Superconducting Junctions Exhibit Precisely Half-Quantized Thermal Conductance under Specific Conditions

Researchers are increasingly focused on understanding heat transport at the nanoscale, particularly in novel topological systems. Daniel Gresta, Fernando Dominguez, and Raffael L. Klees, working with colleagues at the Julius-Maximilians-Universität Würzburg, University of Augsburg, and the Institute for Topological Insulators, present new theoretical insights into thermal conductance quantization within chiral topological Josephson junctions. Their study, conducted in collaboration between the Institute for Theoretical Physics and Astrophysics, the Würzburg-Dresden Cluster of Excellence ct.qmat, and Experimental Physics III, reveals the critical parameters governing robust half-quantized thermal conductance, a phenomenon dependent on the junction’s geometry and doping. This work establishes clear criteria for identifying chiral modes in these junctions and underscores the importance of momentum-space structure in determining thermal transport properties, potentially paving the way for advanced thermal management in future electronic devices.

Researchers have developed a novel approach to identify and characterise chiral Majorana modes within Josephson junctions, paving the way for more reliable topological quantum computing. These Majorana modes, exotic quasiparticles behaving as their own antiparticles, are considered promising building blocks for robust quantum bits, or qubits, due to their inherent resistance to environmental noise.

This work establishes precise criteria for detecting these modes through thermal transport measurements, offering a new pathway to validate their presence in solid-state devices. The study focuses on four-terminal Josephson junctions, complex structures where a normal material is sandwiched between two chiral superconductors, materials exhibiting a unique directional flow of electrons.

These superconductors support topological phases characterised by Chern numbers of 0, 1, and 2, influencing the behaviour of the Majorana modes. Researchers discovered that a single chiral mode, corresponding to a Chern number of 1, yields a robustly half-quantized thermal conductance, a specific measure of heat flow, while simultaneously suppressing electrical conductance.

This distinct thermal signature provides a clear indicator of a genuine Majorana mode. Crucially, this half-quantization of thermal conductance is not universally observed and occurs only under specific conditions: near a superconducting phase difference of π, within a low-doping regime in the central region of the junction, and when the junction’s dimensions are neither too small nor too large.

Furthermore, the application of a Zeeman field, a magnetic field interacting with the electron spin, alters the thermal response, particularly in the case of superconductors with a Chern number of 2, where the thermal conductance can deviate from the expected quantized value. This research highlights the critical interplay between the momentum-space structure of the electrons, the geometry of the device, and specific material parameters in determining thermal transport properties.

By carefully controlling these factors, scientists can now more effectively probe for chiral Majorana modes and advance the development of topologically protected quantum technologies. The findings offer a refined toolkit for designing and interpreting experiments aimed at harnessing the potential of these elusive quasiparticles for future quantum devices.

Chiral Superconducting Leads and Non-Equilibrium Transport in a Josephson Junction

A four-terminal Josephson junction forms the core of this work, meticulously designed to investigate thermal and electrical transport properties of chiral superconducting leads. The device comprises a normal region bridging two transverse superconducting leads, each exhibiting distinct topological phases characterised by Chern numbers of 0, 1, and 2.

Fabrication involves creating this normal region with dimensions nx × ny, carefully controlling its chemical potential μc to induce specific electronic properties. These leads are coupled to normal leads and grounded superconducting terminals maintained at a temperature Ts, with pairing potentials ∆eiφT,B applied to establish a superconducting phase difference.

To induce a temperature gradient and drive non-equilibrium conditions, the left normal lead is biased with a voltage VL and temperature difference TL, while the right normal lead remains grounded. This setup allows precise measurement of both electrical and thermal currents flowing through the junction. The four-terminal configuration effectively eliminates contact resistance and enables accurate determination of the intrinsic thermal conductance.

Thermal conductance is measured across the junction, exploiting its sensitivity to the presence of chiral Majorana modes. Theoretical modelling of the junction’s electronic structure, incorporating spin-orbit coupling, magnetic fields, and superconductivity, engineers a topological superconducting phase. Calculations determine the momentum-space location of Majorana modes and their influence on thermal transport, providing a detailed understanding of how the topology of the superconducting leads and the geometry of the junction affect heat flow. By varying the doping level of the central region and the junction length, researchers systematically explore the conditions necessary for observing robust half-quantized thermal conductance, a key signature of chiral Majorana modes.

Chiral mode signatures and topological transitions in superconducting junctions

Thermal conductance quantization was observed near a superconducting phase difference of π, but strictly within the low-doping regime of the central junction region and for intermediate- to long-junction geometries. Specifically, a half-quantized thermal conductance, representing the signature of a single chiral mode, emerged under these conditions, while non-local electrical conductance remained substantially suppressed due to particle-hole symmetry.

This suppression is crucial, as it isolates thermal transport as a direct probe of the chiral edge modes. The observed thermal conductance approached 0.5κ0, where κ0 is defined as π2k2BT/(3h), confirming the presence of a single, robust chiral mode contributing to heat transport. At finite Zeeman fields, the thermal response generally mirrored the topological characteristics of the isolated superconducting leads when the Chern number was equal to one.

However, when the Chern number reached two, the thermal conductance deviated from the expected quantized value, exhibiting a dependence on the momentum-space location of the Majorana modes. This deviation highlights the importance of considering the detailed momentum-space structure when interpreting thermal transport measurements in these systems. Further analysis revealed that the robustness of the half-quantized thermal conductance is contingent upon the interplay between the Thouless energy, the superconducting gap, and the doping level of the central junction.

Maintaining low doping levels was essential for observing the quantized conductance, indicating that increased carrier density disrupts the topological protection of the chiral modes. The intermediate- to long-junction limit, where the junction length is comparable to or greater than the coherence length, also proved critical for suppressing unwanted conductance pathways and enhancing the visibility of the quantized thermal signal.

The Bigger Picture

The persistent search for robust indicators of topological states in superconducting systems has yielded a particularly intriguing result concerning thermal transport. This work doesn’t simply confirm the theoretical prediction of half-quantized thermal conductance in chiral Josephson junctions; it meticulously maps the conditions under which this delicate effect survives the realities of material properties and device geometry.

For years, demonstrating unambiguous signatures of these exotic states has been hampered by the difficulty of isolating the topological features from background noise and unwanted effects. The precise control over junction length and doping revealed here represents a significant step forward. This investigation distinguishes itself through its focus on the interplay between topology and momentum.

The researchers found that the thermal response isn’t merely a consequence of the overall chiral state, but is intimately linked to the specific arrangement of modes within the system. This is crucial because real materials are never perfectly homogeneous. Understanding how these momentum-space details influence transport opens avenues for designing junctions that are more resilient to imperfections and easier to interpret experimentally.

However, the observed quantization isn’t universal and deviations emerge under certain conditions, highlighting the sensitivity of the thermal signal to external factors like magnetic fields. This isn’t a weakness, but rather a valuable insight, suggesting that careful manipulation of these parameters could provide a new means of probing the internal structure of the chiral states themselves. Future work will likely focus on extending these calculations to more complex geometries and exploring the impact of interactions between electrons, potentially revealing even richer behaviour at the interface between conventional and topological superconductivity.