Gate-tunable zero-frequency current cross correlations of the quartet state in a voltage-biased three-terminal Josephson junction

Abstract

A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dccurrent carrying three-body static phase coherence, known as the "quartet current". We calculate the zero-frequency current noise cross-correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy 0 is connected to three superconductors Sa, S b and Sc with gap ∆, biased at Va = V , V b = −V and Vc = 0, and with intermediate contact transparencies. At zero temperature, nonlocal quartets (in the sense of four-fermion correlations) are noiseless at subgap voltage in the nonresonant dot regime 0/∆ 1, which is demonstrated with a semi-analytical perturbative expansion of the cross-correlations. Noise reveals the absence of granularity of the superflow splitting from Sc towards (Sa, S b ) in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime 0/∆ < ∼ 1, crosscorrelations measured in the (Va, V b ) plane should reveal an "anomaly" in the vicinity of the quartet line Va + V b = 0, related to an additional contribution to the noise, manifesting the phase sensitivity of cross-correlations under the appearance of a three-body phase variable. Phase-dependent effective Fano factors Fϕ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors Fϕ are of order unity in the resonant dot regime 0/∆ < ∼ 1, and they are vanishingly small in the nonresonant dot regime 0/∆ 1.

Theory of nonequilibrium noise in general multiterminal superconducting hybrid devices: Application to multiple Cooper pair resonances

“…In this sense, our results seem to be in qualitative agreement with Ref. [38], which deals with a three superconducting lead device, while also surpassing it for the following reasons.…”

“…In a setup where a single lead is biased, low voltage positive noise crossed correlations were predicted and ascribed to MARs [37]. In a setup consisting of a single quantum dot connected to three terminals, noise crossed correlations were also investigated using perturbative calculations [38] and quartets were shown to have a decreasing noise signal at low subgap voltages for a nonresonant dot, as opposed to the resonant case where a phase-sensitive noise was predicted. The study of out-of-equilibrium noise in multiterminal superconducting junctions in the coherent regime is particularly interesting, as there is still a need to quantify the evolution of current correlations between different terminals, as a function of the phase and the voltage biases.…”

Nonlocal supercurrent of quartets in a three-terminal Josephson junction

“…The nanowires were grown by a gold assisted MBE process, using the well-established vapor-liquid-solid growth technique. Growth was initiated on an un-patterned (100) InAs substrate, where both, single wires and the Y-shape intersections were formed [25]. Devices were fabricated on an oxidized P + -doped Si wafer (with 150nm thick SiO2), with superconducting contacts and local gates made by depositing 5nm/120nm Ti/Al.…”

Engineering the Floquet spectrum of superconducting multiterminal quantum dots

“…This is formally similar to the superconducting quantum point contact 68 relevant to break-junction experiments 69 . In our calculations of the current-current cross-correlations in superconducting-QD, the numerical method relies on recursive Green's functions in energy, combined to sparse matrices algorithms, and adapta-tive integration over the spectral parameter 22,28 . The numerical value of the cross-correlations converges towards the exact answer upon increasing the adjustable level of accuracy.…”

“…1), this can lead to nonperturbative characterization of the quartet 18,19,25 , multipair or phase-MAR 19,20,26 channels. At present time, separation of the dc-current 26 and the currentcurrent cross-correlations 28 into the different physical channels relies solely on the symmetries with respect to phase or voltage inversion 76 .…”