign reversal prompted by the neutral Majorana zero modes. These findings offer the possibility to access topological superconductivity through low-field dc magnetotransport measurements.
A Josephson junction may be driven through a transition where the superconducting condensate favors an odd over an even number of electrons. At this switch in the ground-state fermion parity, an Andreev bound state crosses through the Fermi level, producing a zero-mode that can be probed by a point contact to a grounded metal. We calculate the time-dependent charge transfer between superconductor and metal for a linear sweep through the transition. One single quasiparticle is exchanged with charge $Q$ depending on the coupling energies $gamma_1,gamma_2$ of the metal to the Majorana operators of the zero-mode. For a single-channel point contact, $Q$ equals the electron charge $e$ in the adiabatic limit of slow driving, while in the opposite quenched limit $Q=2esqrt{gamma_1gamma_2}/(gamma_1+gamma_2)$ varies between $0$ and $e$. This provides a method to produce single charge-neutral quasiparticles on demand.
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