Observation of the electronic Pomeranchuk effect in generalized Wigner crystals of twisted MoS$_2$

In the vast landscape of modern physics, there is a quiet revolution happening inside materials that are only a few atoms thick. For decades, scientists have been fascinated by the idea of "flat bands," a condition where electrons lose their usual freedom to zip around quickly and instead move sluggishly, as if wading through thick molasses. When electrons move this slowly, they stop behaving like independent particles and start acting as a single, collective group, influenced heavily by how much they repel one another. This repulsion can force them to arrange themselves into rigid, crystalline patterns, much like people in a crowded room stepping back to give each other space. Usually, heat is the enemy of such order; warming a system typically makes these delicate structures melt back into a disordered, fluid state. However, nature sometimes plays a trick on our intuition, allowing heat to do the opposite: instead of melting a solid, heat can sometimes be the very thing that freezes it.

This counterintuitive phenomenon, known as the Pomeranchuk effect, was first observed in liquid helium, where warming the liquid actually caused it to solidify. Now, researchers have found a similar effect in a completely different realm: a synthetic crystal made of twisted layers of molybdenum disulfide. By stacking two sheets of this material with a slight twist, they created a repeating pattern of hills and valleys that traps electrons. The team, led by scientists at Fudan University and Westlake University, discovered that at specific densities, heating this material from near absolute zero up to about ten degrees above absolute zero does not melt the electron fluid. Instead, the heat triggers the electrons to lock into a highly ordered, insulating crystal. This finding reveals a new way that heat and disorder can work together to create stability, offering a fresh perspective on how matter behaves when pushed to its limits.

The researchers began by building a very specific type of device. They took two single layers of molybdenum disulfide, a material that looks like a sandwich of sulfur and molybdenum atoms, and stacked them on top of each other. They did not align them perfectly; instead, they twisted one layer slightly relative to the other, creating a large-scale interference pattern known as a moiré superlattice. Think of this pattern as a new, larger grid of traps for electrons, where the spacing between the traps is determined by the angle of the twist. In one of their devices, they twisted the layers by 4.1 degrees, and in another, by 3.9 degrees. To ensure they could measure the flow of electricity accurately without the signal getting lost at the edges, they used a special metal, bismuth, to create contacts that allowed electrons to flow in and out smoothly, even at the extremely low temperatures required for the experiment.

Once the device was ready, the team cooled it down to 1.5 Kelvin, a temperature just above absolute zero where thermal jitters are almost non-existent. They then filled the electron traps with a precise number of electrons, targeting specific fractions of the available spots. They focused on two particular scenarios: one where there was one electron for every three traps, and another where there was one electron for every four traps. At these ultra-cold temperatures, the electrons behaved like a fluid. They moved freely, and the electrical resistance followed a predictable pattern that scientists recognize as a "Fermi liquid," a state where electrons act like a calm, flowing river. This was the expected behavior; the system was a conductive metal.

Then, the researchers began to warm the sample up, slowly increasing the temperature from 1.5 Kelvin toward 60 Kelvin. As they did this, something strange happened. Instead of the resistance dropping or staying steady as the electrons moved faster, the resistance began to climb sharply. By the time the temperature reached about 13 Kelvin, the material had transformed from a conductor into an insulator. The electrons, which had been flowing freely moments before, had suddenly stopped moving and locked themselves into place. This was the opposite of what usually happens when you heat a solid; typically, heat provides the energy needed to break bonds and create a liquid. Here, the heat was driving the system to become more solid.

The explanation for this lies in a hidden form of disorder that exists within the electrons themselves. Electrons have a property called "isospin," which can be thought of as a combination of their spin and their valley location within the material's structure. When the electrons are flowing freely in the cold, they tend to pair up in an orderly fashion, which keeps their internal states relatively organized and low in entropy, or disorder. However, when the electrons are forced to stop and sit in specific spots to form a crystal, they become far apart from one another. This distance weakens the interaction between them, leaving their internal isospin states free to spin and point in random directions. This randomness creates a massive amount of entropy.

According to the laws of thermodynamics, systems naturally seek the state with the highest entropy. At low temperatures, the energy cost of forming a crystal is too high, so the electrons stay fluid. But as the temperature rises, the system gains enough thermal energy to pay that cost. Once it does, the system realizes that the "frozen" crystal state actually offers a much higher level of internal disorder than the flowing liquid state. The heat essentially pushes the electrons into the crystal because the crystal allows them to be more chaotic on the inside. This is the electronic version of the Pomeranchuk effect: the system freezes because the solid state is more disordered than the liquid state.

The team confirmed this behavior by applying magnetic fields and observing how the electrons responded. They found that the electrons were indeed locking into a specific pattern, forming what is known as a generalized Wigner crystal. In the case of the one-in-three filling, the electrons arranged themselves in a triangular pattern, while the one-in-four filling created a stripe-like pattern. The researchers also measured how the material responded to magnetic fields and found that the electrons were highly sensitive to them, confirming that their internal states were indeed the key to this transition. The strength of the magnetic response suggested that the electrons were behaving in a way that preserved their internal freedom even while they were physically locked in place.

This discovery is significant because it shows that this strange thermodynamic trick is not limited to simple systems or specific integer numbers of electrons. It works even when the electron density is a fraction, such as one-third or one-quarter of the available spots. This suggests that the competition between the energy of motion and the energy of repulsion is a delicate balance that can be tipped by heat in a wide variety of conditions. The researchers noted that the specific angles of their twisted layers, 4.1 degrees and 3.9 degrees, were crucial for creating the right environment for this effect to occur. If the layers were twisted differently, the balance might shift, and the effect might not appear.

The implications of this work extend beyond just understanding a single material. It provides a new tool for scientists to explore how matter organizes itself when pushed to the edge of stability. By showing that heat can drive crystallization in a two-dimensional material, the study opens the door to designing new electronic devices that could switch between conducting and insulating states simply by changing their temperature. It also deepens our understanding of the fundamental rules that govern how electrons interact, revealing that the path to order can sometimes be paved by disorder. The researchers plan to continue exploring these materials, looking for other fractional states where this effect might appear and trying to map out the full landscape of how these twisted crystals behave under different conditions.

In the end, the story of this twisted molybdenum disulfide is a reminder that the rules of the everyday world do not always apply at the atomic scale. What looks like a simple heating process can, under the right conditions, act as a freezing agent, turning a fluid into a solid. The electrons in this experiment did not just react to the heat; they used it to find a new, more stable form of existence. This electronic Pomeranchuk effect stands as a testament to the complexity and beauty of the quantum world, where the most counterintuitive outcomes are often the most revealing.