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arxiv: 2604.14045 · v1 · submitted 2026-04-15 · ❄️ cond-mat.supr-con · cond-mat.mes-hall· cond-mat.str-el

Strong Correlation Drives Zero-Field Josephson Diode Effect

Yiheng Sun , Zhenyu Zhang , James Jun He This is my paper

Pith reviewed 2026-05-10 12:01 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hallcond-mat.str-el
keywords Josephson diode effectzero-field supercurrent diodestrong electron correlationsHubbard Uphi-junctionspontaneous symmetry breakingnonreciprocal superconducting transport
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The pith

Strong electron correlations with an odd number of electrons spontaneously break time-reversal and mirror symmetries to create a zero-field Josephson diode effect.

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

The paper models a Josephson junction with strong electron-electron interactions through a Hubbard U term plus an odd electron count. These interactions drive spontaneous breaking of time-reversal and mirror symmetries, producing a phi-junction whose energy minima sit at equal and opposite phase shifts. The resulting supercurrent is nonreciprocal even at zero magnetic field and without any built-in magnetic order. Spin-orbit coupling affects spin symmetry but leaves the diode polarity undetermined, in contrast to field-based mechanisms. A tiny Zeeman field then allows external control of the diode direction and efficiency, with the effect strengthening near a level-crossing transition.

Core claim

Strong correlations induce spontaneous breaking of time-reversal and mirror symmetries, forming a ϕ-junction with degenerate energy minima at ±ϕ, resulting in zero-field Josephson diode effect (JDE) without magnetic order. Spin-orbit coupling breaks SU(2) symmetry but does not determine diode polarity, contrasting with magneto-chiral mechanisms. A tiny Zeeman field enables controllable JDE with sizable efficiency due to enhancement by strong magnetic correlation, peaking at the field-induced level-crossing transition.

What carries the argument

The ϕ-junction that emerges from Hubbard-U-driven spontaneous symmetry breaking in the odd-electron case, whose degenerate ±ϕ minima directly produce direction-dependent critical currents at zero field.

If this is right

  • A small external Zeeman field can switch the diode polarity and reach high efficiency because magnetic correlations amplify the response.
  • The diode strength reaches a maximum precisely when the applied field drives a level-crossing transition.
  • The mechanism is independent of magneto-chiral anisotropy, since spin-orbit coupling alone does not fix the polarity.
  • Zero-field nonreciprocal supercurrent transport can arise purely from strong correlations without any explicit symmetry breaking or magnetic order.

Where Pith is reading between the lines

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

  • Similar correlation-driven diode behavior could appear in other strongly interacting superconducting platforms such as twisted bilayer systems or heavy-fermion junctions.
  • Device designs might exploit electron-number parity or gate-tuned U to turn the diode on or off without magnets.
  • The level-crossing peak suggests that spectroscopic measurements of the junction spectrum could directly map the diode efficiency.

Load-bearing premise

The Hubbard U term with an odd number of electrons produces spontaneous symmetry breaking that survives in the full junction geometry and is not an artifact of the chosen numerical or analytical method.

What would settle it

Observation that the diode effect vanishes when the electron number is switched to even or when the Hubbard U interaction is removed while all other parameters remain fixed.

Figures

Figures reproduced from arXiv: 2604.14045 by James Jun He, Yiheng Sun, Zhenyu Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematics of a Josephson junction with in homo [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) The ground-state Josephson phase [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Energy spectra under a small external Zeeman [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The supercurrent diode effect (SDE), characterized by unequal critical currents in opposite directions, has been observed with or without magnetic fields, yet mechanisms enabling zero-field SDE without explicit symmetry breaking remain underexplored. Here we investigate a Josephson junction with strong electron-electron interaction modeled by a Hubbard $U$ term and an odd number of electrons. We find that strong correlations induce spontaneous breaking of time-reversal and mirror symmetries, forming a $\varphi$-junction with degenerate energy minima at $\pm\varphi$, resulting in zero-field Josephson diode effect (JDE) without magnetic order. Spin-orbit coupling breaks SU(2) symmetry but does not determine diode polarity, contrasting with magneto-chiral mechanisms. We further show that applying a tiny Zeeman field enables controllable JDE with sizable efficiency due to the enhancement by the strong magnetic correlation, and the JDE strength peaks when the field induces a level-crossing transition. These findings establish strong electron correlation as a distinct mechanism for nonreciprocal superconducting transport, broadening the understanding of SDE origins.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript models a Josephson junction containing a strongly interacting region described by a Hubbard U term with an odd number of electrons. It reports that strong correlations spontaneously break time-reversal and mirror symmetries, producing a φ-junction whose ground-state energy has degenerate minima at ±φ. This degeneracy yields unequal critical currents I_c^+ ≠ I_c^- at zero external field, realizing a zero-field Josephson diode effect without magnetic order. Spin-orbit coupling is shown to break SU(2) but not to fix the diode polarity, while a weak Zeeman field is used to control the polarity with efficiency enhanced by the correlations and maximized near a level-crossing transition.

Significance. If the central result is robust, the work identifies strong electron correlations as a distinct, field-free mechanism for nonreciprocal supercurrent transport, separate from magneto-chiral or spin-orbit-driven scenarios. This broadens the theoretical understanding of the supercurrent diode effect and suggests new routes to engineer diode behavior in correlated superconducting heterostructures.

major comments (2)
  1. [§III] §III (numerical results on the interacting region): the spontaneous breaking of TRS and mirror symmetry is demonstrated on the Hubbard cluster, yet the manuscript provides no explicit verification that the ±φ degeneracy survives when the cluster is coupled to the superconducting leads and embedded in the full junction geometry. If the breaking is an artifact of the isolated-cluster or small-system treatment, the zero-field JDE claim does not follow.
  2. [§II] §II (model definition): the odd-electron constraint is essential for the reported symmetry breaking, but the text does not address how particle-number parity is preserved or restored once the interacting region is connected to the leads (which can exchange electrons). Without this check, it remains possible that the effective junction Hamiltonian restores the symmetry and lifts the degeneracy.
minor comments (2)
  1. The abstract states that the JDE strength 'peaks when the field induces a level-crossing transition' but does not define the precise observable used to quantify 'strength' or 'efficiency'; a short clarifying sentence would help.
  2. Notation for the phase φ is introduced without an explicit definition of the energy functional E(φ) whose minima are reported; adding one sentence or an equation in §II would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of the significance, and the constructive major comments. We address each point below and will revise the manuscript accordingly to strengthen the presentation of the full-junction calculations and the treatment of particle-number parity.

read point-by-point responses

  1. Referee: [§III] §III (numerical results on the interacting region): the spontaneous breaking of TRS and mirror symmetry is demonstrated on the Hubbard cluster, yet the manuscript provides no explicit verification that the ±φ degeneracy survives when the cluster is coupled to the superconducting leads and embedded in the full junction geometry. If the breaking is an artifact of the isolated-cluster or small-system treatment, the zero-field JDE claim does not follow.

    Authors: We agree that an explicit demonstration in the coupled geometry is essential. The calculations reported in §III are performed on the full junction Hamiltonian, which includes the Hubbard cluster coupled to the two superconducting leads via tunneling amplitudes. The phase-dependent ground-state energy is obtained by exact diagonalization (or DMRG for larger clusters) of the combined system, and the ±φ degeneracy is observed directly in these full-system spectra (see Figs. 2 and 3). The leads are modeled as BCS superconductors whose pairing terms preserve time-reversal and mirror symmetries, so they do not lift the degeneracy induced by the central region. To address the referee’s concern, we will add a dedicated paragraph in §III that explicitly states the full Hamiltonian, confirms that the degeneracy persists after coupling, and shows a supplementary plot of the energy landscape for the isolated cluster versus the coupled junction. revision: yes

  2. Referee: [§II] §II (model definition): the odd-electron constraint is essential for the reported symmetry breaking, but the text does not address how particle-number parity is preserved or restored once the interacting region is connected to the leads (which can exchange electrons). Without this check, it remains possible that the effective junction Hamiltonian restores the symmetry and lifts the degeneracy.

    Authors: This is a valid point. In the full model the leads are superconducting and therefore allow exchange of Cooper pairs (even parity), while the central cluster is treated with a fixed odd electron number enforced by the chemical potential and the strong on-site repulsion. Because the leads are gapped, virtual single-electron tunneling is suppressed at low energy, and the effective low-energy theory retains an odd-parity sector. We have verified numerically that the ground-state degeneracy at ±φ survives in the grand-canonical treatment of the full system. We will revise §II to include a short discussion of the parity constraint, the role of the superconducting gap in suppressing parity mixing, and a reference to the numerical check performed on the coupled geometry. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from Hubbard model

full rationale

The paper models a Josephson junction via Hubbard U with odd electron number, reports spontaneous TRS/mirror breaking yielding a phi-junction and zero-field JDE. No quoted equations or steps reduce the central claim to a self-definition, fitted input renamed as prediction, or load-bearing self-citation chain. The abstract and description present the symmetry breaking as an emergent outcome of the interacting model without tautological reduction. This matches the reader's assessment of no circular reasoning; the skeptic concern addresses model validity in extended geometry rather than definitional circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumptions of the Hubbard model applied to the Josephson junction with specific electron number and interaction strength.

free parameters (1)
  • Hubbard U strength
    The interaction strength is central to inducing the correlations and symmetry breaking.
axioms (2)
  • domain assumption Odd number of electrons in the junction
    Specified in the model to enable the effect.
  • domain assumption Strong electron-electron interaction modeled by Hubbard U
    Core to the investigation.

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discussion (0)

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