[Paper Review] Anomalous Josephson effect in semiconducting nanowires as a signature of the topologically nontrivial phase

Konstantin Nesterov, Manuel Houzet+1 more|arXiv (Cornell University)|Dec 9, 2015

Topological Materials and Phenomena36 references63 citations

TL;DR

This paper proposes that the anomalous Josephson effect—nonzero supercurrent at zero phase difference—is a robust signature of the topologically nontrivial phase in semiconducting nanowires with Rashba spin-orbit coupling and a Zeeman field. Using a Bogoliubov-de Gennes model, it demonstrates that in short junctions, the anomalous current becomes comparable to the critical current when the superconducting regions are tuned into the topological phase, providing a clear experimental signature for Majorana zero modes.

ABSTRACT

We study Josephson junctions made of semiconducting nanowires with Rashba spin-orbit coupling, where superconducting correlations are induced by the proximity effect. In the presence of a suitably directed magnetic field, the system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a phase bias between two superconductors. We show that this anomalous current can be increased significantly by tuning the nanowire into the helical regime. In particular, in a short junction, a large anomalous current is a signature for topologically nontrivial superconductivity in the nanowire.

Motivation & Objective

• To identify a measurable experimental signature for the topologically nontrivial phase in semiconducting nanowires with Rashba spin-orbit coupling.
• To investigate whether the anomalous Josephson effect (nonzero supercurrent at zero phase difference) can distinguish topological superconductivity from trivial phases.
• To determine how the magnitude of the anomalous current depends on the Zeeman field and topological phase transition in short Josephson junctions.
• To assess the robustness of the anomalous current against electrostatic barriers in the normal region of the junction.

Proposed method

• Formulating a Bogoliubov-de Gennes (BdG) Hamiltonian for a nanowire with Rashba spin-orbit coupling, Zeeman field, and proximity-induced superconductivity.
• Using a tight-binding approximation to numerically diagonalize the BdG Hamiltonian and compute the supercurrent via the derivative of the energy spectrum with respect to the superconducting phase.
• Analyzing the current-phase relation and decomposing contributions from continuum states and subgap Andreev bound states.
• Applying perturbation theory in the limit of small Zeeman field along z (|hz| ≪ ∆) to derive analytical expressions for the anomalous current.
• Introducing a normal barrier in the junction to test robustness of the anomalous current against disorder or tunneling barriers.
• Extending analysis to finite magnetic field direction (θ) to explore the full phase space of the topological transition.

Experimental results

Research questions

• RQ1 Can the anomalous Josephson current serve as a reliable experimental indicator of the topologically nontrivial phase in semiconducting nanowires?
• RQ2 How does the magnitude of the anomalous current scale with Zeeman field strength and superconducting pairing in short junctions?
• RQ3 What is the relative contribution of superconducting leads versus the normal region to the anomalous Josephson effect?
• RQ4 Is the anomalous current robust against the presence of a normal barrier in the junction's central region?
• RQ5 How does the current-phase relation evolve in short junctions when the system is tuned into the topological phase?

Key findings

• In short Josephson junctions, the anomalous current becomes comparable in magnitude to the critical current when the superconducting regions are in the topologically nontrivial phase.
• The dominant contribution to the anomalous current arises from the superconducting leads when they are tuned into the topological phase, especially when the Zeeman field is applied throughout the system.
• The anomalous current scales linearly with hz/Δ for small Zeeman fields, with a significant enhancement in the topological regime due to the suppression of competing bands.
• The anomalous current remains robust against the introduction of a normal barrier in the junction’s central region, indicating its resilience to weak disorder.
• The current-phase relation in short junctions exhibits a linear dependence on the phase difference, with a nonzero intercept at ϕ = 0, confirming the anomalous nature of the current.
• The analytical perturbative treatment in the |hz| ≪ Δ limit confirms that the anomalous current is driven by a magnetoelectric coupling between Rashba spin-orbit coupling and the Zeeman field, with a strong enhancement in the topological phase.