Multiterminal Quantized Conductance in InSb Nanocrosses

Khan, Sabbir Ahmed; Stampfer, Lukas; Mutas, Timo; Kang, Jung-Hyun; Krogstrup, Peter; Jespersen, Thomas Sand

doi:10.48550/arxiv.2101.02529

Cited by 3 publications

(4 citation statements)

References 33 publications

(47 reference statements)

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“…The three recent experiments of the Grenoble 29 , Weizmann Institute 30 and Harvard 31 groups show all signs of compatibility with the theory of the quartets [14][15][16][17][18][19][20][21] , in addition to other experiments [32][33][34][35][36][37] on multiterminal Josephson junctions. The reason why some experiments report the quartets while others do not is maybe a complex matter of the materials and geometry.…”

Section: Introductionmentioning

confidence: 55%

Ultralong-distance quantum correlations in three-terminal Josephson junctions

Mélin

2021

Preprint

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In the paper, we address nonlocality and quantum correlations in three-terminal Josephson junctions, where the BCS superconductors S a , S b and S c are voltage-biased at (V a ,V b ,V c ) = (V, −V, 0) and V is a significant fraction of the gap. The constituting two-terminal S a -dot-S c and S c -dot-S b are connected at arbitrary distance R 0 on the grounded S c . The proposed interpretation of the numerical experiments relies on the interplay between the time-periodic Floquet-Josephson dynamics, Cooper pair splitting and the long-range Tomasch effect. We find cross-over between the "Floquet-Andreev quartets" (if R 0 ξ 0 is smaller than the superconducting coherence length), and the "ultralong-distance Floquet-Tomasch clusters of Cooper pairs" if R 0 l ϕ , where l ϕ ξ 0 is the mesoscopic coherence length of the BCS quasiparticles. Analytical theory is presented for the simplest cluster at voltage eV > ∆/2, i.e. the ultralong-distance Floquet-Tomasch octets, where ∆ is the superconducting gap. The range of the effect is conjectured to be the same as in the Tomasch experiment, i.e. the junctions can be remotely separated by the mesoscopic R 0 ≈ 30 µm which is orders of magnitude larger than the zero-energy BCS coherence length ξ 0 . Our results go beyond the paradigm of classical synchronization in the macroscopic Josephson circuits. The effect can be detected with dc-transport and zero-frequency quantum current-noise cross-correlation experiments, and it can be used for fundamental studies of superconducting quasiparticle quantum coherence in the circuits of quantum engineering.

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Section: Introductionmentioning

confidence: 55%

Ultralong-distance quantum correlations in three-terminal Josephson junctions

Mélin

2021

Preprint

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“…This yields the quartet current-phase relation I c,q sin ϕ q in the limit of low values of the contact transparencies. The three recent experiments of the Grenoble [30], Weizmann Institute [31], and Harvard [32] groups show all signs of compatibility with the theory of the quartets [14][15][16][17][18][19][20][21], in addition to other experiments [33][34][35][36][37][38][39] on multiterminal Josephson junctions. The reason why some experiments report the quartets while others do not is maybe a complex matter of the materials and geometry.…”

Section: Introductionmentioning

confidence: 57%

Ultralong-distance quantum correlations in three-terminal Josephson junctions

Mélin

2021

Phys. Rev. B

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In these studies, the distance between the contacts is limited by the zero-energy superconducting coherence length. Here, we demonstrate nonlocality and quantum correlations in voltage-biased three-terminal Josephson junctions over the ultralong distance that exceeds the superconducting coherence length by orders of magnitude. The effect relies on the interplay between the time-periodic Floquet-Josephson dynamics, Cooper pair splitting, and long-range coupling similar to the two-terminal Tomasch effect. We find crossover between the "Floquet-Andreev quartets" (if the spatial separation is smaller than the superconducting coherence length) and the "ultralong-distance Floquet-Tomasch clusters of Cooper pairs" if the separation exceeds the superconducting coherence length, possibly reaching the same 30 μm as in the Tomasch experiments. The effect can be detected with DC-transport and zero-frequency quantum current-noise cross-correlation experiments, and it can be used for fundamental studies of superconducting quasiparticle quantum coherence in the circuits of quantum engineering.

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“…The zero-flux limit of the predicted experimental signal with N = 2q + 1 generalizes the above Eqs. ( 38)- (39):…”

Section: Discussionmentioning

confidence: 99%

“…( 36)-( 37) and χ (3)(0) in Eqs. ( 38)- (39). Thus, χ (3) or χ (3)(0) with N = 3 superconducting leads cannot be used to probe the p = 3terminal dc-Josephson effect independently on the contribution of the p = 2-terminal Josephson effect, see the discussion in section II.…”

Section: Examples With N = 3 4 Superconducting Leadsmentioning

confidence: 99%

The dc-Josephson effect with more than four superconducting leads

Mélin

2021

Preprint

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By definition, the p-terminal dc-Josephson current is sensitive to the superconducting phase variables of p terminals. In the paper, we establish protocol for direct detection of the p-terminal dc-Josephson effect with p ≥ 3 in a device containing N superconducting leads S 1 , S 2 , ..., S N having the phase variables ϕ 1 , ϕ 2 , ..., ϕ N . The calculated signal χ (N) can be probed in microwave experiments, and it corresponds to the higher-order nonlocal inverse inductance obtained from differentiating the current I 1 through S 1 with respect to the remaining N − 2 independent phase differences ϕ 2 − ϕ N , ϕ 3 − ϕ N , ..., ϕ N−1 − ϕ N . We find that the values p ≤ N − 2 do not contribute to χ (N) , and that χ (N) = 0 implies evidence for the p = N − 1 or the p = N-terminal dc-Josephson currents. For N = 4 superconducting leads, we demonstrate that χ (4) = 0 implies evidence for the p = 3 or p = 4 dc-Josephson effect, irrespective of the p = 2-terminal dc-Josephson current. Thus, we provide a way to demonstrate the dc-Josephson effect with more than three terminals (i.e. with p ≥ 3) in a device containing more than four superconducting leads (i.e. with N ≥ 4). The predicted χ (4) is "yes or no" answer to the p ≥ 3 dc-Josephson effect, i.e. for N = 4, nonvanishingly small χ (4) = 0 implies the p = 3 or p = 4-terminal dc-Josephson effect and vanishingly small χ (4) = 0 implies absence of the p = 3 and p = 4-terminal dc-Josephson effect. The paper can be viewed as generalizing the recently considered ϕ-junctions in Andreev molecules to arbitrary number N of the superconducting leads, and it relies on basic properties of the dc-Josephson effect that are not directly related to nontrivial topology and Weyl point singularities.Voltage biasing the S 1 -S 2 -S 3 three-terminal Josephson junction 21,22 on figures 1e and 1f at the voltage differences V 1 − V 2 and V 3 − V 2 is a possibility to reveal [31][32][33] dCAR and the quartets as emergence of the V 1 + V 3 = 0 dc-Josephson resonance line, if one of the elements of the differential conductance matrix is plotted in the (V 1 ,V 3 ) voltage plane while the "central" S 2 is grounded at the reference voltage V 2 = 0. Other dc-Josephson resonance lines were predicted 21,22 and observed [31][32][33] , such as V 1 = V 3 due to dEC. Other experiments [34][35][36][37][38] did not report the quartet dc-Josephson anomaly, which is maybe a matter of the materials and configurations of the devices. In addition, the recent Ref. 39 reports progress in the fabrication of four-terminal devices.Considering more generally p 1 Cooper pairs from S 1 and p 3 from S 3 yields the energy E initial = 2p 1 V 1 + 2p 3 V 3 of the "initial state", and E f inal = 2 (p 1 + p 3 )V 2 for the final state, with E f inal ≡ 0 because V 2 = 0 for the grounded S 2 . Energy conservation E initial = E f inal implies the dc-Josephson resonance

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Multiterminal Quantized Conductance in InSb Nanocrosses

Cited by 3 publications

References 33 publications

Ultralong-distance quantum correlations in three-terminal Josephson junctions

Ultralong-distance quantum correlations in three-terminal Josephson junctions

Ultralong-distance quantum correlations in three-terminal Josephson junctions

The dc-Josephson effect with more than four superconducting leads

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