🔬 mesoscale physics

Same-spin Andreev reflections in the quantum Hall regime: the role of loss

This study demonstrates that chiral Andreev edge states at quantum Hall-superconductor interfaces exhibit robust same-spin Andreev reflections enabled by particle loss, revealing the critical role of non-Hermiticity in the formation of topological superconductors.

Original authors: Chun-Chia Chen, Jordan T. McCourt, John Chiles, Lingfei Zhao, Kenji Watanabe, Takashi Taniguchi, François Amet, Antonio L. R. Manesco, Harold U. Baranger, Gleb Finkelstein

Published 2026-07-30

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CC BY 4.0

Original authors: Chun-Chia Chen, Jordan T. McCourt, John Chiles, Lingfei Zhao, Kenji Watanabe, Takashi Taniguchi, François Amet, Antonio L. R. Manesco, Harold U. Baranger, Gleb Finkelstein

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

Imagine a world where electricity doesn't just flow like water in a pipe, but behaves more like a chaotic dance of tiny, invisible dancers. In the strange realm of quantum physics, specifically when we look at materials under powerful magnetic fields, electrons get organized into neat, one-way lanes called "edge states." Think of these as a highway where cars (electrons) can only drive forward, never backward, and they are sorted by their "spin"—a quirky internal property that acts like a tiny compass needle pointing either up or down. Usually, these lanes are strictly segregated: "Up-spin" cars stay in the up-lane, and "Down-spin" cars stay in the down-lane.

Now, imagine bringing a superconductor—a material that conducts electricity with zero resistance—right up against this highway. When an electron from the highway hits the superconductor, something magical usually happens called "Andreev reflection." The electron gets turned around, but it doesn't just bounce back as an electron; it transforms into a "hole" (a missing electron, acting like a positive charge) and flips its spin to the opposite lane. It's like a car hitting a magical wall, turning into a bicycle, and instantly switching to the opposite side of the road. Scientists have been hunting for these exotic states because they might hold the key to building super-powerful, unbreakable quantum computers. But there's a catch: if the highway is already full of only one type of car (say, only "Up-spin" electrons), the rules of physics say this magical transformation shouldn't happen at all. Or so we thought.

This paper takes a deep dive into that very question: What happens when you try to force this spin-flipping magic to happen on a highway that only allows one type of car? The researchers set up a delicate experiment using a special type of graphene sandwiched between a superconductor and magnetic fields. They created a setup where they could inject only "Up-spin" electrons and then carefully watch what came out the other side. They found that even when the highway was strictly "Up-spin only," they still saw "Up-spin" holes appearing downstream. This was a surprise because, according to the strict rules of a perfect, lossless system, this should be impossible.

The team discovered that the secret ingredient allowing this "impossible" reflection is loss. In their system, the superconductor isn't a perfect mirror; it's a bit leaky. Some of the electrons get absorbed or "lost" into the superconductor (perhaps getting caught in tiny whirlpools called vortices). The authors explain that this loss breaks the strict rules that usually forbid the spin-flip. It's as if the magical wall isn't just a wall anymore; it's a wall with a few holes in it. Because some particles disappear into the wall, the universe doesn't need to balance the books perfectly, allowing an electron to bounce back as a hole in the same lane without breaking the laws of physics.

The researchers didn't just see this happen once; they gathered a massive amount of data by sweeping magnetic fields and watching how the signals fluctuated. They found that the probability of these reflections follows a very specific, predictable pattern (an exponential curve) that can be explained by a mathematical tool called Random Matrix Theory. This theory treats the chaotic scattering of particles like a giant, random dice roll, which surprisingly fits their data perfectly. They also ran computer simulations that confirmed their findings: when you include the "loss" mechanism, the simulations show the same strange behavior where holes appear in the same-spin channel.

So, what does this mean? It suggests that when we try to build these exotic quantum states for future computers, we can't ignore the fact that materials aren't perfect. Loss isn't just a nuisance; in this specific case, it's the very thing that enables a new kind of quantum behavior. The paper argues that we need to rethink our models to include this "non-Hermitian" physics (a fancy way of saying the system isn't perfectly closed or conservative) to truly understand how these quantum highways work. While this doesn't mean we have a working quantum computer today, it gives us a much clearer map of the terrain, showing us that sometimes, losing a few particles is exactly what you need to find the path forward.

Technical Summary: Same-spin Andreev reflections in the quantum Hall regime: the role of loss

Problem Statement
The interface between superconductors (SC) and topological materials, specifically quantum Hall (QH) states, is a primary platform for engineering topological superconductors and chiral Andreev edge states (CAES). A CAES is typically formed when an electron in a QH edge channel undergoes Andreev reflection at an SC interface, converting into a hole in the opposite spin channel (e.g., $e_\uparrow \to h_\downarrow$ ). This process relies on spin-flip mechanisms, often mediated by spin-orbit coupling or disorder.

A theoretical puzzle exists regarding the spin-polarized filling factor $\nu = 1$ . In this regime, only a single spin channel (e.g., spin-up) exists. Standard theory suggests that Andreev reflection should be suppressed or vanish at zero energy in a single-channel, spin-polarized system because the necessary spin-flip processes to create a hole in the same channel ( $e_\uparrow \to h_\uparrow$ ) are forbidden by unitarity and particle-hole symmetry in a closed system. While previous work focused on the unpolarized $\nu = 2$ regime, the behavior of CAES in the $\nu = 1$ regime, particularly regarding the possibility of "same-spin" Andreev reflections, remained an open question.

Methodology
The authors investigated these phenomena using a hybrid device consisting of a graphene QH system proximitized by a Type-II superconductor (MoRe alloy).

Device Geometry: The sample features a central region adjacent to the superconducting contact (Contact C) and upstream/downstream regions controlled by electrostatic gates. The upstream and downstream regions are fixed at filling factor $\nu = 1$ , acting as spin polarizers that allow only spin-up electrons to pass. The central region is tuned via a top gate ( $V_G$ ) to either $\nu = 2$ (unpolarized, both spin channels present) or $\nu = 1$ (spin-polarized).
Measurement Protocol: A bias current is injected from a normal contact (B) to the grounded superconductor (C), injecting spin-up electrons ( $e_\uparrow$ ) into the interface. Downstream voltages are measured at contacts D and F. Contact D measures the spin-up channel directly ( $R_{d\uparrow}$ ), while Contact F measures the total unpolarized signal. The spin-down signal ( $R_{d\downarrow}$ ) is extracted by subtracting the spin-up contribution from the total signal.
Statistical Analysis: To overcome mesoscopic disorder and vortex-induced fluctuations, the authors collected extensive data by sweeping the magnetic field and gate voltage. This generated large datasets of interference patterns, allowing for the construction of statistical histograms of the reflection probabilities.
Theoretical Framework: The experimental data was analyzed using Random Matrix Theory (RMT) to model the scattering matrix of the disordered interface, explicitly incorporating "loss" (absorption of quasiparticles into the superconductor). Tight-binding simulations using the Kwant package were performed to model the transport, including disorder, spin-orbit coupling, and a controlled loss mechanism via a T-shaped geometry.

Key Results

Observation of Spin-Flip Processes at $\nu = 2$ : In the $\nu = 2$ regime, the authors confirmed the existence of CAES. They observed that while spin is largely conserved (producing $e_\uparrow \to e_\uparrow$ and $e_\uparrow \to h_\downarrow$ ), there are clear signatures of spin-flip processes. Specifically, they detected $e_\uparrow$ being reflected as $h_\uparrow$ (same-spin Andreev reflection) and $e_\downarrow$ appearing in the downstream channel.
Exponential Distribution of Probabilities: The distribution of the difference between electron and hole emission probabilities ( $P_{eh} = P_e - P_h$ ) was found to be exponential on a logarithmic scale for both spin channels. The authors modeled this using RMT, treating the system as a large random scattering matrix where loss is represented by additional effective channels. The decay rates for electron and hole probabilities were found to be distinct but related, with the ratio of hole-to-electron decay rates remaining constant ( $\approx 0.5$ ) across magnetic fields.
Independence of Spin Channels: Analysis of the joint 2D histograms of $P_{eh\uparrow}$ and $P_{eh\downarrow}$ revealed that the two channels are uncorrelated. This lack of correlation is consistent with the RMT prediction for a system with strong loss (a large number of effective channels), where scattering events in different channels become statistically independent.
Same-Spin Andreev Reflection at $\nu = 1$ : Crucially, the authors observed robust Andreev reflections in the $\nu = 1$ regime. Despite the theoretical expectation that a single spin-polarized channel should not support $e_\uparrow \to h_\uparrow$ conversion due to unitarity constraints, they detected a significant population of downstream holes ( $h_\uparrow$ ).
Role of Loss: The distributions of $P_{eh}$ for $\nu = 1$ and $\nu = 2$ were found to be nearly identical. The authors argue that the presence of "loss" (the absorption of quasiparticles into the superconductor, effectively breaking unitarity for the edge channel) is the enabling mechanism. Loss allows the system to bypass the unitarity constraints that would otherwise forbid same-spin Andreev reflection in a closed $\nu = 1$ system.

Significance and Claims
The paper claims to provide robust experimental evidence for same-spin Andreev reflections in the quantum Hall regime, a phenomenon previously thought to be suppressed in spin-polarized states. The primary contribution is the identification of loss (non-Hermiticity) as the critical factor enabling these processes.

Mechanism Elucidation: The authors demonstrate that in the presence of loss, the prohibition of same-spin Andreev reflection at $\nu = 1$ is lifted. The loss allows the system to couple different CAES modes ( $e_\uparrow/h_\downarrow$ and $e_\downarrow/h_\uparrow$ ), enabling the emission of holes in the same spin channel as the incident electrons.
Non-Hermitian Physics: The work highlights the importance of non-Hermitian physics in mesoscopic transport. It shows that particle loss, often viewed as a detrimental decoherence mechanism, can fundamentally alter the topological properties of the edge states, allowing for exotic hybridization that is forbidden in Hermitian, unitary systems.
Implications for Majorana Fermions: The findings have direct implications for the search for 1D chiral Majorana fermions. The observation that loss can create independent particle and hole excitations in a single spin channel suggests that signatures of Majorana modes in transport measurements must be interpreted with careful consideration of non-unitary effects and loss mechanisms in hybrid materials.

The authors conclude that their results advance the understanding of spin properties in QH-SC interfaces and provide a concrete example where non-Hermitian physics is directly relevant to the behavior of topological superconductors.

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