A Superconducting Diode

Motivation and Background

• In semiconductors, a p–n junction permits current in one direction but blocks it in the other—a diode effect.
• Achieving a similar unidirectional behaviour for supercurrent (zero-resistance current of Cooper pairs) is challenging, since superconductors naturally conduct without dissipation up to a symmetric critical current.

What Is the Superconducting Diode Effect?

A superconducting diode conducts dissipationless supercurrent up to a critical magnitude that depends on direction:

• Define the positive‐direction critical current as Ic⁺ and the negative‐direction as Ic⁻.
• If Ic⁺ ≠ Ic⁻, then for currents between Ic⁻ and Ic⁺ the device is superconducting one way but resistive the other—a true supercurrent rectifier
• In a Josephson junction (two superconductors separated by a weak link), you also get return‐current asymmetry: the retrapping currents Ir⁺ and Ir⁻ on a downward voltage sweep can differ, giving hysteretic diode behavior

Symmetry Requirements

Two symmetries must be broken for a zero‐voltage superconducting diode effect:

Inversion (𝑃) symmetry

• Without a built-in “left vs. right” asymmetry (as in a p–n junction), there is no preferred direction.
• Inversion can be broken by the crystal structure (non-centrosymmetric materials) or by interface/junction design.

Time-Reversal (𝑇) symmetry

• Onsager reciprocity enforces Ic⁺=Ic⁻ in a 𝑇-invariant system at zero voltage.
• Breaking 𝑇 requires either an applied magnetic field or intrinsic magnetic order.
• Thus a field‐free diode implies an internally 𝑇-broken superconductor

Microscopic Mechanism in a Uniform Superconductor

A particularly transparent picture emerges in a two‐dimensional, Rashba-coupled superconductor under an in-plane field:

Rashba spin–orbit coupling

• Rashba hamiltonian locks spin to momentum and splits the Fermi surface.

Zeeman field

• An in-plane magnetic field B breaks Time-Reversal (𝑇) and further shifts the two spin-split Fermi contours in opposite directions.

Finite-momentum Cooper pairing

• To minimize energy, Cooper pairs pick up a center-of-mass momentum 2q matching the Fermi-surface shift.
• In Ginzburg–Landau language this corresponds to adding a Lifshitz invariant iκ (ψ∗∇ψ−ψ ∇ψ∗) to the free energy, which skews the current–phase relation.

Shifted critical currents

• The supercurrent J(φ) vs. phase (φ) is displaced, so the maxima in the positive and negative directions differ (Ic⁺≠Ic⁻).
• Experimentally, this was seen in NiTe₂ Josephson junctions and matches finite-momentum pairing theory.

Anomalous Josephson– junction Diode

In a Josephson junction barrier with strong spin–orbit coupling and broken 𝑇, an anomalous phase shift φ₀ appears in the current-phase relation:

I(φ)  =  Ic  sin(φ+φ₀)

• Here φ₀≠0 (mod π) only if both inversion and 𝑇 are broken.
• Physically, Andreev bound states acquire a spin-dependent phase as they traverse the barrier, shifting the whole CPR.
• As a result, the forward and reverse critical currents differ, and the return currents Ir⁺,Ir⁻ in a hysteretic junction also become non-reciprocal.

Why It Matters

• Ultra-Low-Loss Logic & Power Routing: Rectify currents without heating—ideal for quantum processors and high-efficiency power grids.
• On-Chip Isolators & Circulators: Non-reciprocal elements without bulky magnets or lossy circulators.
• Quantum Computing Applications:

1. Qubit Readout Isolation: Superconducting qubits require delicate, directional routing of microwave signals to read out states. Embedding diode functionality directly into the qubit readout chain reduces insertion loss and thermal load, enhancing fidelity.
2. Directional Amplification: Non-reciprocal gain elements protect qubits from amplifier back-action. A superconducting diode–based amplifier could operate with zero added noise and minimal footprint.
3. Programmable Signal Flow: Field-trainable Josephson diodes offer memory of polarity (“training”), enabling reconfigurable signal-routing networks at milliKelvin temperatures without mechanical switches.

Superconducting diodes can serve as zero-resistance logic gates and memory bits that combine rectification with hysteresis. This paves the way for dissipationless superconducting computing, marrying ultra-high speed with minimal energy per operation.