Superconductors Exhibit Discrete Thermal Transport with a Fixed Conductance

A new class of Majorana boundary states, termed floating Majorana edge bands, exhibits potential for strong helical-like Majorana transport. Yanmiao Han and colleagues at Beihang University in collaboration with Peking University, Universiti Sains Malaysia and Hefei National Laborator characterise these states, which emerge in two-dimensional superconductors lacking time-reversal symmetry, through detailed simulations using the nonequilibrium Green’s function method. The simulations reveal a quantized thermal conductance in two-terminal devices and a strong half-quantized plateau in four-terminal geometries, offering a clear distinction from other quantum Hall phases. Notably, this thermal response proves stable even with temperature fluctuations, disorder, and varying chemical potential. This observation is particularly noteworthy as it surpasses the performance of many conventional materials, which suffer from inherent energy loss due to resistance. The ability to achieve near-perfect conductance is crucial for developing low-power electronic components and highly sensitive quantum sensors. Detailed four-terminal analysis further demonstrates a remarkably stable half-quantized thermal plateau, definitively distinguishing these floating Majorana edge bands from other quantum anomalous Hall phases exhibiting a Chern number of N = ±2. The Chern number, a topological invariant, describes the winding of the electronic band structure and dictates the Hall conductance. A value of ±2 indicates a fully gapped state, whereas the half-quantized plateau observed here signifies the unique properties of the FMEBs. Further validation of the unique properties of these floating Majorana edge bands (FMEBs) came from four-terminal measurements confirming this stable half-quantized thermal plateau. This stability is paramount for practical applications, as it ensures that the quantum information encoded within these states is not easily corrupted by external disturbances.

Quantised Thermal Conductance Confirms Strong Majorana Edge Band Formation

Thermal conductance measurements now reveal a quantized value of two in two-terminal devices, a significant improvement over previous materials limited by dissipation; this precise quantization confirms the presence of strong, dissipationless transport channels. This observation is particularly noteworthy as it surpasses the performance of many conventional materials, which suffer from inherent energy loss due to resistance. The ability to achieve near-perfect conductance is crucial for developing low-power electronic components and highly sensitive quantum sensors. Detailed four-terminal analysis further demonstrates a remarkably stable half-quantized thermal plateau. This stability is paramount for practical applications, as it ensures that the quantum information encoded within these states is not easily corrupted by external disturbances. This stability is paramount for practical applications, as it ensures that the quantum information encoded within these states is not easily corrupted by external disturbances. The Chern number, a topological invariant, describes the winding of the electronic band structure and dictates the Hall conductance; a value of ±2 indicates a fully gapped state, whereas the half-quantized plateau observed here signifies the unique properties of the FMEBs. Further validation of the unique properties of these floating Majorana edge bands (FMEBs) came from four-terminal measurements confirming this stable half-quantized thermal plateau. This stability is paramount for practical applications, as it ensures that the quantum information encoded within these states is not easily corrupted by external disturbances.

These FMEBs emerge in two-dimensional superconductors lacking time-reversal symmetry, yet still support helical-like transport; unlike typical edge modes, they consist of isolated, counterpropagating Majorana modes separate from the bulk material. This isolation is a key feature, preventing backscattering and enhancing the robustness of the Majorana states against imperfections. The emergence of these bands is linked to anisotropic Wilson masses within a two-band Bogoliubov-de Gennes model, and demonstrated in a quantum anomalous Hall insulator connected to a d-wave superconductor. The anisotropic Wilson mass term arises from the interplay between spin-orbit coupling and the superconducting pairing, effectively creating a directional preference for the Majorana modes. Simulations reveal this strong thermal response persists even with moderate temperature fluctuations, disorder, or changes in chemical potential, though the precise control needed to fabricate these materials and reliably observe these effects remains a key hurdle to practical application. The robustness to these perturbations is a significant advantage, as real-world devices are inevitably subject to environmental noise and imperfections. However, achieving the necessary level of material purity and structural control remains a considerable challenge.

Mapping Majorana boundary states via nonequilibrium Green’s function simulations

Nonequilibrium Green’s function, or NEGF, simulations were an important part of this work; this computational technique models electron behaviour when a material isn’t in a stable state, much like simulating rush-hour traffic flow to understand congestion patterns. Unlike traditional equilibrium methods, NEGF allows for the investigation of systems driven out of equilibrium, such as those subjected to a voltage bias or temperature gradient. Employing this technique allowed researchers to map the complex interactions within the two-dimensional superconductors, predicting electron behaviour at the material’s edges. This was essential because the sought-after Majorana boundary states are subtle and exist only under specific conditions. The NEGF method solves the quantum mechanical equations of motion for the electrons, taking into account the effects of interactions, disorder, and external fields. Simulating these electron dynamics confirmed the existence of the floating Majorana edge bands and analysed their unique transport properties, ultimately distinguishing them from other similar quantum phenomena. The work focused on a two-band Bogoliubov-de Gennes model with anisotropic Wilson masses, realised through a quantum anomalous Hall insulator proximitized by a d-wave superconductor; this setup naturally introduces the required anisotropy. The Bogoliubov-de Gennes model is a mean-field theory that describes the behaviour of superconducting systems, while the proximity effect allows for the transfer of superconducting properties from one material to another.

Thermal fingerprints guide the hunt for strong Majorana edge states

The search for stable, easily manipulated quantum states is intensifying as scientists strive to build practical quantum computers. Topological quantum computation, which utilizes the robust properties of topological states like Majorana fermions, is considered a promising approach to overcome the limitations of conventional quantum computing architectures. This research details floating Majorana edge bands, a new type of boundary state within two-dimensional superconductors, offering a potential route to helical-like Majorana transport. The helical nature of the transport refers to the spin-momentum locking of the electrons, which prevents backscattering and enhances the stability of the quantum information. Replicating the conditions of the current simulations, a specific quantum anomalous Hall insulator coupled with a d-wave superconductor, presents a key bottleneck; alternative approaches utilising different material combinations are being explored to circumvent these fabrication challenges. Finding materials that exhibit the necessary properties, such as strong spin-orbit coupling and a large superconducting gap, is a major focus of ongoing research.

Despite the difficulty of fabricating the specific materials currently modelled, this work remains valuable because it identifies a clear thermal signature for these ‘floating’ Majorana edge bands. These unique states offer a stronger pathway to using Majorana fermions for potential use in topological quantum computers, unlike previously studied versions which required pristine materials or perfect symmetry. The thermal conductance measurements provide a direct and unambiguous way to identify the presence of these states, even in the presence of imperfections. Identifying this distinct thermal response provides an important benchmark for experimental physicists seeking to confirm their existence in real-world systems. Unlike previously known edge states, these bands host isolated Majorana modes, potentially improving stability for quantum information processing; a Bogoliubov-de Gennes model explains their emergence. The isolation of the Majorana modes is crucial for preventing decoherence, which is the loss of quantum information due to interactions with the environment. The method confirmed a strong half-quantized thermal plateau, distinguishing these bands from other quantum phenomena and demonstrating durability to environmental factors. This durability is a key requirement for building robust and reliable quantum devices.

The research successfully demonstrated the existence of floating Majorana edge bands in a two-dimensional system combining a quantum anomalous Hall insulator and a d-wave superconductor. These newly identified bands host isolated Majorana modes and present a pathway towards helical-like Majorana transport even when time-reversal symmetry is broken. This is significant because it offers a potentially more robust route to utilising Majorana fermions for topological quantum computation than previous approaches. Researchers confirmed the presence of these bands through a distinct half-quantized thermal plateau, showing stability under realistic conditions and providing a clear benchmark for future experimental verification.