The guiding spirit of our work is to gather information arising from experimental observations combined with microscopic modeling to obtain insight into the physics of new planar Josephson junctions. A crucial factor for successful research in this field is a tight connection between theory and experiment. To achieve this goal, we take advantage of the complementary background of the partners in this project and the already established collaborations between team members.
TopoFlag is organized into two scientific work packages:
WP1: Supercurrent diode effect in hybrid InSb-nanoflag Josephson junctions
WP1 aims at the investigation of basic aspects of hybrid superconductor/semiconductor devices with strong spin-orbit coupling, with particular focus on the emergence of non-reciprocal transport phenomena. Supercurrent rectification is associated with an anomaly in the current-phase-relation; in addition, a non-negligible magneto-chiral anisotropy coefficient is expected in the Josephson inductance. To be specific, we consider a precise geometry, i.e., a planar Josephson junction, in which the normal region between two superconductors is an InSb nanoflag. We have already demonstrated planar Josephson junctions based on InSb nanoflags with Ti/Nb contacts that show high transparency of interfaces and ballistic superconductivity. Consistent with previous reports, we have observed Shubnikov-de Haas oscillations in these nanoflags, which underlines the two-dimensional nature of their electronic states.
Owing to the intrinsic strong spin-orbit coupling of InSb, this semiconductor is a promising platform to inspect non-reciprocal transport and the superconducting diode effect. From the experimental side, the first activity concerns the optimization of InSb nanoflag-based planar Josephson junctions. High quality InSb nanoflags (mobility 30,000 cm2/Vs at 4 K) for this project will be grown and provided by the group of Lucia Sorba (CNR-Nano Pisa). As lateral superconducting contacts, Ti/Nb, Nb, or NbTiN will be explored, in order to improve interface transparency and achieve good proximity effect, looking for long superconducting coherence length. We will also explore various length-to-width ratios of the weak link. Besides the standard back gate, application of side gates to the nanoflags will be optimized. Theoretical support will help in data analysis and parameter optimization. Low temperature magneto-transport characterization of the devices will be performed in a dilution refrigerator with in-plane magnetic field (with amplitude up to 1 T). The vectorial magnetic field allows probing directly the expected anisotropy in the supercurrent signal that is a hallmark of non-reciprocal supercurrent transport.
In parallel, microscopic modeling of these hybrid structures will be investigated. A first approach will rely on the Bogoliubov-de Gennes picture of propagating electrons and retroreflected holes that carry a dissipationless current in the superconductor-normal-superconductor (SNS) junction. Supercurrent in SNS junctions is carried by Andreev bound states, which are confined in the normal region in-between the superconducting leads, and is driven by a non-zero phase difference between the two superconductors. When the superconducting coherence length is smaller than the distance between the superconductors, the supercurrent can be effectively calculated by combining the scattering properties of the normal region with the Andreev reflection amplitudes at the normal-superconductor interfaces. Both low-energy effective models, which allow for an analytical treatment, and numerical tools based on tight-binding Hamiltonians will be used, in order to describe the SDE and to quantitatively understand experimental findings.
Results:
- Josephson diode effect in high-mobility InSb nanoflags
- Side-gate modulation of supercurrent in InSb nanoflag-based Josephson junctions
WP2: Evidence of topological superconductivity in hybrid InSb-nanoflag Josephson junctions
WP2 focuses on the investigation of possible topological phases that may emerge in an InSb nanoflag-based planar Josephson junction. To tackle this issue, we plan an innovative approach, beyond standard transport measurements, that fully exploits the uncovered surface of the InSb nanoflag Josephson junctions. Together with current-phase relationship measurements (tracking anomalous behavior), we will employ the scanning gate microscopy (SGM) technique to locally probe topological phase transitions by monitoring the supercurrent density distribution. As a first step, we will perform SGM measurements, complemented with proper theoretical modeling, on SNS hybrid structures.
The SGM technique can be faithfully approached theoretically via quantum transport simulations that account for the perturbation of the 2DES induced by the charged tip in the form of a Lorentzian potential. We will thus simulate the impact of the scanning gate on quasiparticles, evaluating critical current maps as a function of superconducting phase difference and SGM tip position.
Furthermore, in SNS devices, the phase transition from trivial to topological superconductivity is controlled by the superconducting phase difference, which can be varied by proper current bias or external in-plane magnetic field. The second part of WP2 will mainly dwell on this issue, aiming at unveiling topological transitions and detecting non-trivial bound states. To look for peculiar features related to the presence of topological states, we will inspect both conventional low temperature DC transport and innovative approaches. These studies will be primarily of theoretical character and will boost future experimental approaches, eventually beyond the timeline of this project. Specifically, we aim at studying the response of planar Josephson junctions, both in the trivial and topological regime, in presence of AC fields. Time-dependent sources applied on different gates, capacitively coupled to the planar Josephson junction, will be modeled to study subsequent wave packet propagation, and how the system would equilibrate in response to external perturbation. Alternative detection schemes, with more complex geometries, will be formulated based on these predictions, in order to reveal clear and unequivocal evidence of topological properties in hybrid junctions.
Results: