Tunable Chern superconductivity of PtBi$_2$ in slab geometry

In the quest to build the next generation of quantum computers, scientists are hunting for a very specific kind of material: one that conducts electricity without resistance while also harboring a hidden, robust order. This elusive state is known as topological superconductivity. Unlike ordinary superconductors, which simply allow electrons to flow freely, these exotic materials possess a unique internal structure that protects their quantum states from being easily scrambled by noise or impurities. The key to this protection lies in the behavior of electrons at the material's surface. In a topological superconductor, the interior is a perfect insulator, but the edges host special particles called Majorana modes. These are not just ordinary electrons; they are their own antiparticles and are incredibly stable, making them ideal candidates for storing quantum information. For decades, creating such a state required complex setups involving external magnetic fields or layers of different materials. However, a few years ago, a material called platinum bismuth, or PtBi2, emerged as a promising candidate that might achieve this state naturally, without needing such complicated engineering.

The challenge with PtBi2 is that it is a three-dimensional crystal with a complex internal structure. Inside, it acts as a Weyl semimetal, a state of matter where electrons behave as if they are massless and move in cone-shaped patterns through the energy landscape. These cones are connected by surface paths known as Fermi arcs. When the material is cooled to extremely low temperatures, its surfaces become superconducting, but the interior remains metallic. To harness the potential of this material for quantum technology, researchers needed to understand how to isolate and control the surface superconductivity without the interference of the bulk metal. In a new study, a team of physicists used computer simulations to model a thin slice, or slab, of this material to see how its properties change when the thickness is reduced. They found that by simply making the material thinner, they could effectively turn off the metallic interior, leaving behind only the fascinating surface states. This allowed them to explore how to switch the material between a trivial, ordinary state and a topological one that hosts the desired protected edge modes.

The researchers built a simplified digital model of the PtBi2 slab, focusing on the essential features: the twelve Weyl cones in the bulk and the six Majorana cones that appear on each of the two surfaces when it becomes superconducting. In their simulation, they discovered that the thickness of the slab acts as a powerful control knob. When the slab is thick, the two surfaces are far apart, and the metallic cones in the middle remain active. However, as the slab is thinned down to just a few atomic layers, the two surfaces begin to interact. This interaction causes the bulk metallic cones to open up a gap, effectively turning off the metal in the center and leaving only the surface states as the active players. This creates a quasi-two-dimensional system where the physics is dominated by the superconducting surfaces.

Once the bulk was silenced, the team investigated how to control the remaining surface states. They identified two competing forces that determine whether the material is topologically interesting or just ordinary. The first force is a natural coupling between the Majorana cones on the top surface and those on the bottom surface. Because these cones have opposite properties, when they get close enough, they can hybridize and cancel each other out, creating a gap that is topologically trivial. This means the material would lose its special protective qualities. The second force is an external magnetic field applied perpendicular to the slab. This field breaks the symmetry that protects the cones, but in a way that opens a gap that is topologically non-trivial. The researchers found that the outcome depends on the balance between these two forces. If the natural coupling is too strong, the material becomes ordinary. But if a magnetic field is strong enough to overpower this coupling, the material enters a new phase known as a Chern superconductor.

In this Chern superconductor phase, the material exhibits a remarkable property: it hosts six distinct, one-way channels of current flowing along its edges. These are the chiral Majorana edge modes, the very particles scientists hope to use for quantum computing. The study revealed that the behavior of these edge channels is not uniform; it depends heavily on which edge of the material is being observed. The researchers mapped out the entire system and found that the width of these edge channels varies depending on the orientation of the edge relative to the internal structure of the material. On some edges, the channels are tightly confined, while on others, they spread out more. This variation is a direct result of how the surface states are projected onto the edge, a detail that could be crucial for designing future devices.

The team also explored how to manipulate the material to reach this desired state. They showed that by adjusting the chemical potential on the surface—essentially changing the electron density through doping or gating—they could shift the position of the Majorana cones in momentum space. This shift changes how strongly the top and bottom cones interact. By carefully tuning this surface potential and applying a magnetic field, it is possible to navigate the material through different phases, moving from a trivial state to the topological Chern state. The simulations suggest that for a slab of a specific thickness, there is a clear region where the topological phase is stable, surrounded by regions where the material is either trivial or gapless.

This work provides a clear roadmap for experimentalists working with PtBi2. It suggests that simply growing a thin enough crystal could be enough to isolate the topological surface states. Furthermore, it indicates that applying a magnetic field or tuning the surface chemistry could switch the material into the desired topological phase. The researchers caution that their model is a simplified representation and that real materials contain additional complexities, such as other electronic states that might interfere. However, the core finding remains robust: the interplay between slab thickness, surface potential, and magnetic fields offers a tunable way to access a state of matter that hosts protected, one-way quantum channels. If these predictions hold true in the lab, PtBi2 could become a practical platform for realizing the stable quantum bits needed for the next generation of computing, all without the need for the complex heterostructures that have been required until now.