Weizmann Institute finds dissipation explains quantum Hall-superconductor junctions

Dissipation as the Missing Piece in Quantum Hall‑Superconductor Junctions

Recent measurements of conductance across interfaces between fractional quantum Hall (FQH) edges and superconductors have shown puzzling, filling‑fraction‑dependent temperature behavior. A new theoretical study from the Weizmann Institute of Science offers a coherent explanation: dissipation into sub‑gap states of the superconductor suppresses coherent hybridization between integer and fractional edge modes, leading to temperature‑independent, non‑quantized conductance in certain cases.

Why Some Fractions Stay Cool

The authors focus on three representative filling fractions: \(\nu = 2/3\), \(\nu = 1/3\) and \(\nu = 2/5\). Experiments reported that conductance at \(\nu = 2/3\) remains essentially flat as temperature varies, while \(\nu = 1/3\) and \(\nu = 2/5\) show a clear increase when the system is cooled. The key distinction, according to the theory, is the presence of an integer edge mode that co‑exists with the fractional mode in the Jain‑type states \(\nu = 1 \pm 1/m\) (odd \(m \ge 3\)). When this integer mode couples strongly to a dissipative channel inside the superconductor, the combined system enters a strong‑coupling regime where the conductance becomes set by microscopic tunneling and crossed‑Andreev‑reflection parameters rather than by universal quantum Hall quantization.

Modeling the Dissipative Channel

The paper builds a low‑energy effective model that includes four processes:

1. Normal electron tunneling across the junction,
2. Crossed Andreev reflection (CAR) that transfers Cooper pairs between counter‑propagating edges,
3. Same‑side electron transfer, and
4. Direct dissipation of charge into sub‑gap states of the superconductor.

By assigning dimensionless strengths \(t\), \(f\), \(s\) and a dissipation factor \(dA\), the authors derive a conductance expression that reproduces the observed temperature‑independent plateau for \(\nu = 2/3\) when \(dA\) is large. In contrast, for filling fractions lacking an integer mode (e.g., \(\nu = 1/3\) and \(\nu = 2/5\)), the model predicts a conventional temperature‑dependent increase, matching the experimental trend.

Testable Predictions

A central proposal is to compare the behavior of \(\nu = 4/3\) (co‑propagating integer and fractional modes) with \(\nu = 2/3\) (upstream fractional mode). The theory predicts that strong dissipation will keep conductance at \(\nu = 2/3\) temperature‑independent, while \(\nu = 4/3\) should show a measurable, temperature‑sensitive contribution from the fractional sector. Such a comparison would directly probe the role of relative chirality between integer and fractional modes, offering a clear experimental check of the model.

Implications for Topological Quantum Computing

Understanding and controlling dissipation is crucial for proposals that aim to host para‑fermionic zero modes at FQH‑superconductor interfaces—building blocks for fault‑tolerant topological qubits. By identifying dissipation as the factor that can either mask or reveal the desired non‑Abelian signatures, the work provides a roadmap for engineering junctions with the right balance of coupling and loss.

Looking Ahead

While the study presents a compelling framework, it remains a theoretical analysis anchored to a pre‑print (arXiv:2611.05555). Experimental verification—particularly the suggested \(\nu = 4/3\) vs. \(\nu = 2/3\) comparison—will be essential to confirm that dissipation indeed governs the observed conductance patterns. If validated, the insight could streamline the design of future quantum Hall‑superconductor devices and bring para‑fermion based qubits closer to reality.

--- For a deeper dive, see the authors’ pre‑print on arXiv.