Transverse Josephson Diode Effect (TJDE)

• TJDE is a phenomenon where asymmetric, field-free transverse supercurrents arise in multiterminal superconducting devices due to Rashba SOC and intrinsic altermagnetic symmetry breaking.
• The effect is enabled by a nonsinusoidal current–phase relation and engineered symmetry breaking, resulting in pronounced unidirectional, diode-like behavior with efficiencies exceeding 1000%.
• Tunability via Néel vector rotation and material parameter adjustments makes TJDE a promising platform for superconducting diodes, quantum logic elements, and sensitive magnetometry.

The Transverse Josephson Diode Effect (TJDE) refers to the nonreciprocal propagation of dissipationless supercurrents in a direction orthogonal to the applied Josephson phase bias in multiterminal superconducting devices, distinguished by an asymmetric dependence of the transverse critical current on current direction. This effect, enabled by engineered symmetry breaking and enhanced by the unique electronic structure of materials such as altermagnets with Rashba spin–orbit coupling, represents a robust, field-free route to realize highly efficient and tunable nonreciprocal transport in quantum devices (Sahoo et al., 17 Sep 2025).

1. Microscopic Mechanism in Altermagnets

TJDE in altermagnet-based devices fundamentally arises from the combined presence of Rashba spin–orbit coupling (SOC) and the intrinsic crystal symmetry of the altermagnet (AM):

• Rashba SOC in the central AM region locks electron spin and momentum, producing a momentum-dependent spin splitting. The Rashba SOC breaks inversion symmetry because it requires a noncentrosymmetric potential gradient.
• Altermagnetic Order and Symmetry: AMs exhibit zero net magnetization but possess opposite-spin sublattices that are related by rotational (rather than translational) operations. This leads to an intrinsic breaking of time-reversal symmetry (TRS) even without external magnetic fields.
• The joint breaking of inversion (by Rashba SOC) and time-reversal symmetry (by AM order) yields an electronic structure asymmetric under momentum reversal ($k \rightarrow -k$). This asymmetry directly leads to a nonsinusoidal and directional current–phase relation (CPR) in the transverse channel.

The asymmetry of the CPR is the microscopic seed for both the transverse anomalous Josephson effect (AJE)—a finite supercurrent at zero phase bias—and the TJDE, i.e., nonreciprocal (diode-like) supercurrents.

2. Four-Terminal Josephson Junction Architecture

The archetypal TJDE device is a four-terminal cross geometry, in which the AM+SOC region is coupled to four superconducting (SC) leads:

• Left and right terminals receive a phase bias $\pm\phi_s/2$; top and bottom terminals are held at zero phase.
• Applying a phase bias $\phi_s$ longitudinally between left and right drives conventional supercurrent along $x$ but, owing to the Rashba- and AM-induced momentum asymmetry, also generates a finite transverse supercurrent (along $y$).
• The transverse current flows into the unbiased top and bottom SC leads and depends on the longitudinal phase bias via an asymmetric, nonsinusoidal CPR.

The phase bias thus indirectly "pumps" transverse supercurrents—a phenomenon that requires both the Rashba SOC–driven lack of inversion symmetry and the AM-induced TRS breaking.

3. Diode Nonreciprocity and Anomalous Phase Shifts

TJDE is characterized by both strong diode-like nonreciprocal response and anomalous phase offsets:

• Nonreciprocal (Diode-Like) Response: The maximum transverse critical current for "forward" and "backward" directions are unequal; i.e., $J_{c}^{y,+} \neq |J_{c}^{y,-}|$.
• Anomalous Josephson Effect (AJE): A finite supercurrent exists even at zero applied phase difference, $J_y(\phi_s=0) \neq 0$, corresponding to a ground-state phase offset $\phi_0$ in the CPR. The general form is $J_y = J_{cy}\sin(\phi_s + \phi_0)$, with $\phi_0 \neq 0$ due to symmetry breaking.

The diode efficiency is quantified by the coefficient

$$\gamma_y = \frac{2(J_y^{\text{max}} + J_y^{\text{min}})}{J_y^{\text{max}} - J_y^{\text{min}}}$$

where $J_y^{\text{max}}, J_y^{\text{min}}$ are the positive and negative critical transverse currents, respectively. A finite $\gamma_y$ signals strong nonreciprocity; extraordinarily, $\gamma_y$ can exceed $1000\%$ for optimized parameters, indicating nearly perfect unidirectionality in transverse current flow.

4. Regimes of Efficiency and Unidirectionality

For certain combinations of Rashba SOC strength ($\alpha$) and altermagnetic exchange ($t_j$), the system can achieve:

• Strictly Unidirectional Transverse Current: Over some parameter regime, the transverse CPR is such that only one current polarity supports a finite critical current, while the opposite is suppressed (even possibly zero).
• Giant TJDE Efficiency: The asymmetry between forward and reverse transverse currents becomes extremely large; $\gamma_y \gg 100\%$ is readily accessible.

This behavior contrasts with typical longitudinal JDE, where efficiency is often limited to $< 100\%$ even in strongly noncentrosymmetric platforms.

5. Tunability via Néel Vector Rotation and Material Parameters

The magnitude and direction (sign) of both the TJDE and transverse AJE are highly tunable:

• Néel Vector Orientation: The Néel vector, which characterizes the antiferromagnetic order of the AM and lies in the $xy$-plane, can be rotated (angle $\varphi$ with respect to $x$-axis). Rotation modifies the effective SOC-driven momentum asymmetry:
  • For $\varphi = \pi/2$ or $3\pi/2$, symmetry is restored along $k_y$, leading to $\gamma_y = 0$.
  • For $\varphi = 0$ or $\pi$, symmetry is restored along $k_x$, suppressing longitudinal diode effects.
• This provides a highly efficient "knob" to modulate not only the magnitude and polarity of the TJDE but also the size and sign of the transverse anomalous phase offset.

Device and material engineering, including the choice or synthesis of altermagnetic compounds with strong Rashba SOC and the integration with high-transparency SC contacts, are crucial for reaching the optimal TJDE regime.

6. Implications for Superconducting Transport and Device Applications

TJDE in field-free altermagnetic–Rashba platforms supplies compelling advantages for superconducting electronics:

• Field-Free Operation: Nonreciprocal and anomalous supercurrents arise without reliance on external magnetic fields. This enhances device integrability and minimizes magnetic sensitivity in circuit environments.
• Multiterminal Logic: The geometry and tunability open prospects for multi-terminal superconducting logic elements, where transverse (not just longitudinal) supercurrent rectification can be exploited, e.g., superconducting diodes, switches, and nonvolatile memory.
• Highly Directional Current Routing: The potential for unidirectional, extremely high-efficiency ($\gamma_y > 1000\%$) transport supports applications in quantum information hardware that demand lossless, nonreciprocal routing of supercurrent in multiterminal layouts.
• Sensitive Magnetometry and Phase Control: The AJE and TJDE, with their sharp dependence on the Néel vector and SOC, could be used in field-sensing or phase-sensitive measurements in hybrid antiferromagnetic–superconducting nanostructures.

In summary, the transverse Josephson diode effect in altermagnet systems is underpinned by the interplay of Rashba SOC and crystal symmetry–broken time-reversal symmetry, enabling field-free, highly efficient, and tunable nonreciprocal superconducting transport in multiterminal devices (Sahoo et al., 17 Sep 2025). The robust, unidirectional transverse supercurrents and large diode coefficients mark these platforms as prime candidates for next-generation superconducting and quantum technologies.