Weizmann Institute finds dissipation explains quantum Hall-superconductor junctions

Researchers at the Weizmann Institute of Science have explained discrepancies in recent measurements of conductance across junctions between fractional quantum Hall edges and superconductors. The work reveals that temperature-independent conductance was observed for filling fraction ν = 2/3, but not for ν = 1/3 and ν = 2/5, a difference the team attributes to dissipation within the superconductor.

The study demonstrates that Jain states at ν = 1 ± 1/m (with odd m ≥ 3) require a “strongly coupled” integer mode to exhibit this temperature-independent behavior, and proposes comparing ν = 4/3 and ν = 2/3 to further test their model of relative chirality.

Dissipation Explains Conductance in Quantum Hall-Superconductor Junctions

The behavior of electrons at the interface between a fractional quantum Hall system and a superconductor is governed by dissipation into sub-gap states within the superconductor. This dissipation explains discrepancies observed in recent conductance measurements, specifically the differing temperature dependencies seen in various fractional quantum Hall states. Researchers found that strong dissipation suppresses coherent hybridization between integer and fractional edge modes within the quantum Hall-superconductor device. The study details how integer edge modes, when subject to strong dissipation, exhibit temperature-independent, non-quantized conductance determined by microscopic parameters.

The team modeled this behavior using parameters relevant to experimental setups, including tunneling and crossed Andreev reflection processes, and found that the relative strength of these processes influences the observed conductance. Analysis of ν = 2/3 quantum Hall edges in a strong-dissipation regime revealed a similar pattern, with conductance largely unaffected by temperature changes. These findings offer a pathway toward understanding and controlling parafermionic zero modes, potentially advancing topological quantum computing platforms.

Jain States and Temperature-Dependent Conductance at ν = 2/3

The behavior of fractional quantum Hall (FQH) edges depends critically on the presence of accompanying integer modes, influencing conductance in junctions with superconductors. Analysis reveals that temperature-independent, non-quantized conductance in Jain states arises specifically when these states are strongly coupled to a dissipative channel featuring an integer mode, such as those found at filling fraction ν = 1 ± 1/m, with odd m greater than or equal to 3.

The observed conductance is not universal, and its magnitude is affected by the direction of propagation relative to these integer modes. For upstream fractional modes, like those at ν = 2/3, strong dissipation within the integer mode consistently results in small conductance values, regardless of the junction’s phase. Conversely, co-propagating edges, such as those at ν = 4/3, allow fractional modes to contribute to conductance, creating a measurable difference between phases.

This distinction provides a potential avenue for experimental verification of the theoretical model. The researchers classified phases within these FQH-superconductor junctions, noting that systems lacking an integer mode, like the Jain sequence at ν = N/(2pN + 1), including 1/3 and 2/5, tend to settle into quantized conductance plateaus. This behavior, however, does not necessarily indicate the opening of a superconducting gap, as gapless phases can also exhibit quantized conductance.

Calculations show that for a specific parameter, g = 3.1 and a dissipation factor $d_A$ = 30/31, the point-contact crossed Andreev reflection coefficient increases as temperature decreases to the power of -2/31, with conductance approaching a defined value. The team’s work provides a comprehensive framework for understanding these complex interactions, classifying systems based on the presence or absence of integer modes and their impact on conductance.

Recent experiments measured the edge conductance from crossed Andreev reflection between counter-propagating FQH edges separated by a narrow superconductor. The observed conductance was small and non-quantized, with two distinct behaviors. Some states show temperature-independent conductance, while others show conductance that grows as temperature decreases.

Crossed Andreev Reflection Measures Edge Conductance

Measurements of edge conductance reveal that dissipation within the superconductor significantly influences behavior in fractional quantum Hall (FQH) systems. Specifically, the observed conductance, stemming from crossed Andreev reflection between counter-propagating FQH edges, is not fully quantized and exhibits varying temperature dependencies.

This dissipation is key to understanding the phase diagram of the FQH-superconductor junction. The strength of this coupling to the dissipative channel is critical; without it, the observed conductance deviates from the temperature-independent behavior. This suggests a structural requirement for maintaining stable, temperature-insensitive conductance in these systems. A normalized crossed Andreev reflection signal, denoted as f, was used to quantify the conductance.

The team details how different transfer mechanisms, normal electron tunneling, crossed Andreev reflection, same-side electron transfer and dissipation into the superconducting bath, contribute to the overall conductance. Comparing the behavior of filling fractions ν = 4/3 and ν = 2/3 could further validate the theory regarding the influence of relative chirality between integer and fractional modes, offering a direct test of the model’s predictions.

Integer Modes Enable Non-Quantized Conductance

The presence of integer modes is critical for achieving temperature-independent, non-quantized conductance in fractional quantum Hall-superconductor junctions, according to recent analysis of edge transport. Specifically, a strong coupling between these integer modes and a dissipative channel is required for this behavior to emerge, a finding that explains discrepancies observed in conductance measurements at different filling fractions. The analysis details how edges containing an integer mode can enter a strong-coupling regime when dissipation is significant, leading to a non-universal conductance unaffected by temperature changes.

This mechanism extends to the fractional sector when dominant integer-fractional transfers couple each fractional electron to the dissipative integer mode, effectively equilibrating them and inheriting the temperature-independent characteristics. When this coupling is absent, fractional modes contribute a quantized conductance, but the integer mode still plays a role in the overall transport.

Role of Sub-Gap Modes in Dissipation Mechanisms

Dissipation within the superconducting material bridging fractional quantum Hall (FQH) edges explains observed variations in conductance, with specific behaviors at filling fractions ν = 2/3 and ν = 4/3. The analysis centers on how these modes influence charge transfer between edges, creating a phase diagram for FQH-superconductor junctions.

The differing behaviors between ν = 2/3 and ν = 4/3 arise from the chirality of the fractional mode, with the microscopic parameters governing normal tunneling, crossed Andreev reflection, and integer mode dissipation playing a major role. The upstream fractional mode contributes through transfer to the integer sector and boundary matching, but strong dissipation suppresses this contribution, leading to the observed conductance values.

Chirality Distinguishes Conductance in ν = 4/3 and 2/3 States

The behavior of edges lacking an integer mode differs markedly from those that possess one, with Jain states at filling fractions ν = 1/3 and ν = 2/5 exhibiting a crossed Andreev reflection signal that increases as temperature decreases. This contrasts with the approximately temperature-independent conductance observed for ν = 2/3 and integer states, indicating a sensitivity to edge structure and the presence of accompanying integer modes. Researchers propose that the differing conductance behaviors stem from how these modes interact with dissipation within the superconductor, influencing charge transfer between edges.

Multimode Edges and the Phase Diagram of FQH Junctions

This finding clarifies why certain filling fractions, like ν = 2/3 and integer states, exhibit this behavior while others, such as ν = 1/3 and ν = 2/5, do not. The analysis reveals that edges supporting an integer mode are a prerequisite for this specific conductance profile. The research extends beyond single-mode edges to examine multimode configurations, specifically those containing a chiral Jain block with or without integer modes, and demonstrates that strong dissipation allows integer modes to contribute to conductance.

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