Phase Signature of Topological Transition in Josephson Junctions

Matthieu C. Dartiailh, William Mayer, Joseph Yuan, Kaushini S. Wickramasinghe, Alex Matos-Abiague, Igor Žutić, and Javad Shabani

Phys. Rev. Lett. 126, 036802 – Published 21 January 2021

Abstract

Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable $Al / InAs$ Josephson junctions in a loop geometry, we measure a $π$ jump in the junction phase with an increasing in-plane magnetic field $B_{∥}$ . This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in $B_{∥}$ . Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states.

Received 18 June 2020
Accepted 16 December 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.036802

Physics Subject Headings (PhySH)

Proximity effect Topological superconductors

Josephson junctions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Matthieu C. Dartiailh ¹, William Mayer¹, Joseph Yuan¹, Kaushini S. Wickramasinghe¹, Alex Matos-Abiague², Igor Žutić ³, and Javad Shabani ¹

¹Center for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, USA
²Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA
³Department of Physics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 126, Iss. 3 — 22 January 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Signatures of trivial and topological superconductivity. (a) Predicted field at which a Zeeman-driven FFLO-like mechanism [18] leads to a minimum in $I_{c}$ as a function of the separation between the superconducting contacts. Solid line: $v_{F} = 5 \times 10^{5} m / s$ . Colored region: from $4 \times 10^{5} m / s$ to $1 \times 10^{6} m / s$ . Dashed line: our simulation for which the FFLO-like mechanism would induce a transition at $\approx 4 T$ . (b) The low-energy ground-state spectrum of a JJ with a semiconducting region at $μ = 5.05 meV$ . The energy gap closes and reopens, indicating a topological phase transition and the emergence of an MBS. Red lines: the evolution of finite-energy states into MBS inside the topological gap $≲ 23 μ eV$ . (c) Probability density of MBS in the JJ for $B = 0.85 T$ , normalized to its maximum value. It clearly indicates the formation of the MBS localized at the end of the junction. White lines: the edges of the normal region.
Reuse & Permissions
Figure 2
Gate control of trivial and topological superconductivity. Measurement of the differential resistance of JJ1 as function of an applied in-plane field along the $y$ axis at two different gate voltages: (a) $V_{g}^{1} = - 1.5 V$ , (b) $V_{g}^{1} = 1.4 V$ . In both cases, JJ2 is depleted ( $V_{g}^{2} = - 7 V$ ) and does not participate in the transport. At high gate (b), a minimum of the critical current is observed around 600 mT for JJ1. (c) Zero-bias differential resistance of JJ2 as a function of the applied in-plane field and the gate voltage. $V_{g}^{1}$ is set to $- 7 V$ .
Reuse & Permissions
Figure 3
Phase signature of topological transition from SQUID interferometry. SQUID oscillations for $B_{y} = 100 mT$ (a) and 850 mT (b) for different $V_{g}^{2}$ at $V_{g}^{1} = - 2 V$ . Dashed lines: position of the maximum at $V_{g}^{2} = - 4 V$ used as a phase reference. Stars: position of the maximum of the oscillation. Solid lines: best fits to the SQUID oscillations used to extract the period and the phase shift between different $V_{g}^{2}$ . (c) Phase difference between the SQUID oscillation at $V_{g}^{2} = - 4 V$ and the oscillation at a different value as a function of $B_{y}$ . Solid lines: linear fits of the data for $B_{y} \leq 450 mT$ . (d) Phase shift from which the linear $B_{y}$ contribution has been subtracted to highlight the phase jump of about $π$ occurring for the three higher $V_{g}^{2}$ values.
Reuse & Permissions
Figure 4
In-plane magnetic-field anisotropy of the gap closing. Differential resistance of JJ1 as function of the bias current and the $y$ component of $B_{∥}$ , applied at an angle $θ$ with respect to the $y$ direction as depicted in Fig. 1.
Reuse & Permissions

Physical Review Letters