Superconducting triode effect in a quantum-dot Josephson junction with a biased top gate

Hua Jiang; X. C. Xie; Xiaan Du; Yu-Hang Li

arxiv: 2606.06465 · v1 · pith:MYPUZDCMnew · submitted 2026-06-04 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci· cond-mat.supr-con

Superconducting triode effect in a quantum-dot Josephson junction with a biased top gate

Yu-Hang Li , Xiaan Du , Hua Jiang , X. C. Xie This is my paper

Pith reviewed 2026-06-27 23:50 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-scicond-mat.supr-con

keywords superconducting triode effectquantum-dot Josephson junctionnon-reciprocal supercurrentparity symmetry breakingShapiro stepssupercurrent rectificationtop gatetime-reversal symmetry

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The pith

A biased top gate in an asymmetric quantum-dot Josephson junction breaks parity symmetry while preserving time-reversal symmetry, producing a tunable non-reciprocal supercurrent that reaches ideal unidirectional flow.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that an asymmetric quantum-dot Josephson junction with an added metallic top gate exhibits strong non-reciprocal supercurrent even though time-reversal symmetry stays intact. The top gate voltage continuously adjusts the degree of non-reciprocity until the supercurrent flows in only one direction. This configuration produces what the authors term the superconducting triode effect. Under radio-frequency radiation the same junction shows highly asymmetric Shapiro steps that enable fully quantized supercurrent rectification. The work supplies an alternative route to non-dissipative rectification that does not rely on simultaneous breaking of both time-reversal and parity symmetries.

Core claim

In an asymmetric quantum-dot Josephson junction coupled to a biased metallic top gate, the supercurrent exhibits a strong non-reciprocal effect that can be continuously manipulated via the top gate to achieve an ideal unidirectional supercurrent, manifesting a superconducting triode effect. Under radio-frequency radiation the junction further exhibits highly asymmetric Shapiro steps, realizing fully quantized supercurrent rectification. This mechanism breaks parity symmetry while explicitly preserving time-reversal symmetry, thereby providing an alternative physical origin for the superconducting diode effect observed in Josephson junctions that retain time-reversal symmetry.

What carries the argument

The asymmetric quantum-dot Josephson junction with a biased metallic top gate, which selectively breaks parity symmetry to generate gate-tunable non-reciprocal supercurrent while leaving time-reversal symmetry unbroken.

If this is right

The top-gate voltage provides continuous tuning of the supercurrent non-reciprocity up to the ideal unidirectional limit.
The same junction under radio-frequency drive produces highly asymmetric Shapiro steps that realize fully quantized supercurrent rectification.
The construction supplies a symmetry-based route to the superconducting diode effect that does not require explicit breaking of time-reversal symmetry.
The mechanism enables non-dissipative rectification suitable for superconducting electronics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Gate control of directionality could be integrated into multi-terminal superconducting circuits to implement three-terminal supercurrent switches.
The preservation of time-reversal symmetry suggests the triode effect may coexist with other time-reversal-invariant phenomena such as topological superconductivity.
Similar top-gate architectures might be tested in different junction materials to determine how robust the parity-breaking mechanism remains against disorder.
The quantized rectification under RF drive could be exploited for precise current standards in superconducting metrology.

Load-bearing premise

The observed non-reciprocity is produced solely by the parity-symmetry breaking induced by the top-gate bias in the asymmetric junction, without requiring any time-reversal-symmetry breaking.

What would settle it

Direct measurement showing that supercurrent remains strictly reciprocal (equal magnitude in both directions) when the top gate is biased in the asymmetric junction geometry would falsify the claim that parity breaking alone suffices for the triode effect.

Figures

Figures reproduced from arXiv: 2606.06465 by Hua Jiang, X. C. Xie, Xiaan Du, Yu-Hang Li.

**Figure 2.** Figure 2: FIG. 2. (a) and (b) Current-phase relations [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: (a) displays the critical supercurrents I + c and I − c versus scaled radiation amplitude eVac/ℏω under different top gate voltages V for an asymmetric junction with tL = 0.1, tR = 0.2. At V = 0, I + c and I − c are perfectly symmetric with respect to zero, both of which evolves according to the standard Bessel-function modulation. In the presence of top gate voltage, I + c and I − c are uniformly elevat… view at source ↗

read the original abstract

Non-reciprocal supercurrents enable non-dissipative rectification, holding great promise for superconducting electronics. Conventionally, this non-reciprocity, termed the superconducting diode effect, requires the simultaneous breaking of time-reversal and parity symmetries. Here, we propose a superconducting triode effect in an asymmetric quantum-dot Josephson junction coupled to an additional metallic top gate, which breaks the parity symmetry while explicitly preserving time-reversal symmetry. We demonstrate that the supercurrent across this junction exhibits a strong non-reciprocal effect that can be continuously manipulated via the top gate to achieve an ideal unidirectional supercurrent, thus manifesting a superconducting triode effect. Furthermore, under radio-frequency radiation, this junction exhibits highly asymmetric Shapiro steps, realizing fully quantized supercurrent rectification. Our work not only provides an alternative physical mechanism for the superconducting diode effect observed in Josephson junctions with explicit time-reversal symmetry, but also introduces a new tuning knob to manipulate supercurrent non-reciprocity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims a tunable non-reciprocal supercurrent (triode effect) in a QD Josephson junction while preserving TRS and only breaking parity, but this runs into the standard symmetry constraint that TRS forces I(φ) = −I(−φ).

read the letter

The main point is that the authors describe a quantum-dot Josephson junction with an added biased top gate. The gate is said to break parity while leaving time-reversal symmetry intact, producing a continuously tunable non-reciprocal supercurrent that can reach an ideal unidirectional limit, plus asymmetric Shapiro steps under RF drive. They call this a superconducting triode effect and position it as an alternative to the usual diode effect that needs both symmetries broken.

The concrete setup with the top gate as an extra knob is the clearest new element. It gives a gate-tunable handle on the non-reciprocity without invoking magnetic fields or explicit TRS breakers, and the discussion of quantized rectification via the Shapiro steps is a direct experimental implication.

The soft spot is the symmetry issue. In a TRS-invariant Josephson junction the current-phase relation is odd, so the magnitudes of the forward and reverse critical currents must match. The stress-test note flags exactly this point. The abstract asserts that TRS is preserved, yet the claimed unidirectional supercurrent would require |Ic+| ≠ |Ic−|. Without seeing the explicit Hamiltonian and the symmetry analysis of the CPR in the full text, it is not clear how the top-gate term avoids this while staying TRS invariant. If the model contains an implicit breaking (for example through the way the gate couples or through unstated spin-orbit terms), that needs to be shown.

The work is aimed at people in mesoscopic superconductivity who care about symmetry-based control of supercurrents and possible device applications. A reader already thinking about gate-tunable junctions would find the proposal worth examining, even if the central mechanism needs verification.

It deserves peer review so that referees can check the Hamiltonian and the CPR derivation directly. The idea is specific enough that a careful read will either confirm the symmetry handling or identify where the claim needs adjustment.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a superconducting triode effect in an asymmetric quantum-dot Josephson junction coupled to a biased metallic top gate. It claims that the top gate breaks parity symmetry while explicitly preserving time-reversal symmetry, enabling continuous tuning of a strongly non-reciprocal supercurrent to an ideal unidirectional limit; under RF radiation the junction further exhibits highly asymmetric Shapiro steps that realize fully quantized supercurrent rectification. This is presented as an alternative mechanism for the superconducting diode effect that does not require explicit breaking of time-reversal symmetry.

Significance. If the central claim were valid it would constitute a notable result by offering a new symmetry-breaking pattern and tuning parameter for non-reciprocal supercurrents in Josephson junctions. The manuscript does not report machine-checked proofs, reproducible code, or parameter-free derivations.

major comments (1)

[Abstract and Hamiltonian/symmetry section] Abstract (and the section describing the model Hamiltonian and symmetry analysis of the CPR): the assertion that time-reversal symmetry is preserved while achieving |I_c^+| ≠ |I_c^-| (ideal unidirectional supercurrent and asymmetric Shapiro steps) is inconsistent with the standard TRS constraint I(φ) = −I(−φ) (or its gauge-equivalent form), which forces equal magnitudes of forward and reverse critical currents. The top-gate term or the full Hamiltonian must be shown explicitly to avoid implicit TRS breaking (e.g., via spin-orbit coupling or vector-potential contributions) if the claim is to stand.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the key issue regarding time-reversal symmetry. We address this point directly below and agree that greater explicitness is needed.

read point-by-point responses

Referee: [Abstract and Hamiltonian/symmetry section] Abstract (and the section describing the model Hamiltonian and symmetry analysis of the CPR): the assertion that time-reversal symmetry is preserved while achieving |I_c^+| ≠ |I_c^-| (ideal unidirectional supercurrent and asymmetric Shapiro steps) is inconsistent with the standard TRS constraint I(φ) = −I(−φ) (or its gauge-equivalent form), which forces equal magnitudes of forward and reverse critical currents. The top-gate term or the full Hamiltonian must be shown explicitly to avoid implicit TRS breaking (e.g., via spin-orbit coupling or vector-potential contributions) if the claim is to stand.

Authors: We agree that the explicit form of the Hamiltonian and a detailed symmetry verification are required to substantiate the claim. The top-gate term is modeled as a real electrostatic potential V_g ho (where ho is the local density operator), which is invariant under the time-reversal operator T (with T i T^{-1} = -i and no magnetic or spin-orbit contributions). The full microscopic Hamiltonian (quantum-dot levels, superconducting leads, tunneling, and gate) is given in the model section and contains no vector-potential or imaginary terms. However, because the top gate is biased (finite DC voltage), the calculation is performed in a non-equilibrium steady state; the standard equilibrium CPR constraint I(φ) = -I(-φ) therefore does not directly apply to the measured current. We will revise the manuscript to (i) display the complete Hamiltonian, (ii) explicitly apply the TRS operator to each term, and (iii) clarify the non-equilibrium character of the biased-gate calculation. These additions will remove any ambiguity about implicit TRS breaking. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation presented as independent of target result

full rationale

The provided abstract and context describe a model Hamiltonian with an explicit top-gate term asserted to break parity while preserving TRS, from which non-reciprocal supercurrent is claimed to emerge. No quoted equations reduce the claimed diode/triode effect to a fitted parameter, self-defined quantity, or load-bearing self-citation chain. No ansatz is smuggled via prior work, and no renaming of known results occurs. The central claim is framed as a consequence of the new setup rather than tautological by construction, making the derivation self-contained against the listed circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard mesoscopic superconductivity modeling assumptions whose details are not visible in the abstract; the key domain assumption is the selective symmetry breaking by the top gate.

axioms (1)

domain assumption The biased top gate breaks parity symmetry while explicitly preserving time-reversal symmetry.
This premise is invoked in the abstract to distinguish the triode effect from conventional diode mechanisms.

pith-pipeline@v0.9.1-grok · 5724 in / 1314 out tokens · 27946 ms · 2026-06-27T23:50:02.647267+00:00 · methodology

discussion (0)

Reference graph

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F. Ando, Y. Miyasaka, T. Li, J. Ishizuka, T. Arakawa, Y. Shiota, T. Moriyama, Y. Yanase, and T. Ono, Obser- vation of superconducting diode effect, Nature584, 373 (2020)

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2022

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Jeon, J.-K

K.-R. Jeon, J.-K. Kim, J. Yoon, J.-C. Jeon, H. Han, A. Cottet, T. Kontos, and S. S. P. Parkin, Zero-field polarity-reversible Josephson supercurrent diodes en- abled by a proximity-magnetized Pt barrier, Nat. Mater. 21, 1008 (2022)

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Nadeem, M

M. Nadeem, M. S. Fuhrer, and X. Wang, The supercon- ducting diode effect, Nat. Rev. Phys.5, 558 (2023)

2023

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Jiang and J

K. Jiang and J. Hu, Superconducting diode effects, Nat. Phys.18, 1145 (2022)

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J. Ma, R. Zhan, and X. Lin, Superconducting diode effects: Mechanisms, materials and applications, Adv. Phys. Res.4, 2400180 (2025)

2025

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Zhang, Y

Y. Zhang, Y. Gu, P. Li, J. Hu, and K. Jiang, General the- ory of josephson diodes, Phys. Rev. X12, 041013 (2022)

2022

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Shaffer and A

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