From two dimensions to wire networks in a dice-lattice Josephson array

Abstract

We investigate Josephson arrays consisting of a dice-lattice network of superconducting weak links surrounding rhombic plaquettes of proximitized semiconductor. Josephson coupling of the weak links and electron density in the plaquettes are independently controlled by separate electrostatic gates. Applied magnetic flux results in an intricate pattern of switching currents associated with frustration, $f$. For depleted plaquettes, the switching current is nearly periodic in $f$, expected for a phase-only description, while occupied plaquettes yield a decreasing envelope of switching currents with increasing $f$. A model of flux dependence based on ballistic small-area junctions and diffusive large-area plaquettes yields excellent agreement with experiment.

Figures (4)

• Figure 1: (a) Scanning electron micrograph of a hybrid Josephson junction array in dice-lattice geometry showing superconducting Al islands (light) on a semiconducting InAs heterostructure (dark), taken prior to gate fabrication. (b) Schematic cross section of a junction showing the dual gate configuration. The frame-gate (lower layer, kept at 0 V throughout the experiment) follows the Al geometry extending over the junctions, and tunes the inter-island coupling. The global top-gate (top layer) tunes the carriers in the plaquettes. (c) Optical image of device 1 overlaid with the measurement setup.
• Figure 2: Differential resistance, $dV/dI$, as a function of current bias, $I$, and flux-threading magnetic field, $B$, taken at different top-gate voltages, (a) $V_\text{TG}=0$, (b) $-1.06$ V, and (c) $-2.5$ V. The switching current, $I_\text{SW}$, is periodically modulated by $B$, showing sharp peaks at integer frustration values, $f=\Phi/\Phi_0$. For populated plaquettes ($V_\text{TG}=0$ and $-1.06$ V), the envelope of $I_\text{SW}$ decays sharply with increasing $B$. For depleted plaquettes ($V_\text{TG}=-2.5$ V), the envelope is effectively flat throughout the measured range.
• Figure 3: (a) Enlarged electron micrograph of a single plaquette. (b) Switching current of the system, $I_{\rm SW}$, is modeled by considering contributions from the junctions (red) and plaquettes (green); see Eq. (\ref{['model']}). Because of the different areas, the contribution from the plaquettes is suppressed at higher fields, leaving the slow-decaying contribution from the junctions.
• Figure 4: (a) Envelope of the switching current, $I_\text{SW}$, for three characteristic top-gate voltages, $V_\text{TG}$, as a function of flux threading magnetic field, $B$, measured at integer values of frustration, $f=\Phi/\Phi_0$. The dashed lines are fits to Eq. (\ref{['model']}). (b) Extracted junction, $I_\text{JJ}$, and plaquette, $I_\text{P}$, switching-current amplitudes; for fitting details see Supplemental Material Supplement. The sum of the two contributions agree well with the experimental $I_\text{SW}$ at $B=0$. (c) and (d) Extracted dimensionless scaling factors for junction, $a_\text{JJ}$, and plaquette, $a_\text{P}$, areas as a function of $V_\text{TG}$. When plaquettes are depleted (around $V_\text{TG}=-1.5$ V), $a_\text{P}$ becomes undefined, since $I_\text{P}\to0$.