Evidence for 4e charge of Cooper quartets in a biased multi-terminal graphene-based Josephson junction

Abstract

In a Josephson junction (JJ) at zero bias, Cooper pairs are transported between two superconducting contacts via the Andreev bound states (ABSs) formed in the Josephson channel. Extending JJs to multiple superconducting contacts, the ABSs in the Josephson channel can coherently hybridize Cooper pairs among different superconducting electrodes. Biasing three-terminal JJs with antisymmetric voltages, for example, results in a direct current (DC) of Cooper quartet (CQ), which involves a four-fermion entanglement. Here, we report half a flux periodicity in the interference of CQ formed in graphene based multi-terminal (MT) JJs with a magnetic flux loop. We observe that the quartet differential conductance associated with supercurrent exhibits magneto-oscillations associated with a charge of 4e, thereby presenting evidence for interference between different CQ processes. The CQ critical current shows non-monotonic bias dependent behavior, which can be modeled by transitions between Floquet-ABSs. Our experimental observation for voltage-tunable non-equilibrium CQ-ABS in flux-loop-JJs significantly extends our understanding of MT-JJs, enabling future design of topologically unique ABS spectrum.

Selective control of conductance modes in multi-terminal Josephson junctions

“…These three sets of MAR signatures can be understood as independent Andreev reflections between all three pairs of terminals. We also observe a signature of Cooper quartet transport 35 – 38 , 42 , indicated by a lower resistance feature along the line V 1 = − V 2 . The differential resistance maps can also be plotted as a function of V 1 , V 2 where the quartet signature is clearly visible along the V 1 = − V 2 diagonal (see Supplementary Fig.…”

“…MTJJs may also find application as circuit elements for coupling multiple qubits 14 , 25 – 27 . Additionally, they have shown rich transport features such as the coexistence of superconducting and dissipative currents 28 , multi-terminal fractional Shapiro steps 29 , 30 , generalizations of multiple Andreev reflections (MAR) 31 , 32 , multi-loop superconducting interferometry 33 , 34 and exotic Cooper quartet transport 35 – 38 .…”

Dynamical Stabilization of Multiplet Supercurrents in Multiterminal Josephson Junctions

“…9 The classically derived cos 2φ term in U(φ) along the resonance could also yield the observed Φ 0 /2 magnetooscillations in ref. 8 However, the π − 0 transition observed in that work cannot be explained by our model, and may thus be conclusive evidence of the observation of quartet states. The robust classical 2φ periodicity observed along the quartet resonance may be useful in developing new quantum devices such as cos 2φ qubits, 15,36,37 using flux loops 23,24 to control the trajectory in phase space.…”

“…For example, in a three-terminal device such as the one shown in Figure a, when V L = − V R ≠ 0, ⟨φ L + φ R ⟩ is stationary with respect to the grounded bottom contact. The microscopic origin of the resulting supercurrent has commonly been attributed to “quartets”, an entangled set of four electrons. − Supercurrents generated by the static phase states exist for any combination of nV L + mV R = 0, with integers n and m and involve the entanglement of multiplets consisting of four or more electrons.…”

Multiterminal Inverse AC Josephson Effect

“…The added complexity makes multiterminal junctions an ideal medium for engineering novel quantum and topological phenomena. For example, the energy spectrum of multiterminal Josephson junction based on a few-mode semiconductor has been predicted to emulate the band structure of topologically nontrivial materials. − This exciting prospect led to renewed efforts toward experimental realizations of multiterminal Josephson junctions, − which calls for new insights into their phase dynamics.…”