Gate tunable enhancement of supercurrent in hybrid planar Josephson junctions

TL;DR

The paper tackles realizing robust quasi-1D topological superconductivity in planar JJs by engineering the normal region via patterned Al coverage and electrostatic gating. It reports gate-tunable enhancement of the critical current $I_c$ at finite in-plane field by depleting hole regions with a top gate $TG$, supported by Fraunhofer patterns and a two-gate design that controls the hole-region chemical potential $\, u_h\,$$ (represented as $\mu_h$). The experimental findings are reproduced by Bogoliubov–de Gennes simulations using Kwant and by a simplified two-strip model, showing that optimal depletion improves quasiparticle wave-function matching across the junction and can lead to non-monotonic $I_c$ behavior with $\mu_h$ and $E_Z$. This wavefunction engineering approach provides a pathway to modulate subband occupancy and the topological gap, advancing the realization of robust Majorana bound states in planar JJs.

Abstract

Planar Josephson junctions (JJs) have emerged as a promising platform for the realization of topological superconductivity and Majorana zero modes. To obtain robust quasi one-dimensional (1D) topological superconducting states using planar JJs, limiting the number of 1D Andreev bound states' subbands that can be present, and increasing the size of the topological superconducting gap, are two fundamental challenges. It has been suggested that both problems can be addressed by properly designing the interfaces between the JJ's normal region and the superconducting leads. We fabricated Josephson junctions with periodic hole structures on the superconducting contact leads on InAs heterostructures with epitaxial superconducting Al. By depleting the chemical potential inside the hole region with a top gate, we observed an enhancement of the supercurrent across the junction. Such an enhancement is reproduced in theoretical simulations. The theoretical analysis shows that the enhancement of the JJ's critical current is achieved when the hole depletion is such to optimize the matching of quasiparticles' wave-function at the normal/superconductor interface. These results show how the combination of carefully designed patterns for the Al coverage, and external gates, can be successfully used to tune the density and wave functions' profiles in the normal region of the JJ, and therefore open a new avenue to tune some of the critical properties, such as number of subbands and size of the topological gap, that must be optimized to obtain robust quasi 1D superconducting states supporting Majorana bound states.

Figures (6)

• Figure 1: Device geometry and Fraunhofer patterns at different gate configurations. (a) False-color scanning electron micrograph of the measured device. (b) schematic of the device and the material stacks. (c),(d) Differential resistance as a function of the bias current and out-of-plane magnetic field for JG = 0 V and TG = 0 V (c) and JG = 0 V and TG = -5 V (d).
• Figure 2: Supercurrent gate dependence at different in-plane magnetic fields. (a) Differential resistance as a function of the bias current and TG voltages at zero magnetic field. (b) Differential resistance as a function of the bias current and TG voltages at $B_y$ = 200 mT. The Supercurrent is significantly enhanced when a more negative voltage is applied to TG. (c),(d) Differential resistance as a function of the bias current and JG voltages at $B_y$ = 200 mT when TG = 0 V (c) and TG = - 5 V (d). Supercurrent is always monotonically decreasing with decreasing JG voltages.
• Figure 3: Supercurrent in-plane field dependence at different gate configurations. (a) Switching current extracted from panels (b) and (c). (b) Differential resistance as a function of the bias current and $B_y$ when JG = 0 V and TG = 0 V. (c) Differential resistance as a function of the bias current and $B_y$ when JG = 0 V and TG = -5 V, the supercurrent shows an almost linear decreasing with increasing $B_y$.
• Figure 4: (a) Schematic of simulation setup to model the experiments. (b) $I_c$ as a function of $E_Z$ for $\mu_h=\mu=1.25\Delta$ (red) and $\mu_h=-1.25\Delta$ (green). (c), (d) $I_c$ vs $\mu_h$ for $E_Z=0$ and $E_Z=1.14\Delta$, respectively. In (c) and (d) $I_0$ is the value of $I_c$ when $\mu_h=\mu$.
• Figure 5: (a) Profile of $J_x$ for the case when $E_Z=0$ and $\mu_h=\mu$, M1 point in Fig. \ref{['fig:sim']} (c). (b), (c), (d) Profiles of $J_x$ for the case when $E_Z=1.14\Delta$ and $\mu_h$ corresponds to the points N1, N2, N3 in Fig. \ref{['fig:sim']} (d), respectively. $J_0$ is the average current density for the case when $E_Z=0$, $\mu_h=\mu$. The red dashed lines indicate the boundary of the normal strip. The red boxes show positions of some of the depleted holes.