🔬 mesoscale physics

Josephson-Phase Reversal of Non-Bloch Andreev Propagation

This paper demonstrates that in a spin-orbit-coupled planar Josephson junction, tuning the Josephson phase can reverse the non-Bloch propagation of low-energy Andreev bands and switch their boundary accumulation by reshaping the band's composition to create a phase-controlled loss imbalance between counterpropagating modes.

Original authors: X. Z. Zhang, Hechen Ren

Published 2026-09-01

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CC BY 4.0

Original authors: X. Z. Zhang, Hechen Ren

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quantum world, energy levels are not always rigid; they can be shaped, stretched, and even made to flow in unexpected directions. For decades, physicists have known that when a system loses energy to its surroundings—a process called dissipation—it does more than just fade away. It can fundamentally alter how waves travel, sometimes forcing them to pile up at one edge of a material while leaving the other side empty. This phenomenon, known as the non-Hermitian skin effect, turns the usual rules of wave propagation on their head. In a typical setup, the direction of this pile-up is fixed by the physical structure of the device or the specific way it loses energy. Once built, the direction is set in stone, determined by the materials and contacts that cannot be easily changed. This creates a significant hurdle for engineers who wish to control these exotic states in real-world devices, as they cannot simply flip a switch to reverse the flow without rebuilding the entire system.

A team of researchers has now demonstrated a way to overcome this rigidity using a standard superconducting device. They show that by simply adjusting the phase difference between two superconductors, they can reverse the direction in which quantum waves accumulate, all without touching the device's physical structure or changing the way it loses energy. The experiment takes place in a planar Josephson junction, a thin strip of material sandwiched between two superconducting banks. This strip contains a special type of coupling that links the motion of electrons to their spin, a property that acts like a tiny internal compass. Crucially, the device is connected to a fixed reservoir that drains energy from the system in a specific way, acting as a one-way drain for certain types of quantum states. In previous setups, this fixed drain would always push the waves toward one specific end of the junction.

The researchers found that by changing only the phase difference between the two superconductors, they could reshape the internal composition of the waves traveling through the strip. These waves, known as Andreev states, are made of a mixture of electrons and holes, and their behavior depends heavily on their spin orientation. By tuning the phase, the scientists altered the balance of this mixture, effectively changing how the waves interacted with the fixed energy drain. The result was a complete reversal of the decay direction. When the phase was set to one value, the waves lost energy faster as they moved to the right, causing them to pile up at the left end. When the phase was shifted to another value, the loss dynamics flipped: the waves now lost energy faster moving to the left, causing them to accumulate at the right end. This switch happened smoothly and continuously, driven entirely by the phase adjustment while the physical drain remained exactly the same.

The mechanism behind this reversal relies on a delicate interference between different energy levels within the device. As the waves begin to move, they borrow characteristics from other available quantum states. The fixed reservoir interacts with these borrowed characteristics in a way that depends on the direction of travel. By tuning the phase, the researchers changed the interference pattern among these states, effectively canceling out the preference for one direction and then building a preference for the opposite. This process did not involve closing an energy gap or switching to a different type of wave; the same band of energy simply changed its behavior. The team confirmed this through detailed simulations, showing that the accumulation point could be moved from one end of the junction to the other by sweeping the phase across a specific range. At a critical phase value, the accumulation became neutral, with the waves spreading evenly, before flipping to the opposite side.

This discovery offers a new way to control non-Hermitian transport in solid-state platforms. Instead of engineering complex, asymmetric structures to direct the flow of energy, scientists can now use a coherent control parameter—the superconducting phase—to reconfigure the system in place. The study shows that the direction of dissipation is not an immutable property of the environment but a dynamic response that depends on the state of the system itself. By reshaping the wave function, the fixed environment can be made to act in opposite directions. This provides a practical route to creating reconfigurable quantum devices where the flow of information or energy can be switched on demand, bridging the gap between coherent quantum control and the management of dissipative effects in established materials.

Technical Summary: Josephson-Phase Reversal of Non-Bloch Andreev Propagation

Problem Statement
Non-Hermitian physics demonstrates that dissipation can fundamentally reshape quantum spectra, topology, and wave propagation, notably through the non-Hermitian skin effect where bulk modes accumulate exponentially at boundaries. While Non-Bloch band theory explains this via complex momenta selected by boundary conditions, controlling this response in situ in solid-state devices remains a significant challenge. In conventional systems, loss channels are fixed by material properties, interfaces, and contacts, making them difficult to tune independently of the coherent Hamiltonian. The central problem addressed is whether the direction of non-Bloch spatial accumulation can be reversed without re-engineering the dissipative structure (the reservoir) or relying on a Hermitian gap closing.

Methodology
The authors propose a theoretical model of a spin–orbit-coupled planar Josephson junction situated between two superconducting banks with a phase difference $\phi$ . The system includes a fixed, local, spin-selective reservoir coupled to the weak link. The dynamics are described by a retarded effective Bogoliubov–de Gennes (BdG) Hamiltonian:
$H_{\text{eff}}(k, \phi) = H_{\text{BdG}}(k, \phi) - i f_{\text{res}}(y) [\Gamma_0 \tau_0 + \gamma \mathbf{m} \cdot \boldsymbol{\sigma} \tau_z]$
where $\Gamma_0$ and $\gamma$ represent scalar and spin-selective decay parameters, respectively, and $\mathbf{m}$ is a fixed spin axis.

The study tracks a specific low-energy positive-energy Andreev band ( $A$ ) by wave-function overlap rather than simple energy ordering to ensure continuity. The analysis employs two primary theoretical frameworks:

Weak-Loss Perturbation Theory: To leading order in the decay strength, the spatial exponent $\kappa_A$ (determining accumulation direction) is derived as a function of the reservoir's spin-selective weight and the group velocity of counterpropagating states.
Generalized Brillouin Zone (GBZ) Analysis: Under open boundary conditions, the system is solved for complex momenta to determine the exact spatial profiles and accumulation directions.

Key Contributions and Mechanism
The paper establishes that the Josephson phase $\phi$ , a purely Hermitian control parameter, can reverse the direction of non-Bloch propagation without altering the reservoir. The mechanism relies on the phase reshaping the spin and electron–hole composition of the Andreev band.

Interference-Driven Reversal: The directional decay is governed by the coefficient $o_1$ , which measures the change in spin-selective reservoir weight as the state begins to propagate. This coefficient arises from the interference between the motion vertex ( $V_x$ ) and the loss operator ( $O_{\text{loss}}$ ) across virtual BdG levels.
Cancellation of Contributions: The total $o_1$ is a coherent sum of contributions from the electron–hole conjugate level ( $\bar{A}$ ) and all other remaining BdG levels. The paper demonstrates that as $\phi$ is swept, the contributions from these levels interfere destructively. At a critical phase $\phi^\star$ , $o_1$ passes through zero, reversing the sign of the spatial exponent $\kappa_A$ .
Distinction from Gap Closing: Crucially, this reversal occurs while the energy isolation from the next positive-energy band ( $\Delta_{\text{iso}}$ ) and the electron–hole separation ( $\Delta_{\text{ph}}$ ) remain finite. Thus, the reversal is driven by multilevel interference rather than a topological phase transition or gap closing.

Results

Phase-Controlled Accumulation: Numerical simulations of an open finite chain show that sweeping $\phi$ transfers the boundary accumulation of the tracked Andreev band from one end of the junction to the other. For $\phi < \phi^\star$ , the band accumulates at the right; for $\phi > \phi^\star$ , it accumulates at the left.
Momentum and Energy Selectivity: The reversal phase $\phi^\star(k)$ depends on momentum. Consequently, at a fixed phase, different momentum sectors (and thus different energy windows within the band) can exhibit opposite propagation biases.
Robustness: The effect persists under fixed reservoir parameters and weak probes, with the accumulation direction determined by the ratio of end-to-end transmission weights, which flips sign as the phase crosses $\phi^\star$ .

Significance
The paper claims to provide an in situ route to reconfigurable non-Hermitian transport in established solid-state platforms. By demonstrating that a purely Hermitian parameter (the Josephson phase) can reverse a dissipative spatial response, the work bridges coherent quantum-phase control and non-Bloch transport. It suggests that reservoir-induced propagation directions need not be fixed by the environment but can be dynamically reconfigured by reshaping the wave function's composition. This extends the functional role of the Josephson phase beyond controlling Andreev spectra and supercurrents to actively controlling the direction and energy window of dissipative quasiparticle propagation.

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