Quantized heat flow in moiré chern bands of bilayer graphene

In the microscopic world of solid materials, electrons do not simply drift like water in a stream; they move through a landscape defined by the atoms they pass. When scientists place a material in a strong magnetic field, these electrons are forced into tight, circular paths. If the material also has a repeating pattern, like a grid of atoms, the electrons must navigate a conflict between the magnetic force and the atomic grid. This competition creates a complex, fractal map of allowed energy levels, a structure so intricate it resembles a butterfly with many wings. Within the gaps of this map, electrons can form special states that are topologically protected, meaning their behavior is governed by global rules rather than local details. For decades, scientists have been able to measure how electricity flows through these states, confirming that the electrical current is quantized, or locked into specific, unchangeable steps. However, a fundamental question remained unanswered: does heat travel through these same paths in the same rigid, universal way? While electricity has been mapped, the flow of thermal energy through these exotic quantum states had remained a mystery, leaving a gap in our understanding of how heat and topology interact.

A team of researchers has now filled this gap by measuring the flow of heat through these fractal energy states in a specific type of material. They constructed a device using two layers of graphene, a material made of a single sheet of carbon atoms, sandwiched between layers of hexagonal boron nitride. By carefully aligning the graphene with the boron nitride, they created a large, repeating pattern known as a moiré superlattice, with a wavelength of about fourteen nanometers. When they applied a magnetic field to this setup, the electrons organized themselves into the fractal energy spectrum described above. The researchers then used a highly sensitive technique called Johnson-noise thermometry to measure how much heat was carried by the electrons as they moved along the edges of the material. This method allowed them to detect the tiny temperature changes caused by the moving electrons without disturbing the delicate quantum states.

The results were striking and clear. The researchers found that the thermal conductance, or the ability of the material to carry heat, was perfectly quantized. Just as the electrical current is locked to specific values, the heat flow was locked to steps determined solely by a number called the Chern number, which describes the topology of the electron's path. This quantization held true regardless of how the state was formed. Whether the electrons were behaving as standard quantum Hall states, as Chern insulators created by the material's structure, or as symmetry-broken states driven by strong interactions between the electrons themselves, the heat flow remained consistent. In every case, the amount of heat carried was directly proportional to the topological number, independent of the microscopic details of the material or the specific mechanism that created the state.

Crucially, the team also addressed a potential complication that had confused previous experiments. In earlier studies on similar materials, the measured heat flow was often lower than expected, a phenomenon attributed to a heat Coulomb blockade effect that blocked one channel of heat flow. In this new work, the researchers designed their device with a very thin insulating layer and a large capacitance, which effectively eliminated this blocking effect. As a result, they observed the intrinsic, unblocked quantized thermal conductance for the first time in these moiré systems. They measured states with different topological numbers, including those with values of two, three, and four, and in every instance, the heat flow matched the theoretical prediction exactly. Even for states where the electrons interacted strongly to create new, complex patterns, the heat transport remained universal and predictable.

This discovery establishes thermal conductance as a powerful and reliable tool for probing the topology of quantum matter. By showing that heat flows in a universal, quantized manner across different types of topological states, the work confirms that the connection between the bulk properties of a material and its edge behavior holds true for heat just as it does for electricity. The findings suggest that scientists can now use heat measurements to explore even more exotic phases of matter, such as fractional Chern insulators, where the rules of topology might lead to entirely new forms of quantum behavior. The ability to measure these thermal signatures with such precision opens a new window into the fundamental nature of topological quantum materials, proving that the flow of heat is just as deeply tied to the geometry of the quantum world as the flow of electricity.