Inverse AC Josephson Effect in Ballistic Multiterminal Graphene Josephson Junctions

Abstract

In multi-terminal Josephson junctions, the superconducting coupling is established between each pair of contacts across a common normal channel. The state of such junction is described by N-1 independent phase differences between pairs of contacts, where N is the number of terminals. The added complexity makes multi-terminal junctions an ideal medium for engineering novel quantum phenomena. For example, the energy spectrum of multi-terminal Josephson junction has been predicted to effectively emulate the band structure of topologically non-trivial materials. This exciting prospect led to renewed interest toward experimental realizations of multi-terminal Josephson junctions. Figure 1a shows a scanning electron microscope image of a three-terminal junction, in which the normal region is made of ballistic graphene encapsulated in hexagonal boron nitride. Biasing the individual junctions, we observe three superconducting branches, corresponding to pair-wise coupling between pairs of junctions (Figure 1d). We further explore the phase dynamics of these junctions when exposed to microwave radiation. The microwave drive causes inverse AC Josephson effect, which has been explored in detail in conventional Josephson junctions. In this phenomenon, the phase of the junction locks to the drive frequency, and the I−V curves acquire “Shapiro steps” of quantized voltage V=nhf/2e with integer n. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account, resulting in a complicated energy landscape (Figure 1c). Experimentally, we observe robust Shapiro steps with fractional n (Figure 2). We demonstrate that these steps cannot be attributed to non-sinusoidal current-phase characteristics of the junctions. Instead, they can be explained by considering the device as a completely connected Josephson network. We explore the stability of these steps and related phenomena, such as correlated switching events between different junctions. We successfully simulate the observed behaviors using a modified two-dimensional resistively and capacitively shunted junction model (Figure 1b). Our results suggest that multi-terminal Josephson junctions may be a highly-tunable playground for possible applications in quantum information processing.